Contents€¦ · Contents Kappa Mu Epsilon National Ofﬁcers 3 ... Murray Klamkin’s Duality Principle for Triangle Inequalities 10 Daniel Sitaru The Problem Corner 15

Spring 2016 1

T H E P E N T A G O N

A Mathematics Magazine for Students

Volume 75 Number 2 Spring 2016

Contents

Kappa Mu Epsilon National Officers 3

Several Theorems Concerning the Irrationality ofCertain Infinite Series Involving Tetrations 4Joshua Stucky

Murray Klamkin’s Duality Principle for Triangle Inequalities 10Daniel Sitaru

The Problem Corner 15

Report of the North Central Regional Convention 25

Report of the Great Lakes Regional Convention 27

Kappa Mu Epsilon News 29

Active Chapters of Kappa Mu Epsilon 50

c© 2016 by Kappa Mu Epsilon (http://www.kappamuepsilon.org). Allrights reserved. General permission is granted to KME members for non-commercial reproduction in limited quantities of individual articles, inwhole or in part, provided complete reference is given as to the source.Typeset in Scientific Word and WinEdt. Printed in the United States ofAmerica.

2 The Pentagon

The Pentagon (ISSN 0031-4870) is published semiannually in December and Mayby Kappa Mu Epsilon. No responsibility is assumed for opinions expressed by in-dividual authors. Papers written by undergraduate mathematics students for un-dergraduate mathematics students are solicited. Papers written by graduate stu-dents or faculty will be considered on a space-available basis. Submissions shouldbe made by means of an attachment to an e-mail sent to the editor. Either a TeXfile or Word document is acceptable. An additional copy of the article as a pdffile is desirable. Standard notational conventions should be respected. Graphs,tables, or other materials taken from copyrighted works MUST be accompaniedby an appropriate release form the copyright holder permitting their further repro-duction. Student authors should include the names and addresses of their facultyadvisors. Contributors to The Problem Corner or Kappa Mu Epsilon News areinvited to correspond directly with the appropriate Associate Editor.

Editor:

Doug BrownDepartment of MathematicsCatawba College2300 West Innes StreetSalisbury, NC [email protected]

Associate Editors:

The Problem Corner:Pat CostelloDepartment of Math. and StatisticsEastern Kentucky University521 Lancaster AvenueRichmond, KY [email protected]

Kappa Mu Epsilon News:Peter SkonerDepartment of MathematicsSaint Francis University117 Evergreen DriveLoretto, PA [email protected]

The Pentagon is only available in electronic pdf format. Issues may beviewed and downloaded for free at the official KME website. Go to http://www.pentagon.kappamuepsilon.org/ and follow the links.

Spring 2016 3

Kappa Mu Epsilon National Officers

Rhonda McKee PresidentDepartment of Mathematics

University of Central MissouriWarrensburg, MO 64093-5045

[email protected]

Brian Hollenbeck President-ElectDepartment of Mathematics and Economics

Emporia State UniversityEmporia, KS 66801

[email protected]

Mark Hamner SecretaryDepartment of Mathematics and Computer Science

Texas Woman’s UniversityDenton, TX [email protected]

David Dempsey TreasurerDepartment of Mathematical, Computing, & Information Sciences

Jacksonville State UniversityJacksonville, AL 36265

[email protected]

Peter Skoner HistorianDepartment of Mathematics

Saint Francis UniversityLoretto, PA 15940

[email protected]

David Gardner WebmasterDepartment of Mathematics and Computer Science

Texas Woman’s UniversityDenton, TX 76204

KME National Website:http://www.kappamuepsilon.org/

4 The Pentagon

Several Theorems Concerning theIrrationality of Certain Infinite Series

Involving Tetrations

Joshua Stucky, student

TN Gamma

Union UniversityJackson, TN 66002

Abstract

The author examines a simple proof for the irrationality of e and appliesthe proof method used to series involving higher order factorials. Theauthor also looks at the irrationality of other series involving tetrations.

1. Introduction

There exist many varieties of the proof that e is irrational, most of whichrely on the same line of logic. In fact for many irrationality proofs, thestrategy is the same: if α is the sum of a convergent series, first assumeto the contrary that α is rational. Then, through the use of auxiliary func-tions, show that some number that must be an integer must also be strictlybetween two consecutive integers.

As an example, Fourier’s proof for the irrationality of e is given below.The purpose of this article is to apply this proof strategy to higher orderfactorials (defined below), as well as to examine another theorem concern-ing the irrationality of certain infinite series and apply it to series involvingtetrations.

2. Fourier’s Proof for the Irrationality of e

The most well known and perhaps simplest proof of e’s irrationality isFourier’s proof by contradiction. A version of his proof is given below,adapted from [3].Remark. All series considered in this paper are assumed to be convergent.For the sake of brevity, we shall say the series is irrational rather than thesum of the series is an irrational number.

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Theorem 1 (Fourier) The series

e =

∞∑n=0

1

n!

is irrational.

Proof. Assume to the contrary that e is rational. Then for some integersa and b,

a

b=

∞∑n=0

1

n!.

Here and throughout, we will assume b ≥ 1, as it results in no loss ofgenerality. Multiplying each side by b!,

a(b− 1)! =

∞∑n=0

b!

n!=b!

0!+b!

1!+ · · ·+ b!

b!+

1

(b+ 1)+

1

(b+ 1)(b+ 2)+ · · · .

Subtracting b!0! + · · ·+ b!

b! ,

a(b− 1)!−(b!

0!+ · · ·+ b!

b!

)=

1

(b+ 1)+

1

(b+ 1)(b+ 2)+ · · · .

Note that the left hand side is an integer k. Since b ≥ 1,

k =1

(b+ 1)+

1

(b+ 1)(b+ 2)+ · · · > 0.

However, k is strictly less than1

(b+ 1)+

1

(b+ 1)2+ · · · = 1

b

which, since b ≥ 1, is at most 1. Hence k must be strictly between 0 and 1,a contradiction since k is an integer. Therefore the series is irrational.

3. Main Results

Definition. The hyperfactorial H(n) is defined as

H(n) = 11 · 22 · · ·nn =

n∏k=1

kk.

Theorem 2 The series∞∑n=1

1

H(n)

is irrational.

Proof. Following Fourier’s method, assume to the contrary that the series

6 The Pentagon

above is rational. Then for some integers a and b,

a

b=

∞∑n=1

1

H(n)=

1

11+

1

11 · 22+

1

11 · 22 · 33+ · · · .

Multiplying each side by H(b),

a(11 · 22 · · · bb−1) =H(b)

11+

H(b)

11 · 22+

H(b)

11 · 22 · 33+ · · ·+ H(b)

H(b)+ · · · .

Subtracting(H(b)11 + H(b)

11·22 + · · ·+ H(b)H(b)

),

a(11 · 22 · · · bb−1)−(H(b)

11+

H(b)

11 · 22+ · · ·+ H(b)

H(b)

)=

1

(b+ 1)b+1+

1

(b+ 1)b+1 · (b+ 2)b+2+ · · · .

Note that (1) is an integer k. Since b ≥ 1, (2) is greater than 0. However,(2) is also strictly less than

1

b+ 1+

1

(b+ 1)2+

1

(b+ 1)3+ · · · = 1

b

which is at most 1. Hence k must be strictly between 0 and 1, a contradic-tion since k is an integer. Therefore, the series is irrational.

Next, we prove the more general case for higher order hyperfactorials.Here it is useful to introduce the standard notation for tetration.

Definition. The m-tall tetration mn is defined as

mn = n. . .n︸︷︷︸m

where the exponents are evaluated from right to left.

As an example, 33 = 333

= 3(33) = 327. Using tetration we define

higher order hyperfactorials as follows.

Definition. The m-tall hyperfactorial H(n,m) is defined as

H(n,m) = m1 · m2 · · ·mn =

n∏k=1

mk.

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Theorem 3 For all natural m, the series∞∑n=1

1

H(n,m)

is irrational.

Proof. Assume to the contrary that the series above is rational. Then forsome integers a and b,

a

b=

∞∑n=1

1

H(n,m)=

1

H(1,m)+

1

H(2,m)+ · · · .

Multiplying each side by H(b,m),a

bH(b,m) =

H(b,m)

H(1,m)+H(b,m)

H(2,m)+ · · ·+ H(b,m)

H(b,m)+ · · · .

Subtracting(

H(b,m)H(1,m) + H(b,m)

H(2,m) + · · ·+ H(b,m)H(b,m)

),

j =a

bH(b,m)−

(H(b,m)

H(1,m)+H(b,m)

H(2,m)+ · · ·+ H(b,m)

H(b,m)

)=

1m(b+ 1)

+1

m(b+ 1) · m(b+ 2)+ · · · .

Clearly, j > 0 since the terms of (4) are all greater than zero. However,just as before with k, j is strictly less than

1

b+ 1+

1

(b+ 1)2+

1

(b+ 1)3+ · · · = 1

b

which is at most 1. Hence j is strictly between 0 and 1, a contradictionsince j is an integer. Therefore, the series is irrational.

4. Other Results

Another result concerning the irrationality of certain infinite series dueto [1] is the following:

Theorem 4 (Badea) Let (bn) and (an), n ≥ 1 be two sequences of posi-tive integers such that the relation

an+1 >bn+1

bna2n −

bn+1

bnan + 1

holds for every large n. Then the series∞∑n=1

bnan

is irrational.

The theorem essentially says that if (an) grows quickly enough relative

8 The Pentagon

to (bn), the series∞∑n=1

bnan

cannot converge to a rational number.

Badea’s result can be applied to series of reciprocals of tetrations, asthe following theorem states.

Theorem 5 For all natural x ≥ 2, the series∞∑n=1

1nx

is irrational.

Proof. First, note that nx has the following properties

x(nx) = n+1x

(nx)k = xk(n−1x).

Let x ∈ N, x ≥ 2. We begin by showing that n+1x ≥ (nx)2. First,suppose n = 1. Then

2x = xx ≥ (1x)2 = x2

which holds for all natural x ≥ 2. Next, suppose the inequalityn+1x > (nx)2

holds for some natural n. Then x(n+1x) ≥ x(

nx)2 since x > 1. Using (5),we obtain (n+2)x ≥ x(

nx)2 . Since, for any α > 2, α2 > 2α, we havex(

nx)2 > x2(nx). Using (6),

n+2x > x(nx)2 > x2(

nx) = (n+1x)2.

And thus by mathematical induction, n+1x > (nx)2 for all natural n andx ≥ 2.

It is clear that 1− nx < 0 for x ≥ 2. Using (7),n+1x > (nx)2 > (nx)2 + 1− nx.

Letting (bn) = {1, 1, . . .} and (an) = nx with x ≥ 2, the theorem followsby application of Badea’s theorem.

Another, perhaps trivial, result of Badea’s theorem is the following:

Theorem 6 The series∞∑n=1

1nn

is irrational.

The proof is similar to that of the preceding theorem; I leave it as anexercise to the reader.

Spring 2016 9

5. For Further Investigation

In 1697, Bernoulli [2] proved what is now known as the Sophomore’sDream identity. It states∫ 1

0

1

xxdx =

∞∑n=1

1

nn≈ 1.291285997.

Unfortunately, neither Fourier’s nor Badea’s method is adequate for de-termining what seems likely to be the irrationality of the above series.Fourier’s method cannot be used since each term of the sequence {nn}∞n=1

is not divisible by its preceding terms. Also, the series converges tooslowly for Badea’s method to be used; I leave it to the reader to showthat (n+ 1)n+1 < n2n − nn + 1 for sufficiently large n.

References

[1] C. Badea. The irratinality of certain infinite series. Glasgow Mthe-matical Journal, 29:221-8, July 1987.

[2] Jean Bernoulli. Johannis Bernoulli...Opera Omnia. Lausann, 1742. p.216-21.

[3] Janot de Stainville. Mlanges d’Analyse Algebrique et de Geomtrie [AMixture of Algebraic Analysis and geometry]. Veuve Courcier, 1815.p. 340-341.

10 The Pentagon

Murray Klamkin’s Duality Principle forTriangle Inequalities

Daniel Sitaru

Mathematics Department

Colegiul National Economic Theodor CostescuDrobeta Turnu - Severin, Mehedinti, Romania

Abstract

In this article we build inequalities using Murray Klamkin’s duality princi-ple. This is a way to solve inequalities in six variables, three of them beingthe lengths of sides in a triangle and the other three positive numbers.

1. Introduction

In 1979, M. S. Klamkin published in "Elements der Mathematik" [3]the article “Triangle Inequalities from Triangle Inequalities” about the du-ality principle. Famous inequalities such as Euler’s, Leibniz’s, Ionescu-Weitzenbock’s, Mitrinovic’s, Carlitz’s, and Curry’s can be restated usingthis principle. Using some notations in a new, constructed triangle, theseinequalities are rediscovered in a classical form. We begin with Klamkin’stheorem.

Theorem 1 If P ∈ Int(∆ABC), letPA = x, PB = y;PC = z,AB =c,BC = a, andCA = b. Then ax, by, cz can be the lengths of the sides ofa triangle.

Proof. [3] [4] Let z1, z2, z3, z4 ∈ C be such that the points A,B,C, andP . correspond to z1, z2, z3 and z4, respectively. We can easily prove theidentity:

(z1 − z4)(z2 − z3) + (z2 − z4)(z3 − z1) + (z3 − z4)(z1 − z2) = 0

and hence

−(z3 − z4)(z1 − z2) = (z1 − z4)(z2 − z3) + (z2 − z4)(z3 − z1).

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Then

| − (z3 − z4)(z1 − z2)| = |(z1 − z4)(z2 − z3) + (z3 − z4)(z3 − z1)|≤ |z1 − z4| · |z2 − z3|+ |z2 − z4| · |z3 − z1|

Hence: cz < ax+ by. Analogously: ax < by + cz and by < ax+ cz.

Now let ∆MNP have sides of lengths ax, by, cz, and let s be thesemiperimeter, S the area, R the exradius and r the inradius. Then:

s =ax+ by + cz

2

S =1

4

√(ax+ by + cz)(ax+ by − cz)(ax− by + cz)(by + cz − ax)

R =abcxyz√

(ax+ by + cz)(ax+ by − cz)(ax− by + cz)(by + cz − ax)

r =

√(ax+ by + cz)(ax+ by − cz)(ax− by + cz)(by + cz − ax)

2(ax+ by + cz)

=1

2

√(ax+ by − cz)(ax− by + cz)(by + cz − ax)

ax+ by + cz.

2. Applications

Application 1 Let be P ∈ Int(∆ABC) and let PA = x, PB = y,and PC = z.Prove that:

(ax+ by − cz)(ax− by + cz)(by + cz − ax) ≤ abcxyzProof. The inequality can be written:

(ax+ by − cz)(ax− by + cz)(by + cz − ax)(ax+ by + cz)

≤ abcxyz(ax+ by + cz)

or, equivalently,

abcxyz√(ax+ by − cz)(ax− by + cz)(by + cz − ax)(ax+ by + cz)

≥2√

(ax+ by − cz)(ax− by + cz)(by + cz − ax)(ax+ by + cz)

2(ax+ by + cz).

This is equivalent to R ≥ 2r, which is Euler’s Inequality for ∆MNP .

12 The Pentagon


a2x2 + b2y2 + c2z2

a2b2c2x2y2z2

≤ 9

(ax+ by + cz)(ax+ by − cz)(ax− by + cz)(by + cz − ax)

Proof. The inequality can be written:

(ax)2 + (by)2 + (cz)2

≤ 9(abcxyz)2

(√

(ax+ by + cz)2(ax+ by − cz)(ax− by + cz)(by + cz − ax))2

which is equivalent to

(ax)2 + (by)2 + (cz)2 ≤ 9R2.

This is Leibniz’s Inequality for ∆MNP .


(a2x2 + b2y2 + c2z2)2

≥ 3(ax+ by + cz)(ax+ by − cz)(ax− by + cz)(by + cz − ax).


(ax)2 + (by)2 + (cz)2

≥ 4√

3 · (ax+ by + cz)(ax+ by − cz)(ax− by + cz)(by + cz − ax)

4or, equivalently,

(ax)2 + (by)2 + (cz)2 ≥ 4√

3S,

which is Ionescu - Weitzenbock’s Inequality for ∆MNP .


27(by + cz − ax)(ax+ cz − by)(ax+ by − cz) ≤ (ax+ by + cz)3


27(by+cz−ax)(ax+cz−by)(ax+by−cz)(ax+by+cz) ≤ (ax+by+cz)4

Spring 2016 13

or, equivalently,27 · 16 · S2 ≤ (ax+ by + cz)4.

Then12√

3 · S ≤ (ax+ by + cz)2

so that6√

3 · r · (ax+ by + cz) ≤ (ax+ by + cz)2.It follows that

6√

3 · r ≤ ax+ by + czor

6√

3 · r ≤ 2sand hence that

3√

3r ≤ s.This last is Mitrinovic’s Inequality for ∆MNP .


(ax+by+cz)3(ax+by−cz)3(ax−by+cz)3(by+cz−ax)3 ≤ 27(abcxyz)4

Proof. The inequality can be written:√(ax+ by + cz)(ax+ by − cz)(ax− by + cz)(by + cz − ax)

≤√

3(abcxyz)2

3

or, equivalently,

4S ≤√

3 · 3√

(ax)2 · (by)2 · (cz)2.Then

4S√3≤ 3√

(ax)2 · (by)2 · (cz)2,which is Carlitz’s Inequality [1] for ∆MNP .


(ax+by+cz)3(ax+by−cz)(ax−by+cz)(by+cz−ax) ≤ 27(abcxyz)2


(ax+by+cz)(ax+by−cz)(ax−by+cz)(by+cz−ax) ≤ 27(abcxyz)2

(ax+ by + cz)2

or, equivalently,

16(S)2 ≤ 27(abcxyz)2

(ax+ by + cz)2.

14 The Pentagon

Then

4S ≤ 3√

3abcxyz

ax+ by + czand hence

4√

3S ≤ 9(ax)(by)(cz)

(ax) + (by) + (cz),

which is Curry’s Inequality [2] for ∆MNP .

References

[1] L. Carlitz and F. Leuenberger, Problem E 1454, American Mathemat-ical Monthly, Vol. 68, pg. 177 and 805–806, 1961.

[2] T. R. Curry, Problem E 1861, American Mathematical Monthly, Vol.75, pg. 199, 1966.

[3] M. S. Klamkin, Triangle Inequalities from Triangle Inequalities. Ele-ments der Mathematik, 1979, vol. 34, pp 49–55.

[4] Daniel Sitaru, Math Phenomenon. Paralela 45, Publishing House,Pitesti, Romania, 2016.

Spring 2016 15

The Problem Corner

Edited by Pat Costello

The Problem Corner invites questions of interest to undergraduate stu-dents. As a rule, the solution should not demand any tools beyond calcu-lus and linear algebra. Although new problems are preferred, old ones ofparticular interest or charm are welcome, provided the source is given. So-lutions should accompany problems submitted for publication. Solutionsof the following new problems should be submitted on separate sheets be-fore March 15, 2017. Solutions received after this will be considered upto the time when copy is prepared for publication. The solutions receivedwill be published in the Spring 2017 issue of The Pentagon. Preferencewill be given to correct student solutions. Affirmation of student statusand school should be included with solutions. New problems and solu-tions to problems in this issue should be sent to Pat Costello, Departmentof Mathematics and Statistics, Eastern Kentucky University, 521 LancasterAvenue, Richmond, KY 40475-3102 (e-mail: [email protected], fax:(859) 622-3051).

NEW PROBLEMS 780-788

Problem 780. Proposed by Daniel Sitaru, Colegiul National EconomicTheodor Costescu, Drobeta Turnu – Severin, Mehedinti, Romania.

Prove that if a, b, c ∈ [1,∞), then ab+ bc+ ca ≥ 3 + 2 ln(abbcca).

Problem 781. Proposed by Daniel Sitaru, Colegiul National EconomicTheodor Costescu, Drobeta Turnu – Severin, Mehedinti, Romania.

Prove that if a, b, c ∈ (0,∞), then

∑a

√(b4 + c4)

2≥ a2(b+ c) + b2(a+ c) + c2(a+ b)− 3abc.

16 The Pentagon

Problem 782. Proposed by Jose Luis Diaz-Barrero, School of CivilEngineering, Barcelona Tech - UPC, Barcelona, Spain.

Let a, b, c be the lengths of the sides of triangle ABC and ma,mb, andmc the lengths of its medians. Prove that

2ma + 2mb + 2mc

2a + 2b + 2c< 1.

Problem 783. Proposed by Jose Luis Diaz-Barrero, School of CivilEngineering, Barcelona Tech - UPC, Barcelona, Spain.

Find all real solutions to the following system of equations:

x3 + 2x+ y = 9 + 3x2

3y2 + 6y + z = 21 + 9y2

5z3 + 10z + x = 33 + 15z2.

Problem 784. Proposed by D.M. Batinetu-Giurgiu, “Matei Basarab”National College, Bucharest, Romania, Neculai Stanciu, “George EmilPalade”, Buzau, Romania.

Prove that in any triangle ABC with BC = a,CA = b, AB = c andarea F, the following inequalities are true.

(b2 + c2) sin A2 + (c2 + a2) sin B

2 + (a2 + b2) sin C2 ≥ 4

√3F ,

ab(1 + sin2 C2 ) + bc(1 + sin2 A

2 ) + ca(1 + sin2 B2 ) ≥ 4

√3F .

Problem 785. Proposed by Iuliana Trasca, Scornicesti, Romania.

Show that if x, y, z > 0, then

x6z3 + y6x3 + z6y3

x2y2z2≥ x3 + y3 + z3 + 3xyz

2.

Problem 786. Proposed by Thomas Chu, Macomb, Illinois.

If x, y, z > 1, then

(x2 + y2 + z2)(x+ y + z) + x3 + y3 + z3 > 4xy + 4xz + 4yz.

Spring 2016 17

Problem 787. Proposed by the editor.

Mike buys some pants and shorts at the Great Pants Store. Mike buysshorts that cost $11each and pants that cost $14 each. His total before taxesis $283. How many shorts and how many pants did Mike buy?

Problem 788. Proposed by George Heineman, Worcester PolytechnicInstitute, Worcester, MA.

A SujikenTM puzzle has a triangular grid of cells containing digits from1 to 9. You must place a digit in each of the empty cells with the constraintthat no digit can repeat in any row, column, or diagonal. Additionally,no digit can repeat in the 3x3 large squares withthick borders or the threetriangular regions with thick borders. The puzzle below is of intermediatedifficulty.

18 The Pentagon

SOLUTIONS TO PROBLEMS 760-768

Problem 760. Proposed by Mathew Cropper, Eastern KentuckyUniversity, Richmond, KY.

Consider a 5× 5 grid. There are(2513

)ways to fill the grid with exactly

13 X’s and 12 O’s. How many of these have at least one row, one column,or one diagonal with 5 X’s?

Solution by the proposer.

For 1 ≤ j ≤ 5, let Rj and Cj represent the set of all 5 × 5 grids thathave all X’s in row j or column j. Similarly, let D1 and D2 representthe set of all grids that have all X’s on the diagonals 1 and 2. Clearly,∣∣∣∣ 5⋃1Rj

5⋃1Cj ∪D1 ∪D2

∣∣∣∣ is the desired number we seek. By placing 5 X’s

in a row, column or diagonal, there are 20 remaining spots to place 8 X’s.

Hence |Rj | = |Cj | =

(208

)and |Dj | =

(208

)We need to use the

Principle of Inclusion-Exclusion to get the desired result. We first need in-

tersections of 2 sets. |Rj∩Rk | = |Cj∩Ck| =(

153

)because 10 spaces are

filled by X’s. |D1 ∩ D2| =(

164

)=∣∣Rj ∩ Ck

∣∣ =∣∣Rj ∩ Dk

∣∣ =∣∣Cj ∩ Dk

∣∣Then we need intersections of 3 sets and ways to form the three sets. It isimpossible for 3 different rows or columns to contain all X’s. When youhave two rows and a column or two columns and one row, they will usethe 13 X’s in precisely one way. The number of ways to choose two rows

and one column is(

52

)∗ 5 = 50. Similarly, the number of ways to

choose two columns and one row is 50. When you have two rows and adiagonal, they will use up the 13 X’s in precisely one way. The number of

ways to choose two rows and one diagonal is(

52

)∗ 2 = 20. Similarly,

two columns and a diagonal take up all 13 X’s in one way and there are 20ways to form these intersections. The other intersections of 3 sets are:∣∣Rj ∩ Ck ∩ Dn

∣∣ = 13 when j 6= k and ways to form the intersection =5*4*2 = 40;∣∣Rj ∩ Ck ∩ Dn

∣∣ = 1 when j = k and ways to form the intersection = 5*2= 10;|D1 ∩ D2 ∩ Rn| = 13 when n 6= 3 and ways to form the intersection = 4;

Spring 2016 19

|D1 ∩ D2 ∩ Rn| = 1 when n = 3 and ways to form the intersection = 1;|D1 ∩ D2 ∩ Cn| = 13 when n 6= 3 and ways to form the intersection = 4;|D1 ∩ D2 ∩ Cn| = 1 when n = 3 and ways to form the intersection = 1.

All 4-way intersections are empty. By inclusion-exclusion,∣∣∣∣∣5⋃1

Rj

5⋃1

Cj

⋃D1

⋃D2

∣∣∣∣∣ = 12

(128

)−(

52

)(153

)−(

52

)(153

)− (1 + 5 ∗ 5 + 5 ∗ 2 + 5 ∗ 2)

(164

)+ 1 ∗ 50 + 1 ∗ 50 + 1 ∗ 20 + 1 ∗ 20 + 13 ∗ 40

+ 1 ∗ 10 + 13 ∗ 4 + 1 ∗ 1 + 13 ∗ 4 + 1 ∗ 1

= 1419596.

Problem 761. Proposed by Ovidiu Furdiu, Technical University ofCluj-Napoca, Cluj, Romania.

Let n ≥ 0 be an integer and let T2n denote the 2nth Taylor polynomialcorresponding to the cosine function at 0:

T2n(x) =

n+1∑k=1

(−1)k−1x2k−2

(2k − 2)!

Let

In =

∞∫0

T2n(x)− cosx

x2n+2dx.

1. Prove thatIn = − 1

(2n+ 1)(2n)In−1, n ≥ 1.

2. Calculate In.

20 The Pentagon


a) We integrate by parts twice and we get that

In =T2n(x)− cosx

(2n+ 1)x2n+1|∞0 +

1

2n+ 1

∞∫0

T2n′(x) + sinx

x2n+1dx

=1

2n+ 1

∞∫0

T2n′(x) + sinx

x2n+1dx

=T2n′(x) + sinx

(2n+ 1)(2n)x2n|∞0 +

1

(2n+ 1)(2n)

∞∫0

T2n′′(x) + cosx

x2ndx

=1

(2n+ 1)(2n)

∞∫0

T2n′′(x) + cosx

x2ndx.

A simple calculation shows that

T2n′(x) =

n+1∑k=2

(−1)k−1x2k−3

(2k − 3)!

and

T2n′′(x) =

n+1∑k=2

(−1)k−1x2k−4

(2k − 4)!= −

n∑i=1

(−1)i−1x2i−2

(2i− 2)!= −T2n−2(x).

Thus

In = − 1

(2n+ 1)(2n)

∞∫0

T2n−2′′(x)− cosx

x2ndx = − 1

(2n+ 1)(2n)In−1.

b) The integral equals (−1)n2(2n+1)!π.

We have, based on the recurrence formula, that

In =(−1)n

(2n+ 1)(2n) · · · 3 · 2I0 =

(−1)n

(2n+ 1)!

∞∫0

1− cosx

x2dx.

We calculate the last integral by parts and get that∞∫0

1− cosx

x2dx = − 1− cosx

x

∣∣∣∣∞0

+

∞∫0

sinx

xdx =

π

2.

Spring 2016 21

Thus

In =(−1)n

2(2n+ 1)!π.

Also solved by Henry Ricardo, New York Math Circle, New York.

Problem 762. Proposed by Mohammad K. Azarian, University ofEvansville, Evansville, IN.

If x 6= 0, x 6= 1, y > 0, and y 6= 1, then find y as a function of xprovided

y′ + y(ln y)2 − 1

x(x− 1)y ln y = 0.

Solution by Henry Ricardo, New York Math Circle, New York.

Let y = e1/z where z = z (x) is nonzero and differentiable for allreal values of x. Then y′ = (z−1)′e1/z = −z−2z′e1/z and the dif-ferential equation becomes z′

z2 e1/z + e1/z(1z

)2 − 1x(x−1)e

1/z 1z = 0 or

z′ +(

1x(x−1)

)z = 1, a linear nonhomogeneous equation in z. The stan-

dard integrating factor technique gives us z =(

xx−1

)(x− lnx+ C) and

thus y = e1/z = ex−1

x(x−ln x+C) .

Also solved by the proposer.


Let x ∈ and

A(x) =

x+ 1 1 1 1

1 x+ 1 1 11 1 x+ 1 11 1 1 x+ 1

.

Compute the matrix product A(0) ∗A(1) ∗A(2) ∗A(3).

22 The Pentagon


We have A(0) =

1 1 1 11 1 1 11 1 1 11 1 1 1

= E,A(x) = E + x · I4,

E2 = 4E, where I4 is the 4× 4 identity matrix.A(x) ·A(y) = (E + xI4) (E + yI4) = E2 + (x+ y)E = (xy) I4,A(0) ·A(1) = 5E,A(2) ·A(3) = 9E + 6I4.Hence

A(0) ·A(1) ·A(2) ·A(3) = 5E (9E + 6I4)

= 45E2 + 30E

= 45 · 4E + 30E = 210E.



Calculate

limn→∞

√n(

((n+ 1)!)1/2(n+1) − (n!)1/2n).

Solution by Angel Plaza, Universidad de Las Palmas de Gran Canaria,Spain.

The proposed limit may be written as limn→∞

n(((n+1)!)1/(n+1)−(n!)1/n)√n(((n+1)!)1/2(n+1)+(n!)1/2n)

.

Now the result follows easily since by the Stirling approximation for n!,√n(

((n+ 1)!)1/2(n+1) + (n!)1/2n)∼√n(√

n+1√e

+√n+1√e

). Therefore

limn→∞

n√n(((n+1)!)1/2(n+1)+(n!)1/2n)

=√e2 . On the other hand, see for exam-

ple [1], limn→∞

(((n+ 1)!)1/(n+1) − (n!)1/n

)= 1

e and then the desired limit

is equal to 12√e.

[1]Gh. Toader. Lalescu sequences, Univ. Beograd. Publ. Elektrotehn.Fak. Ser. Mat. 9 (1998)25-28.


Spring 2016 23

Problem 765. Proposed by Marcel Chirita, Bucharest, Romania.

Let a, b, c be the lengths of the sides of a triangle in which b2+c2 = a2.Prove that

b3 + c3 < 3abc+(

2√

2− 1)a3.

Solution by Titu Zvonaru, Comanesti, Romania and Neculai Stanciu,“George Emil Palade“ School, Buzau, Romania.

We shall prove a stronger inequality, i.e., we shall prove that b3 + c3 <(2√

2− 1)a3. By the MA-MQ inequality and the hypothesis b2 + c2 = a2,

we have that 2√

2a3 = 2a2√

2(b2 + c2) > 2a2(b + c). So it suffices toshow thatb3 + c3 < 2a2(b+ c)− a3 ⇔ (b+ c)(b2 − bc+ c2) + a3 < 2a2(b+ c)

⇔ a3 = a2(b+ c) + bc(b+ c),

which is true since by the triangle inequality we have a3 = a2a < a2(b+c)and we are done.

Also solved by Nicusor Zlota, “Traian Vuia“ Technical College, Focsani,Romania; and the proposer.

Problem 766. Proposed by Marcel Chirita, Bucharest, Romania.

Let x be an integer. Prove that if x5 + 5x3 + 15x2 > 21x, thenx5 + 5x3 + 15x2 − 21x ≥ 30.


We note that y = x5 + 5x3 + 15x221x = (x5x) + 5(x3x) + 15(x2x).Since x2x = x(x1) is a multiple of 2, the term 15(x2x) is a multiple of30. Since x3x = x(x1)(x + 1) is a multiple of 6, the term 5(x3x) is amultiple of 30. Finally, (x5x) = x(x1)(x+ 1)(x2 + 1) is a multiple of 30.It follows that since y > 0 and a multiple of 30, y > 30.

Also solved by Angel Plaza, Universidad de Las Palmas de Gran Canaria,Spain.


Prove that the number 1317 cannot be written as the sum of a squareand a fifth power of another integer.

Solution by Neculai Stanciu, “George Emil Palade“ School, Buzau, Ro-

24 The Pentagon

mania and Titu Zvonaru, Comanesti, Romania.

We work modulo 11. We have 13172174(25)34(−1)3 − 47(mod11).We have x20, 1, 3, 4, 5, 9(mod11) and y50, 1, 10(mod11). Hence the equa-tions x2 + y5 = 1317 and x2 − y5 = 1317 cannot have positive integersolutions. So the equation x2 + y5 = 1317 cannot have integer solutions.

Also solved by by Caleb Garascia (student), Eastern Kentucky University,Richmond, KY; Henry Ricardo, New York Math Circle, New York; and theproposer.


Calculate the value of the series∞∑n=0

(1/2)n

(n+ 2)(n+ 4).

Solution by the Missouri State University Problem Solving Group, Mis-souri State University, Springfield, MO.

It is well known that for all x in [−1, 1), log(1 − x) = −∞∑n=1

xn

n . By

partial fractions decomposition we have∞∑n=0

(1/2)n

(n+ 2)(n+ 4)=

∞∑n=0

(1/2)n+1

n+ 2−∞∑n=0

(1/2)n+1

n+ 4

=

∞∑n=2

(1/2)n−1

n−∞∑n=4

(1/2)n−3

n

= 2

∞∑n=2

(1/2)n

n− 8

∞∑n=4

(1/2)n

n

= 2

[ ∞∑n=1

(1/2)n

n− 1

2

]− 8

[ ∞∑n=1

(1/2)n

n− 1

2− 1

8− 1

24

]= −2 log (1− 1/2)− 1 + 8 log (1− 1/2) + 16/3

= 13/3− 6 log(2)

Also solved by Henry Ricardo, New York Math Circle, New York ; An-gel Plaza, Universidad de Las Palmas de Gran Canaria, Spain; and theproposer.

Spring 2016 25

KAPPA MU EPSILONNorth Central Regional Convention Report

April 1-2, 2016Submitted by Dr. Katherine Kime, North Central Regional Director

The KME North Central Regional Convention was held April 1 - 2, 2016 atthe University of Nebraska at Kearney. There were fifty-nine registrants,with representatives from eight different chapters: KS Alpha, KS Beta,KS Delta, MO Alpha, MO Eta, MO Theta, TN Gamma, and NE Beta. Thehost chapter was Nebraska Beta. Seven student abstracts for papers weresubmitted and presented, with awards going to the top three papers. Thefirst prize was an Amazon Fire tablet, the second prize a clock with math-ematical formulas replacing the usual numerals and a Fractiles magnetictiling set, and the third prize a clock. The award winners were:

• Joshua Stucky, Union University, TN Gamma– Irrationality of Certain Infinite Series

• Brian Mosier, Emporia State University, KS Beta– Nowcasting the Flu

• Taylor Balsmeier, Washburn University, KS Delta– Statistical Analysis of Trends in Ranking and Salaries for Washburn

University

Papers presented:

• John Vallelonga and Nathan Dahlin, Evangel University, MO Theta– Uniform Additive Square Matrices

• Adam W. Zheng, University of Nebraska at Kearney, NE Beta– Exploring Context-Free Grammars and their Similarities to Fractals

using Recursive Drawing

• Brian Mosier, Emporia State University, KS Beta– Nowcasting the Flu

• Candy Smith, University of Nebraska at Kearney, NE Beta– A Study of Interdependency of English Literacy and Mathematics

Among the Deaf and Hard of Hearing

• Taylor Balsmeier, Washburn University, KS Delta– Statistical Analysis of Trends in Ranking and Salaries for Washburn

University

26 The Pentagon

• Alexandria Linnerson, University of Nebraska at Kearney, NE Beta– The Evolution of Cryptography

• Joshua Stucky, Union University, TN Gamma– Irrationality of Certain Infinite Series

• Invited presentation: Dr. Mark Hall, Hastings College; Hastings, Ne-braska– Game Theory: More Than Just Fun and Games

Presenters who did not win prizes received a math mug, and each visitingchapter received a Go board set as a door prize. A planetarium show washeld Friday night in Bruner Hall. The KME North Central Regional Con-vention was held in Kearney in 1982. Dr. Charles Pickens, UNK ProfessorEmeritus, NE Beta corresponding secretary at that time, attended the 2016convention.

Spring 2016 27

KAPPA MU EPSILONGreat Lakes Regional Convention ReportFriday, April 8-Saturday, April 9, 2016

Submitted by Peter R. Skoner, National Historian

The joint KME Regional Convention/MAA Ohio Section Meeting washosted by the Ohio Eta Chapter of Kappa Mu Epsilon National Mathemat-ics Honor Society at Ohio Northern University in Ada, Ohio. The OhioMAA Section meeting was celebrating a centennial because the Mathe-matical Association of America was formed in Columbus, Ohio on De-cember 31, 1915. Several of the presentations, including the banquet in-vited address, described some of the rich history of mathematics in Ohio.The other invited addresses were about Leibniz, number theory, women‘scontributions to the history of computing, and mentoring women and mi-norities in mathematics.

The meeting began on Friday, April 8, at 12:00 Noon with a student prob-lem solving competition. At 1:30, a welcome and introductions were fol-lowed by the MAA Ohio retiring president‘s address, an invited address,and a contributed papers session.

Kappa Mu Epsilon chapters were invited to a meeting at 5:30, which wasmoderated by National Historian Pete Skoner and attended by four chap-ters GA Zeta, OH Eta, PA Mu, and WV Alpha. There was discussion abouthaving this joint MAA/KME meeting and the consensus was that it wasworking, mostly because the meeting infrastructure was already in placethrough the MAA Section, and that KME schools could promote the meet-ing through its network and enjoy the mathematics content of the meetingand fellowship with KME and other MAA schools all at once. There wasalso discussion about activities at the chapter level including the use ofInstagram, probability nights, board game nights, graduation cords, com-bined activities with mathematics clubs, communicating with students inother majors (engineering, chemistry, and so on), tutoring centers throughcalculus, undergraduate research, and movie nights for undecided majors.

Friday activities concluded with some social time, a student pizza party, abanquet, and an after-dinner address for both faculty and students.

The Saturday schedule included two invited talks, and another contributedpapers session. Throughout the entire event, book vendors and exhibitswere available in the break room. There were 43 contributed talks during

28 The Pentagon

the convention, 34 by faculty and 9 by students. Included in the 9 studentstalks were talks by two students from Kappa Mu Epsilon chapters. Theseinclude:• Michelle Haver, Ohio Northern University, OH Eta

– On the R. Lemke Oliver–K. Soundararajan recent “prime conspir-acy"

• Leah Buck, Muskingum College, OH Zeta– Constructing a Universal Differential Equation Based on Certain

Trigonometric Relationships

Chapter School Faculty Student(s)Georgia Zeta Georgia Gwinnett College 0 1Ohio Alpha Bowling Green University 5 1Ohio Gamma Baldwin-Wallace College 2 0Ohio Epsilon Marietta College 1 0Ohio Zeta Muskingum College 1 1Ohio Theta Capital College 0 3Ohio Eta Ohio Northern University 12 9Pennsylvania Mu Saint Francis University 2 4West Virginia Alpha Bethany College 1 5

Nine Kappa Mu Epsilon Chapters Attending 24 24

Spring 2016 29

Kappa Mu Epsilon NewsEdited by Peter Skoner, Historian

Updated information as of June 2016

Send news of chapter activities and other noteworthy KME events toPeter Skoner, KME Historian

Saint Francis University117 Evergreen Drive, 313 Scotus Hall

Loretto, PA 15940or to

[email protected] News

KAPPA MU EPSILONInstallation Report

Illinois Kappa, Aurora UniversityAurora, Illinois

The Illinois Kappa Chapter of Kappa Mu Epsilon was installed at 2:00P.M. on Tuesday, May 3, 2016 at a ceremony held on the campus of Au-rora University in Aurora, Illinois. The meeting was conducted by Dr.Sebastian Wyman. KME national president-elect Dr. Brian Hollenbeckserved as the installing officer.

Ten students and one faculty member were initiated as the charter mem-bers of the Illinois Kappa Chapter. They are: Heather Gehlhaar, TeasiaKimmons, Brayden Teele, Jacob Stockman, Lauren Sander, Matt Swan-son, Michelle Murray, Nicole Noonan, Sean Smith, Stephanie Stellman,and Dr. Sebastian Wyman. The first officers of the chapter were installed:Heather Gehlhaar, President; Brayden Teele, Vice President; Jacob Stock-

30 The Pentagon

man, Secretary-Treasurer; Dr. Wyman, Corresponding Secretary; and Dr.Gina Rahn, faculty sponsor.

Following the installation ceremony, Dr. Hollenbeck presented a talk ti-tled, When the “Best” Strategy Fails, during which attendees played andanalyzed the dice game, Kyboi. About 14 members of the department at-tended the event.

KAPPA MU EPSILONInstallation Report

Missouri Xi, William Woods UniversityFulton, Missouri

The Missouri Xi Chapter of Kappa Mu Epsilon was installed at 1:00 P.M.on Wednesday, February 17, 2016 at a ceremony held in the Cox Scienceand Language building on the campus of William Woods University in Ful-ton, Missouri. The meeting was conducted by Chris Schneider,a WilliamWoods Faculty member who was initiated into KME as an undergraduateat Missouri State University. KME national president Dr. Rhonda McKeeserved as the installing officer, and Raymond Hune, chair of the Divisionof Mathematics and Science, welcomed and congratulated the initiates.

Kiersten Lockman and Anne Wehner were initiated as the charter membersof the Missouri Xi Chapter. The first officers of the Missouri Xi chapterwere installed and are as follows: Kiersten Lockman, President; AnneWehner, Vice President; Dr. Chris Schneider, Corresponding Secretaryand faculty sponsor.

Following the installation ceremony, Dr. McKee presented a talk titled,Spirograph Math, after which the attendees enjoyed cake, punch and so-cializing. About 15 students, faculty, staff and family members attendedthe event.

Spring 2016 31

Chapter News

AL Gamma – University of MontevalloChapter President – Brandon McMahan; 8 New MembersOther Fall 2015 Officers: Jordan Romine, Vice President; Anna Lein-heiser, Secretary; Dr. Scott Varagona, Corresponding Secretary; and Dr.Michael Sterner, Faculty SponsorNew Initiates – William D. Brannon, Andra Jackson, Anna Leinheiser, Miranda Mathew-son, Christina Meyer, Kayla Pilkington, Jordan Romine, Jasmyn Walker, and Amy Web-ber.AL Zeta – Birmingham-Southern CollegeChapter President – Sam Crowder; 26 Current Members; 26 New Mem-bersOther Fall 2015 Officers: Julia Creager, Vice President; Andy Crowder,Secretary; Nirja Patel, Treasurer; and Maria Stadnik, Corresponding Sec-retary and Faculty SponsorOn Monday, October 19, 2015, Dr. Frank Patane from Samford Universitycame to give a KME Colloquium. His interesting talk in the area of numbertheory was entitled “Sums of squares and beyond.” On Friday, November6, 2015, we welcomed Dr. Julia Barnes from Western Carolina Universityto give a KME Colloquium talk. Her talk on interesting results in theintersection of complex dynamics and complex analysis was entitled, “Anyway you slice it, it comes up Julia Sets.”New Initiates – Amer Babi, Sarah Bowman, Elisha Brooks, Andrew Brown, Yorisha Bryant,Henry Edward Crosby III, Ansleigh Davies, Marjory Day, Harper Dewine, David Good-loe, Majd Habash, William Mercer Heath, Amy Heldt, Cynthia M. Kagambirwa, RachelLee, Cameron Mills, Patrick S. Newsom, Taylor Oliver, Katherine Potts, Jackson BaileyRhodes, William Rice, Georgia Robles, Noah Rowe, Liza Spencer, Mary Stewart Wachter,and Haoran Yang.AL Eta – The University of West AlabamaCorresponding Secretary – Hazel Truelove; 17 New MembersNew Initiates – Brooke Babb, Ashton Baugh, Jessica Brock, Sha’Ecclesia Colvin, KristaElam, Isobelle Foster, Manuel Grossmann, Kaleigh Henders, Mitchell Holgate, DanielManning, Luigi Mendez-Rossello, Alisha Moore, James Napp, Amber Nelson, Trent South,Nickolas Spradling, and Lindsey Warner.AL Theta – Jacksonville State UniversityChapter President – Shannon Bolton; 50 Current Members; 24 New Mem-bersOther Fall 2015 Officers: Paitra Onkst, Vice President; Tucker Davis, Sec-retary; Shawanna Roper, Treasurer; and Dr. David Dempsey, Correspond-

32 The Pentagon

ing Secretary and Faculty SponsorThe Alabama Theta chapter opened the 2015-16 academic year with aPizza/Game party on September 11; it was such a success, we did thisagain on October 2. We met biweekly, and planned other activities, includ-ing an October 29 Halloween party, complete with a math-themed costumecontest and pumpkin carving. We ended the semester with a December 4holiday party, including games and a “dirty Santa” gift swap for those whowanted to participate. The annual Spring Initiation Ceremony is plannedfor February 29, 2016. Several spring activities are being planned, includ-ing bowling and a trip to Birmingham, AL, to a “Lockout” facility solvinga series of puzzles as a group to successfully complete a mission and exitthe room.New Initiates - Kyle Glenn Clark, Amberley Mercedes Echols, Daniel Scott Evans, NicoleMcInerney Everhart, Preston Riley Graben, Addie Noelle Hardy, Blake Austin Jackson,Taylor Nicole Jackson, Abby Jaskowski, Lauren Michelle Johnson, Wyvolyn Kirkland,Phillip Krosnar, Kelly Krystal Manley, Vanessa Marroquin, Michael McCreless, KatelynMcDonald, Natalie Elizabeth Millar, Daniel Alex Miradakis, Christopher Mount, PhilipMurray, Ashley Ann Nadrotowski, Kristen Colleen Norred, Amber Nicole Pruitt, and Lind-sey Claire Weathers.CA Epsilon – California Baptist UniversityCorresponding Secretary – James Buchholz; 26 New MembersNew Initiates – Cassandra Ault, Elliott Best, Bryce Block, Dominic Bundrick, VincentCastelluccio, Dominique Dominguez, Sheraya Erickson, Zachary Garcia, Ryan Gibeault,America Hidalgo, Naomie Houck, Austin Hulen, Isaak Juntunen, Derek Kouns, MichaelLuong, Audrie Minnich Jillian Moyes, David Sandy, Michael Sandy, Evan Schneider, An-drew Shubin, Scott Teichert, Trent Villaverde, Gabriel Watler, Rebecca Whitaker, and SethWijnhamer.CA Eta – Fresno Pacific UniversityChapter President – David Maes; 9 Current MembersOther Fall 2015 Officers: Elaine Draper, Vice President; Terence Yi, Cor-responding Secretary; and Ron Pratt, Faculty SponsorCO Delta – Colorado Mesa UniversityCorresponding Secretary – Erik Packard; 11 New MembersNew Initiates – Jared Bourget, Samual Hebenstreit, Crystal Hainlin, Shanna Hoopengard-ner, Audrey Howe-Carlson, Harrison Kalina, Joseph Labrum, Alyssa Lehmann, AlexanderMartinez, Robert Millican, and Cecilla O’Connor.CT Beta – Eastern Connecticut State UniversityChapter President – Mehdi Khorami; 443 Current MembersOther Fall 2015 Officers: Mehdi Khorami, Vice President, Secretary, Trea-

Spring 2016 33

surer, Faculty Sponsor, and Corresponding SecretaryFL Delta – Embry Riddle Aeronautical UniversityCorresponding Secretary – Dr. Jayathi Raghavan; 18 New MembersNew Initiates – Immanuel A. Compomizzi, Killian J. Hitsman, Kelsey Klein, KatherineB. Lenninger, Andrea Martinez, Andrew McClary, Charles R. Miller, Shreya M. Mittal,Claudia D. Morello, Austin J. Ogle, Himani Parekh, David J. PeQueen, Sarena DanielleRobertson, Patrick H. Rupp, James Stenzhorn, Genesis Vargas, Jessica Voyt, and SophiaZaccarine.GA Beta – Georgia College and State UniversityCorresponding Secretary – Rodica Cazacu; 4 New MembersNew Initiates – Emily D. Baum, Kendall M. Brown, Charles W. Quinn, and Austin N.Sanders.GA Gamma – Piedmont CollegeCorresponding Secretary - Hope Menzel; 3 New MembersNew Initiates – Stephen M. Owensby, Krishna Khatri, and Rudradatt Persaud.GA Epsilon – Wesleyan CollegeCorresponding Secretary - Dr. Joe Iskra; 7 New MembersNew Initiates – Jessica Etheridge, Sunada Khadka, Keshika Marambe, Xinyi Pan, Son-akchhi Shrestha, Anjola Uprety, and YunFan Zhou.GA Zeta – Georgia Gwinnett CollegeChapter President – Shahriyar Roshan Zamir; 42 Current Members; 8New MembersOther Fall 2015 Officers: Bess Burnett, Vice President; Heather McAfee,Secretary; Christopher Lohrmann, Treasurer; Dr. Jamye Curry, Corre-sponding Secretary; and Drs. Jenny Sinclair and Livy Uko, Faculty Spon-sorsHI Alpha – Hawaii Pacific UniversityChapter President – Keila Elderts; 15 Current Members; 3 New MembersOther Fall 2015 Officer: Tara Davis, Corresponding Secretary and FacultySponsorWe had an induction dinner on November 19, 2015 to induct 3 new mem-bers. Several older members and math faculty also attended.New Initiates – Lisa Barroga, Wesley Chai, and Jason Badua Yadao.IA Alpha - University of Northern IowaChapter President - Jacob Oswald; 27 Current Members; 8 New MembersOther Fall 2015 Officers: Julie Kirkpatrick, Vice President; Lindsey Ped-erson, Secretary; Katy Goodmudson, Treasurer; and Mark D. Ecker, Cor-responding Secretary and Faculty SponsorOur first KME meeting was held on October 1, 2015 at Professor Ed Rath-mell’s house where student member Jake Snyder demonstrated his VisualBasic program that he wrote, entitled “Visual Basic Random Quiz Gener-

34 The Pentagon

ator Program.” We enjoyed walking through the vegetation maze at Pro-fessor Rathmell’s house after our business meeting. Student member Lu-cas Beving presented his paper entitled “Measurement of Sodium DoubletSeparation with an Interferometer” at our second meeting on November 3,2015 at Professor Mark Ecker’s home. Student member Marcus McMahonaddressed the fall initiation banquet with “What Truly Determines Wins inthe NFL.” Our fall banquet was held at Old Chicago restaurant in CedarFalls on December 8, 2015, where eight new members were initiated.New Initiates – Heather Bavido, Ashley Brown, Keith Doore, John Fisher, Danusha Manohar,Marcus McMahon, Jordan Ratz, and Jordan Reinard.IA Gamma – Morningside CollegeCorresponding Secretary – Chris Spicer; 6 New MembersNew Initiates – Kelsey Brenner, Travis Metzger, Austin Naylor, Jace Neubaum, AndrewRichardson, and Tessa Weinstein.IA Epsilon – Central CollegeChapter President – Ashley Hulsing; 12 Current Members; 8 New Mem-bersOther Fall 2015 Officers: Melissa Ketcham, Vice President, Secretary, andTreasurer; and Dr. Russell E. Goodman, Corresponding Secretary andFaculty SponsorThe Iowa Epsilon chapter of KME is growing! We initiated 8 new mem-bers in the spring of 2015 and have been recruiting all year long for a largeanticipated spring 2016 recruiting class.New Initiates – Abigail Davis, Mikaela Dunkin, Joseph Eilers, Gretchen Kistenmacher,Tiffany Latshaw, Sydney Lunardi, Madison Megonigle, and Sydney Pratt.IL Beta – Eastern Illinois UniversityCorresponding Secretary – Nancy Van Cleave; 27 New MembersNew Initiates – Alejandra Alvarado, Carlos Antonetti, Kodi Avery, Jordan Boerngen, BrianBourne, Megan Childers, Marissa Ford, Brett Haines, Jessica Helf, Janie Howse, Eliza-beth Howze, John M. Janasik, Chad Kelterborn, Grant Lakeland, Ross Mattingly, BradleyOgilvie, Bogdan Petrenko, Jenalee Reardon, Jessica L. Reid, William Tyler Reynolds,Michael Sassaman, Alina Schoenecke, Ellie Short, Rebecca Small, Tyler Vollmer, CalebM. Will, and Brittany Yunker.IL Zeta – Dominican UniversityCorresponding Secretary and Faculty Sponsor – Aliza Steurer; 23 CurrentMembers; 4 New MembersKME and Math Club operate together as one organization at DominicanUniversity. In fall 2015, we held two special lectures involving MathClub/KME, one about the mathematics behind ranking football teams and

Spring 2016 35

a panel about research opportunities and internships in mathematics.New Initiates – Amy Do, Rosario Hernandez, Jennifer Ryan, and Aaron Zerhusen, Ph.D.IL Iota – Lewis UniversityCorresponding Secretary – Margaret M. Juraco; 52 New MembersNew Initiates – Jacqueline Argenbright, Vanessa Basick, Ramsey Baya, Kurt Becker, WyattBlatti, Amy Choi, Jessica Dreher, Drew Flowers, Ramica Ford, Taylor Foytik, Jacob Gillis,Jeremy Gregory, Melanie Harrison, Amanda Harsy, Eric Herbert, Jesse Hertz, CaitlinHodgson, John Hodul, Lisa Janes, Jaclyn Kenyon, Ernest Knight, Eliot Kovitz, StephenKurek, Anthony Kurt, Erica Kwiatkowski-Egizio, Elizabeth Langland, Eric Lazarski, SeanLillis, Alyssa Malzone, Sarah Massoglia, Alessandro Mazza, Cassandra Myers, StevenNeubauer, Meghan Nichol, Joseph Onesto, Sarah Parker, Christopher Pelech, Alec Pick-ett, Leanna Pitsoulakis, Jeromy Rech, Lenin Roa-Tapia, Brandon Schabel, Elie Shmayel,Micahel D. Smith, Michael R. Smith, Penilope Strid, Piotr Szczurek, Christopher Troxell,Andrea Veeneman, Nicole Ware, Zachary Widel, and Nicole Yuede.IN Beta – Butler UniversityCorresponding Secretary – Bill Johnston; 15 New MembersNew Initiates – Jesse Allen, Kaija Bole, Elizabeth Demuth, Michael Garey, AmandaHashimoto, Helen Heimark, Kristopher Hill, Leesa Jing, Kaitlyn Lee, Jackson O’Brien,Alexander Olivero, Taylor Pieper, Priyanka Prasad, Gabrielle Skwarcan, and Bryton Wise.KS Beta – Emporia State UniversityChapter President – Brian Mosier; 55 Current Members; 16 New Mem-bersOther Fall 2015 Officers: Michelle Foster, Vice President and Secretary;Kandace Miller, Treasurer; Connie Schrock, Corresponding Secretary;and Brian Hollenbeck, Faculty SponsorDuring the 2015-2016 school year, KME members hosted social events,did community service, and went to two conventions. Two social eventsthat were hosted by KME was a Cosmic bowling night and a dinner andmovie night. We also participated in the Math Department Picnics. A funactivity that we did was going to the Linda Hall Library to look at historicmath books. On this trip we were also able to watch the Royals play inthe World Series. Members of KME also volunteered at Family Day atEmporia State as well as Family Math Night at Emporia Middle School.A group of members of KME traveled to San Francisco this year for theannual NCTM meeting. Another group of members traveled to Nebraskafor the regional KME convention.New Initiates – Ashlea Chapman, Rachel Eck, Cortez Gray, Glynnis Jackson, Amanda Led-better, Julianna Luton, Thomas Mahoney, Kandace Miller, Lotanna Nweke, Nkem Nwogu,Jesus Pineda-Rodriquez, Ty Reasnor, Ryan Sawyer, Toby Smith, Darwin Sweetman, and

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Tara Thackert.KS Delta – Washburn UniversityChapter President – Branden Childers; 20 Current Members; 8 New mem-bersOther Fall 2015 Officers: Katelynn Robinson, Vice President and Sec-retary; Jonathan Tyler, Treasurer; and Kevin Charlwood, CorrespondingSecretary and Faculty SponsorWe met three times over lunch this fall with our math club, Club Mathe-matica, and had speakers on two occasions. One speaker was from Wash-burn’s School of Business, who talked on “alphas” and some regressionanalysis of 30-day moving averages in the stock market. Our new actuar-ial science hire, Dr. Jason Shaw, spoke on the mathematics behind severalcard tricks.New Initiates – Taylor Balsmeier, Dylan Flohrschutz, Kendall Golder, Kevin Mosier, AlexRottinghaus, Katelyn Skillingstad, Kent Van De Mark, and Jason Shaw.KS Epsilon – Fort Hays State UniversityCorresponding Secretary – Jeffrey Sadler; 5 New MembersNew Initiates – Kellen Griffin, Sarbori Mitra, Will Pingsterhaus, Earl Watkins, and ShanZhong.MA Alpha – Assumption CollegeCorresponding Secretary – Dr. Robert Fry; 82 New MembersNew Initiates – Cassandra A. Algar, Timothy M. Bates, Alicia M. Batista, Jennifer M.Benassi, Marisa C. Berti, Shaun M. Bradley, Marissa L. Bylsma, Kaitlyn M. Cardey, Tim-othy M. Carroll, Gina M. Casadonte, Alexander D. Casey, Kathleen N. Cetin, Kara V.Coyne, Michael C. Daly, Nicholas I. DiAntonio, Kristin M. Donahue, Thanas Dudo, Ja-son R. Duke, Meghan T. Dwyer, Carly M. Eckles, Veronica M. Eramo, Jennifer L. Faenza,Robert D. Flynn, Megan F. Folan, Melanie B. Freitas, Andrea K. Gagnon, Lauren A. Gi-acomoni, Tiffani M. Grillo, Michelle A. Hemeon, Kaitlin G. Henry, William J. Jellesma,Kyle S. Johnson, Katie A. Kennedy, Ryan E. Kitlinski, Catherine A. Kooyomjian, KerianneC. Lamontagne, Christine E. Lesieur, Ryan John Leverone, Megan E. Libbey, Cortney M.Lima, Bethany A. Lloyd, Samantha A. Lohnes, Kathryn E. Luby, Kevon A. Lumsden, Jus-tine R. MacKinnon, Sarah V. Massiwer, Katherine T. McClafferty, Ethel E. McGinn, MaryT. McGunnigal, Samantha E. Minieri, Kaylee A. Miodonka, Paul V. Morse, Elizabeth L.Murdoch, Bernard Kambale Musondoli A.A., Daniel M. O’Brien, Ashley L. O’Donoghue,Zachary R. Okolowitcz, Meghan M. Olsen, Catherine Porter, Shannon M. Ray, ShannonM. Rice, Kaitlyn E. Riley, Colleen Ritzer, Lea A. Rossi, Lia E. Samra, Timothy A. Savoy,Annie M. Schneider, Lindsay P. Schoen, Korleen A. Sheridan, Michael J. Smith, Natalie R.Snow, Nichole K. Spilios, Lucas J. Spina, Brittany E. Stewart, Jeffrey C. Swan, KimberlySysopha, Theresa A. Taylor, Stephanie R. Twiss, Evan Anthony Villanova, Kara R. Vitale,

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Patrick F. Wells, and Michael N. Weselcouch.MA Beta – Stonehill CollegeCorresponding Secretary – Timothy Woodcock; 12 New MembersNew Initiates – Christina Barbas, Daniel Besser, Michael Carr, Alexis Johnson, Jane HyoJin Lee, Christopher McKay, Danielle Misiaszek, Jenna Rapoza, Rachel Ricciuti, ChristinaSzczesny, Ashlee Teceno, and Elizabeth Vetter.MD Alpha – Notre Dame of Maryland UniversityCorresponding Secretary – Margaret Sullivan; 9 New MembersNew Initiates – Sarah Ahmad, Kaylynn Barber, Katlyn Connor, Kristin Kneller, LoreenGwion, Margaret Pedersen, Stephanie Roche, Diana Sagastume, and Kezia Sowah.MD Beta – McDaniel CollegeCorresponding Secretary – Spencer Hamblen; 4 New MembersNew Initiates – Cole Cooper, Kaitlin Robinson, Blake Schildhauer, and Christina Wrob-lewski.MD Delta – Frostburg State UniversityChapter President – Dustin Ullery; 33 Current Members; 9 New MembersOther Fall 2015 Officers: Morgan Allman, Vice President; Amanda Mona-han, Secretary; Tyler Ram, Treasurer; Mark Hughes, Corresponding Sec-retary and Faculty Sponsor; and Frank Barnet and Justin Dunmyre, Fac-ulty SponsorsThe Maryland Delta Chapter had its first meeting in September featuringpizza and some interesting math videos. Our October meeting was de-voted to planning a coffee and bake sale fundraiser and the chapter’s par-ticipation in the university’s annual Majors Fair. Our final meeting of thesemester was held the first week of December and featured a lecture byfaculty sponsor Dr. Frank Barnet on the 2017 solar eclipse which will bevisible in America.New Initiates – Allen Benton III, Valerie Ehimhen, Caleb Friend, Rebecca Lee, Amie Lette,Emma Seibert, Keith Stahl, Kevin Vinciguerra, and James West.MD Epsilon – Stevenson UniversityCorresponding Secretary – Dr. Benjamin Wilson; 12 New MembersNew Initiates – Katelyn Abbott, Lindsay Beyer, Sarah Blanset, Nicholas Cassera, RobertChen, Anna Foote, Clayton Foxwell, Bryan Gieselman, Jeremy Kline, Sarah Modzelewski,Lauren Rose, and Benjamin Wilson.MI Alpha - Albion CollegeCorresponding Secretary – Mark Bollman; 4 New MembersNew Initiates – Stefan Blachut, Erik Davis, Angela Morrison, and Shuqi Zhou.MI Delta – Hillsdale CollegeChapter President – Michael Tripepi; 22 Current Members; 31 New Mem-bersOther Fall 2015 Officers: Sarah Jane Onken, Vice President; David Peters,

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Secretary; Linnet Mbogo, Treasurer; and David Gaebler, CorrespondingSecretary and Faculty SponsorThe Michigan Delta chapter of KME welcomed an entirely new slate ofofficers in Fall 2015, as all four previous officers were graduating seniors.The new leadership planned and executed a Gathering for Gardner-themedsocial event in November with ice cream, talks, and puzzles, which drewabout 40-45 students from around campus. We also had 12 new students(not included in the above count of 22 active members) accept the invita-tion to join, and pay their dues; they are set to be inducted on Pi Day, alongwith any new recruits from the spring semester.New Initiates – Emily Albert, Hannah Andrews, Noah Alan Bader, Corianna Baier, Kate-lyn Bercaw, Lydia Blondin, Ryan Bushling, Noah Diekemper, David Gaebler, James G.Inwood, Emily Kendro, Eric Larose, Linnet Wambui Mbogo, Nathanael Meadowcroft,Jonathon Paul Misiewicz, Stephen Nus, David Peters, Joshua Ramette, Lindsey Redfern,David Schwartzman, John B. Shannon, Addison Stumpf, Andrew Swanson, Eva Tang (Xi-aoqi), Elizabeth Thistleton, Savannah Tibbetts, Michael Tripepi, Paul Douglas Wendt, EricWert, M. Evan Willis, and Tanner Orion Wright.MI Epsilon – Kettering UniversityCorresponding Secretary – Boyan Dimirov; 35 Current MembersOther Fall 2015 Officers: Ada Cheng and Ruben Hayrapetyan, FacultySponsorsI start with several sad news for events that happened this year. Threemore faculty KME members passed away in short time. We lost our (al-ready retired colleague and KME member) professor Robert (Bob) Brown(my dear personal friend and mentor) in January 21, 2016 at age of 81.Robert (Bob) Brown started teaching at GMI in 1955. Prior to joiningthe Mathematics Faculty, Bob served during World War II on a cruiser inthe Pacific; after leaving the military, he worked at the FBI crime lab inWashington, DC. Bob, as all who knew him will recall, was a gentleman;always well dressed - I doubt he ever taught a class without a sports coatand tie; courteous to students and colleagues when courtesy was appro-priate; and always considerate. Bob enjoyed Detroit-Tigers baseball, finedining, and relaxing with a perfect Rob Roy cocktail (a Rob Roy consistsof scotch and vermouth; equal parts sweet and dry vermouth produce theperfect Rob Roy). Robert Brown retired in 1995. After his retirement (Itook his position as a tenured math faculty) he traveled a lot. Every timeafter a travel Bob used to come at my home to show pictures and shareimpressions from his travel. It was a dear precious time my family hadwith him. It is my duty to say more about one of the best known pro-fessors and KME member, Professor Reginald (Reg) Bell, rememberedfor his heart, teaching, and commitment. Reg died on Tuesday, July 21,

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2015. Longtime Kettering chemistry Professor Reg Bell will forever beremembered for his inspiration, his love of the university and the com-munity and the impact he made. Bell, who started his teaching career in1963 at Flint’s GMI, which became Kettering University (1999), alwaystook time to get to know his students and was known by many in the Flintcommunity. “The university will never be the same again. He’s an ab-solute fixture,” said Tyler Finnegan, a 2009 Kettering graduate. “He waslike family.” Our President, Dr. Robert McMahan said he - and othersaround the community - were heartbroken by the news. Bell, a native ofNorth Carolina, was one of a kind and made a huge impact on everyonehe knew. “When you choose to go into education one of the reasons thatyou do is your hope that somehow you’ll make a difference in somebody’slife. That you’ll have an impact,” McMahan said. “And Reg did that forthousands of people. Thousands. I have met so many people whose ca-reers and whose professional and personal success they attributed to Reg.I’ve never met anybody in education who is so singularly devoted to stu-dents and to teaching.” According to Flint Journal files, it’s safe to sayBell was in his late 70s, but it was a running joke around the universitythat Bell never told people how old he was. In 2013, the Kettering com-munity celebrated his 200th consecutive teaching term, without taking asingle term off. Since that time, Regs unbroken teaching run continuedup until this very last term. Reg used to say “this is my favored student,teacher, friend, associate, etc.” Now this saying is common in remem-brance of him. He left millions of donations for Kettering, and a Chemistrylab furnished, equipped and named after Reg Bell. We, of the Ketteringcommunity, loved Reg Bell and save best memory of his bright personal-ity, friendship, restless work, Several initiatives happen related to the her-itage of Reg Bell. More on the sites https://my.kettering.edu/remembering-professor-reg-bell and http://www.mlive.com/news/flint/index.ssf/2015/07/longtime_kettering_professor_r.html

We experienced more losses. Dr. Philip Henry Richard Jr. served at our In-stitution from 1984 (then General Motors Institute) until he retired in 2012(already Kettering University, due to his severe illness). In 2003 he re-ceived the Outstanding Teacher of The Year Award at Kettering. He passedaway on November 28, 2015, at the age of 62. He was a bright, honest per-son, and worked even after he lost a leg after amputation, without losing hissense of humor and enthusiasm of teaching. Deep bow before him and tohis memory. I loved Phil all my tenure in his institution. Some more aboutPhil on http://www.legacy.com/obituaries/lsj/obituary.

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aspx?pid=176957086

But, lets talk about positive events: Kettering mathematical life contin-ues despite the problems with these dear personal losses, and within theKME chapter. This year we had a new recipient of the Applied Mathe-matics Award at Kettering. Lili Tang ’15 was recognized with the AppliedMathematics Student Research Award for her thesis evaluating crime datain Flint, Michigan. Tang is the first Kettering University undergraduateto receive this award since Matthew Causley in 2003. Causley is now aprofessor in the Department of Mathematics at Kettering. Lili Tang thesiswork “Analysis of crime statistics” earns math graduate prestigious the-sis award. One of her findings: “There are significant relationships be-tween crime and unemployment rate.” Tang examined crime data obtainedfrom the Federal Bureau of Investigation (FBI) from 1950 to 2012 andcorrelated it with population and unemployment trends in the area. An-nual reports were only available online starting in 1995 so Tang requestedscanned copies dating back to 1950 from the Boston Public Library. “Iran tests on them to find the relationships. There are significant relation-ships between crime and unemployment rate,” Tang said. However, Tangnotes that the peaks and valleys in crime in Flint are consistent with na-tional trends during the same time periods. Tang presented her researchat the International Statistics Conference on campus in June 2014 and wasawarded $500 for winning the student research award in October 2015. Dr.Boyan Dimitrov and Dr. Leszek Gawarecki served on her thesis commit-tee. Tang’s undergraduate thesis is unique in the math department becauseit’s academic. Most of her peers opt for a co-op thesis that contributes di-rectly to their employers. Tang completed her co-op at Albar Industriesin Lapeer, Michigan, but chose to pursue an academic thesis in order toheighten her understanding of statistical tools and better comprehend thepatterns in her surrounding community. “I wanted to do a research thesis,Tang said. For me, it was very interesting to first discover this data and thendetermine trends and relationships over a long period of time.” More abouthis event - please look at: https://my.kettering.edu/news/analysis-crime-statistics-earns-math-graduate-prestigious-thesis-award. We continue running our Mathe-matics Olympiads. The last one was held on Saturday, Nov. 21, 2015 atKettering University Campus in Flint, MI and Kettering Fairmont HighSchool in Kettering, OH . The winners were: First Place: Ajay Arorafrom Novi, Michigan. Ajay is a Freshman and attends Novi High School.Ajay’s Math teachers are Catherine Brach and Kristina Stefanou. Sec-ond Place: Peter Zhu from Mason, Ohio. Peter is a Sophomore and at-

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tends William Mason High School. Peter’s Math teacher is Mrs. Ev-erette. Third Place: Vishal Nayak from Canton, Michigan. Vishal is aFreshman and attends Canton High School. Vishal’s Math teacher is Ms.Aiello. Fourth - Seventh Place: (In alphabetical order) William Garlandfrom Grand Blanc, Michigan. William is a Senior and attends Grand BlancHigh School. William’s Math teacher is Sarah Johnson. Lily Ireton fromBrighton, Michigan. Lily is a Senior and attends Brighton High School.Lily’s Math teacher is Mr. Thumser. Laura Hohnstadt from Clarkston,Michigan. Laura is a Senior and attends Lutheran High School Northwest.Laura’s Math teacher is Mr. Karl Weber. James Zhu from Mason, Ohio.James is a Senior and attends William Mason High School. James’s Mathteacher is Mrs. Everette.

We are proud of the achievements of our all of the US High school stu-dents. This Olympiad is rated SECOND in The Nation math competitionevent. Our mathematics Olympiads run regularly, and enjoy lots of popu-larity. More about it - on the site https://paws.kettering.edu/~acheng/Olympiad/. Next Olympiad will be held the coming lateFall 2016. The Michigan Epsilon chapter of KME at our Institution passesthrough some crisis. I definitely miss those traditional twice a term mathmovie meetings with pizza and discussions. Up to certain extend our MathDepartment (by the initiatives of Dr. Leszek Gawarecki, the Head) orga-nizes a freshmen math students welcome meetings with all the faculty, andanother Math advisory meetings at the end of each term(something likea fare well meeting) for all math majors and the faculty. Our co-op stu-dents have one term on campus, and one work term at their co-op jobs.Every term we have different alternating group of math students, and thiscreates some scheduling problems. Leszek virtuously resolves these prob-lems with his restless work as mathematician and administrator.MO Alpha – Missouri State UniversityChapter President – Mena Whalen; 38 Current Members; 25 New Mem-bersOther Fall 2015 Officers: Meagan Leppien, Vice President; Ashley Kingston,Secretary; Paige Buchmueller, Treasurer; and Jorge Rebaza, Correspond-ing Secretary and Faculty Sponsor1. As in every semester, we had three seminars:

– Seminar 1: Wednesday September 23rd. Dr. Steven Senger, facultymember in the Mathematics Department at MSU, presented the talk“Kirkman’s School Girl Problem.” Pizza and soda were served.

– Seminar 2: Monday October 19th. Dr. Ken Brown, Head of the De-partment of Economics at MSU, presented the talk “Thinking Out-

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side the Major: Opportunities for Mathematicians in Economics.”Pizza and soda were served. At this event, we also initiated 11 newKME members.

– Seminar 3: Tuesday November 10th.Three students from the SeniorSeminar class (MTH 497) presented their papers: “Mathematics be-hind SET game,” by Meagan Leppien, “Understanding Game The-ory” by Mena Whalen, and “Prime Number Conjectures,” by JohnSutton. Pizza and soda were served.

2. As in every fall semester, we organized a picnic on Wednesday Septem-ber 9th, starting at 5PM at Phelps Grove Park. As usual, we had a greatturnout of students, faculty, and their families!

3. We also had an end-of-semester party on Thursday December 3rd, thelast day of classes. We had lots of games music, food, drinks, anddesserts. The Secret Santa gift exchange was a great success!

New Initiates – Shannon Beardslee, Abigail Best, Thomas Callaway, Symantha Camp-bell, Adolfo Cancino, John Carter, Daytona Davis, Nicholas Delamora, Maddison Dobyns,Jacquelyn Drury, Christopher Eakins, Cassandra Fehlig, Sarah Gericke, Jonah Henry, AubreyHormel, Sara Jones, Ryan Justice, Stephanie Markes, Bethany Morgan, Travis Pennewell,Ian Peters, Cassandra Taber, Tara Walton, Yu Wang, and Alison Wiedl.MO Beta – University of Central MissouriChapter President – Amos Bailey; 26 Current Members; 12 New MembersOther Fall 2015 Officers: Madison Ultican, Vice President; ChristinaDuerr, Secretary; Nicholas Purcell, Treasurer; Rhonda McKee, Corre-sponding Secretary; and Steve Shattuck and Nicholas Baeth, Faculty Spon-sorsThe Missouri Beta Chapter held monthly meetings during the fall semester.Programs included students talking about summer internships, creating thePlatonic solids using Zome Tools and a geometry video. We also held abook sale to raise funds for activities and travel to the regional convention.New Initiates – Daniel Robert Akin, Madi Bayne, Ashley Beard, Courtney Cairns, JoannaGossell, Justin Istas, Jacob Koelling, Thomas Kotecki, Tyler Mattoon, Blake AllenSchollmeyer, Keaton Smith, and Lauiva’a C. Tavai.MO Eta – Truman State UniversityCorresponding Secretary – David Garth; 10 New MembersNew Initiates – Luke Arrigoni, Erica Van Cleave, Elizabeth Hale, Jennie Huynh, JosephineLampe, Trang Le, Chad Robertson, Margaret Tauser, and Lacey Woods.MO Theta – Evangel UniversityChapter President – Kevin Grimes II; 13 Current Members; 10 New Mem-

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bersOther Fall 2014 Officers: Kaitlyn Hong, Vice President; and Don Tosh,Corresponding Secretary and Faculty SponsorMeetings were held monthly. In December we held an Ice Cream Socialat the home of Don Tosh.New Initiates – Brittany Annas, Marc Blankenship, Katie Cook, Kellie Dennis, Maria Don-nay, Megan Evans, Ryan Frye, Brianna Maybee, Haley Osborne, and Catherine Ross.MO Xi – William Woods UniversityCorresponding Secretary – Chris Schneider; 2 New MembersNew Initiates – Kiersten Lockman and Anne Wehner.MS Alpha - Mississippi University for WomenChapter President – Audra Polk; 10 Current Members; 2 New MembersOther Fall 2015 Officers: Ciara Peoples, Vice President; Mandy Elam,Secretary; Audra Polk, Treasurer; and Joshua Hanes, Corresponding Sec-retary and Faculty SponsorIn the fall semester, we gathered supplies and put together boxes for Oper-ation Christmas Child.New Initiates – Hayley Hampton and Danielle Pitre.MS Epsilon – Delta State UniversityCorresponding Secretary – Paula Norris; 6 New MembersNew Initiates - Anna Kate Boden, Jennifer Duke, Christy Hart, Rebecca Hudson, HopeRainey, and Sydney Claire Sullivant.NC Epsilon – North Carolina Wesleyan CollegeCorresponding Secretary – Bill Yankosky; 9 New MembersNew Initiates - Michael Bhujel, Carolynn Davern, Lucia D. Davids, Emalyn M. Jessup,Bobbie Jean Legg, Monica Salazar Reyes, Micheal Smith, Bikash Thapa, and Katie Tyson.NE Beta – University of Nebraska-KearneyCorresponding Secretary – Dr. Katherine Kime; 7 New MembersNew Initiates – New Initiates - Poe Dee, Quinn Feikert, Keathan Fertig, Alexandria Lin-nerson, Madison Mickey, Candy Smith, and Shelby Study.NE Delta – Nebraska Wesleyan UniversityChapter President – Connor Bohlken; 7 Current Members; 7 New Mem-bersOther Fall 2015 Officers: Spencer Randazzo, Vice President; WilliamReimer, Secretary/Treasurer; and Kristin Pfabe, Corresponding Secretaryand Faculty SponsorIn September, we hosted an event on cryptography that included a scav-enger hunt with secret codes. In October, there was a panel discussionon careers in mathematics that featured a lawyer, actuary, middle schoolteacher and financial analyst as panelists. We concluded activities with a

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holiday party in December.New Initiates – Andrew Chleborad, Caleb Craven, Allison Kalal, Joel Maxwell, MadisonMontgomery, Jaret Polivka, and Karissa Vandenberg.NH Alpha – Keene State CollegeCorresponding Secretary – Vincent J. Ferlini; 9 New MembersNew Initiates – Leeann Cipriani, Melina Comstock, Ryan Hayward, Ann-Catherine Keat-ing, Maureen Moran, Shannon Nee, Christine Nigzus, Amanda Petrow, and Natalie Wat-son.NY Iota – Wagner CollegeCorresponding Secretary – Marisa Scarpa; 17 New MembersNew Initiates – Christina Alessio, Lukshmi Asirwatham, Nicole Bianco, Lejla Bolevic,Rabije Cekovic, Tyler Cropley, Kelsey Gwynne, Kelsey Hopland, Ashley Michaela Kraus,John Lynn, Nicole Marchese, Sydney McNutt, David Riccardi, Michael Sayad, JenniferShamah, Amanda Taylor, and Lucille Elise Whisler.NY Mu – St. Thomas Aquinas CollegeCorresponding Secretary – Heather A. Rave; 11 New MembersNew Initiates – Kelsey Barnes, Michael Berezin, Phillip John Demetrops, Stefan Eapen,Mark Haber, Marissa Johnson, Nyenyeri Anna Magdalena Kanefu, Carolyn Kopf, AlexaMunderville, Paul Francis Owens, and Katari Salvesen.NY Omicron – St. Joseph’s CollegeChapter President – Matthew R. Stitt; 15 Current Members; 14 New Mem-bersOther Fall 2015 Officers: Sara E. Schmidt, Vice President; Nicole A.Danisi, Secretary; Giovanni Mayo, Treasurer; Elana Reiser, Correspond-ing Secretary; and Donna Pirich, Faculty SponsorWe held a fundraiser to buy Christmas gifts for a local charity. Membersalso volunteered to tutor local high school students at our math clinic.New Initiates – Eric A. Brodzinski, Melissa De Jesus, Matthew G. Dioguardo, MichelleD. Lorentzen, Kayla A. MacFarlane, Christine Malinowski, Angelo J. Mauro, Kimberly J.Mazza, Michael S. Mirrione, Victoria Russell, Angela M. Vetere, Travis S. Villez, AliciaM. Waldron, and Ariana R. Wanderlingh.NY Pi – Mount Saint Mary CollegeCorresponding Secretary – Lee Fothergill; 10 New MembersNew Initiates – Kristen R. Berish, Anastasia Frank, Joseph Ianniello, Alexandra L. Magliato,Melissa Louise Medici, Elizabeth Pozzulo, Hope Schaumburg, Ryan Seifts, Shannon Som-mer, and Kiana Sullivan.NY Rho - Molloy CollegeCorresponding Secretary – Manyiu Tse; 13 New MembersNew Initiates – Jennifer Bonziglia, Chelsea Brandimarte, Alexa Carvelli, Melissa Comis,Marissa Croce, John Cronin, Andrew Dacunto, William Hudson, Ashley Keon, Timothy

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Klotsche, Victoria Palazzo, Denise Redfern, and Joanna Verde.OH Gamma – Baldwin Wallace UniversityCorresponding Secretary – David Calvis; 23 New MembersNew Initiates – Jennifer Burdick, Natalie Castrigano, C J Colaric, Stephanie Egler, JeremyFoust, Clay Gillman, Casey Greene, Corrinne Horvath, Callie Jakuszeit, Jesse Kovach,Justin Malave, Hannah Montgomery, Yousef Mustafa, Grace Nocero, Stephen Osborn,Zachary Ricker, Brandon Shipley, Andrew Sierawski, Braden Terry, William Vaccariello,Jonah Vicente, Griffin Williams, and Sandra Zlojutro.OH Zeta - Muskingum UniversityCorresponding Secretary – Richard Daquila; 5 New MembersNew Initiates – Robert Allbright, Cassidy Cochrum, Alexander Meyers, Zachary Snively,and Cara Uetrecht.OH Eta – Ohio Northern UniversityChapter President – Michelle Haver; 16 Current Members; 8 New Mem-bersOther Fall 2015 Officers: Michael Potter, Vice President; Kayla Hummell,Vice President; Tyler Bernardy, Treasurer; Dr. Ryan Rahrig, Correspond-ing Secretary and Faculty SponsorEvents: Our chapter participated in a “Fill the Fireplace” event. Fundswere raised and used to purchase gifts for local families in need during theChristmas season.New Initiates – Zachary R. Goodchild, Nicole Graf, Jessica Anne Lewe, Olivia Paganelli,Gia Saturday, Ian Simpson, Andrew Tompkins, and David P. Zirkle.OH Zeta – Muskingum UniversityCorresponding Secretary – Richard Daquila; 5 New MembersNew Initiates – Robert Allbright, Cassidy Cochrum, Alexander Meyers, Zachary Snively,and Cara Uetrecht.OH Theta – Capital UniversityChapter President – Abigail Neininger; 12 New MembersOther Fall 2015 Officers: Julia Kunkel, Vice President; Jamie Ashworth,Secretary; Oscar O‘Flaherty, Treasurer; Paula Federico, CorrespondingSecretary; and Jonathan Stadler, Faculty SponsorThe Ohio Theta Chapter of Kappa Mu Epsilon at Capital University wasinstalled on Friday, April 24, 2015. At this ceremony three faculty andthirteen students were initiated as new members. Only four student mem-bers were at Capital during the fall semester and they joined forces withthe MAA student chapter to plan some activities for Spring 2016. Thechapter is looking forward to adding new members in the Spring semesterand is planning the induction ceremony on April 1, 2016.New Initiates – Rachel Bender, Cody Circle, Sarah Fryman, Victoria Garcia, Jack Gedeon,Nicolas Hernandez, Noah Holzapfel, Jacob Kemery, Kevin Siebert, Beau Streety, Anne

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Wesley, and Jennie White.PA Epsilon – Kutztown UniversityCorresponding Secretary – Dr. Padraig McLoughlin; 12 New MembersNew Initiates – Edward Andrescavage, Nathaniel Benjamin, William Harwi, StephanieKlein, Hallie Langley, Laura Myers, Charles Nace, Felipe Porcella, Curtis Reigle, JustineRossi, Danielle Sienko, and Duc Tran.PA Theta – Susquehanna UniversityCorresponding Secretary – Kenneth Brakke; 13 New MembersNew Initiates – Yihe Chen, Abby Conway, Diane Isaacs, Amy Kaschak, John Matthews,Yilan Miao, Torin Nelson-Maggiani, Heather Porter, Anthony Rice, Theodore Slechta, An-ton Soloviev, Andrew Steely, and Aviel Stein.PA Kappa – Holy Family UniversityChapter President – Dominic McAllister; 6 Current Members; 5 NewMembersOther Fall 2015 Officer: Sister Marcella Wallowicz, Corresponding Sec-retary and Faculty SponsorThe PA Kappa Chapter collaborates with the Math Club on activities. OnSunday, November 15, 2015 a high school math competition was held withapproximately 35 participants from local schools. The one hour writtencontest includes problems from Algebra I to Trig/Pre-Calculus. A familyGame Night is planned for February, 2016.New Initiates – Melissa Goodwill, Tara Kelly, Jean Claude Petit Homme, Walter Webb,and Anna Zawistowska.PA Lambda – Bloomsburg University of PennsylvaniaCorresponding Secretary – Eric B. Kahn; 11 New MembersNew Initiates – Ember Baker, Tyler Behrent, Ethan Farr, Alec Freedman, Lauren Kerstetter,Ian Lamey, Amanda Leamon, Harrison Ludewig, Ariana Mychajliw, Joshua Pfluger, andShana Wagner.PA Mu – Saint Francis UniversityChapter President – Casey Gallaher; 39 Current Members; 19 New Mem-bersOther Fall 2015 Officers: Lydia Mignogna, Vice President; William Shee,Secretary; Jay Pillot, Treasurer; Josh Vinglish, Historian; Hannah Patton,Webmaster; Pete Skoner, Corresponding Secretary; and Brendon LaBuz,Faculty SponsorNew Initiates – Bartholomew Blair, Sabrina Blake, Hannah Boyd, Michael Brady, KyleDumouchelle, Elizabeth Dyer, Alec Dylan Foo-Kune, Nicholas Frank, Alyiah Hilton, Kay-lyn Hines, Mary Hinz, Rebekah Krupa, David Madl, Brandyn Pryce, Nicholas Pyo, Jessica

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Reilly, Austin Renz, Staci Shoemaker, and Zachary Sterner.PA Nu – Ursinus CollegeCorresponding Secretary – Nicholas Scoville; 8 New MembersNew Initiates – Berett Babrich, Christopher Husson, Jie Lin, Melissa Meeker, Matan Peleg,Julia Senkevich, Olivia Tierney, and Ashlyn Welch.PA Pi – Slippery Rock UniversityCorresponding Secretary – Elise Grabner; 9 New MembersNew Initiates – Nicholas G. Cercone, Amanda Ciarkowski, Brittany Joy Drew, DanielleMarie Faggioli, Rebecca Helen Fox, Kalene Ireland, Alessandra Mitchell, Ellis Neilly, andMiranda Ryan.PA Tau – DeSales UniversityChapter President – Christine Holmes; 9 Current Members; 9 New Mem-bersOther Fall 2015 Officers: Zachary Moser, Vice President; Julie A. Farmer,Secretary/Treasurer; and Bro. Daniel P. Wisniewski,O.S.F.S., Correspond-ing Secretary and Faculty SponsorNew Initiates –Laura Burns, Morgan J. Coleman, Father John I. Extejt, O.S.F.S., MatthewA. Jesiolowski, Daniel L. Lamson, Timothy A. Rath, Scott M. Springer, Ryan C. Vignogna,and Henry J. Wickus.RI Beta – Bryant UniversityChapter President – Stephen Lamontagne; 25 Current MembersOther Fall 2015 Officers: Allison Orr, Vice President; Krystin Sinclair,Treasurer; Sarah French, Secretary; John Quinn, Corresponding Secre-tary; and Alan Olinsky, Faculty SponsorSC Gamma - Winthrop UniversityChapter President – MaLyn Lawhorn; 12 Current Members; 12 New Mem-bersOther Fall 2015 Officers: Kristin Hinson, Vice President; Matt Farmer,Secretary; Alison Tighe, Treasurer; and Jessie Hamm, Corresponding Sec-retary and Faculty SponsorWinthrop’s chapter of Kappa Mu Epsilon will be participating in a com-munity outreach this April. The students of KME will be doing fun mathactivities with 60 local middle schoolers. These activities will be thingsthat they would not see in the classroom in order to enrich their under-standing and appreciation of mathematics.TN Alpha – Tennessee Technological UniversityCorresponding Secretary – Andrew Hetzel; 20 New MembersNew Initiates – Erin Ekart, Osama Elkelany, Nicole Gonzalez, Samuel Hines, Mary Keen,Daniel King, Mary-Elizabeth Ledford, Miranda Maples, Mason Marks, Silvio Mayolo,Elizabeth Morrisette, Catherine Murphy, Cassidy Ortman, Emily Reynolds, Rachel Robin-

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son, Alice Ta, Paul Tinker, Jeremiah West, Matthew Whitaker, and Michaela Williamson.TN Beta – East Tennessee State UniversityChapter President – James Dustin Chandler; 30 Current Members; 18New MembersOther Fall 2015 Officers: William ‘Ty‘ Frazier, Vice President; AustinPatrick, Secretary; Nathan Molder, Treasurer; and Robert Gardner, Cor-responding Secretary and Faculty SponsorThe TN Gamma chapter held a back-to-school pizza party of September17, 2015. We also sponsored a child at the annual Carl Perkins ChristmasDinner.New Initiates – Cory Ball, Carrie Elliot, Russell Harper, Katie Heidt, Miranda Hilton,Amanda Justus, Derek Kiser, David Lewis, Leanna Murdock, Thomas Robacker, BrettShields, Alex Smyth, Rebekah White, and Alyssa Williams.TN Gamma – Union UniversityChapter President – Nicole BantzOther Fall 2015 Officers: Dillon Lisk, Vice President; Rachel Brewer, Sec-retary/Treasurer; Joshua Stucky, Webmaster/Historian; Bryan Dawson,Corresponding Secretary; Matt Lunsford, Faculty SponsorThe TN Gamma chapter held a back-to-school pizza party on September17. We also sponsored a child at the annual Carl Perkins Christmas Dinner.TX Gamma – Texas Woman‘s UniversityCorresponding Secretary – Dr. Mark S. Hamner; 8 New MembersNew Initiates – Oscar Alvarez, Maria Delgado, Tracey Hahn, Camila Novoa, Amanda Pike,Dijannae Robinson, Jessie Ross, and Emily Smith.TX Iota – McMurry UniversityCorresponding Secretary – Dr. Kelly L. McCoun; 8 New MembersNew Initiates – Chelsi Boswell, Alyssa Fields, Taylor Freehauf, Kent Grimes, Casey Hurt,Marcus Medellin, Carissa Terrry, and Michael Von Ende-Becker.TX Mu – Schreiner UniversityCorresponding Secretary – Clint Coles; 7 New MembersNew Initiates – Tyler Jordan Amison, Hyunsuk Choi, James Dale Johnson, Daniel RaulPrimera, Lizet L. Ramirez, James Roddy, and Shaila Taylor Wolter.VA Delta – Marymount UniversityChapter President and Secretary – Lucy Ogbole; 37 Current MembersOther Fall 2015 Officers: Bernadette Wunderley, Vice President/Treasurer;and Will Heuett, Corresponding Secretary and Faculty SponsorWI Gamma – University of Wisconsin-Eau ClaireCorresponding Secretary – Carolyn Otto; 23 New MembersNew Initiates – Joseph Ackerson, Vinnisha A N Chandrasegar, Alice Ching, Lillian Cook,Kassandra Daniels, Andrew Duxbury, Jessica Ecker, Emily Gullerud, Sara Isakson, NicoleJones, Claire Kelk, Sarah McKlveen, Dannelle Martinuea, Joseph Radlinger, Colton Robach,

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Yim Kee Shen, Meghan Smith, Darian Sowers, Scott Spear, Jordan Thill, Carissa Varick,Thyviyan Velappan, and Joseph Westenberg.WV Alpha – Bethany CollegeChapter President and Secretary – Adam C. Fletcher; 5 New MembersNew Initiates – Timothy Kobina Boafo—Adade, Jesse James Elliott, Robert Austin Mu-rano, Bethany A. Pohjala, and Alyssa Kathleen Smydo.

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Active Chapters of Kappa Mu EpsilonListed by date of installation

Chapter Location Installation DateOK Alpha Northeastern State University, Tahlequah 18 Apr 1931IA Alpha University of Northern Iowa, Cedar Falls 27 May 1931KS Alpha Pittsburg State University, Pittsburg 30 Jan 1932MO Alpha Missouri State University, Springfield 20 May 1932MS Alpha Mississippi University for Women, Columbus 30 May 1932MS Beta Mississippi State University, Mississippi State 14 Dec 1932NE Alpha Wayne State College, Wayne 17 Jan 1933KS Beta Emporia State University, Emporia 12 May 1934AL Alpha Athens State University, Athens 5 Mar 1935NM Alpha University of New Mexico, Albuquerque 28 Mar 1935IL Beta Eastern Illinois University, Charleston 11 Apr 1935AL Beta University of North Alabama, Florence 20 May 1935AL Gamma University of Montevallo, Montevallo 24 Apr 1937OH Alpha Bowling Green State University, Bowling Green 24 Apr 1937MI Alpha Albion College, Albion 29 May 1937MO Beta University of Central Missouri, Warrensburg 10 Jun 1938TX Alpha Texas Tech University, Lubbock 10 May 1940KS Gamma Benedictine College, Atchison 26 May 1940IA Beta Drake University, Des Moines 27 May 1940TN Alpha Tennessee Technological University, Cookeville 5 Jun 1941MI Beta Central Michigan University, Mount Pleasant 25 Apr 1942NJ Beta Montclair State University, Upper Montclair 21 Apr 1944IL Delta University of St. Francis, Joliet 21 May 1945KS Delta Washburn University, Topeka 29 Mar 1947MO Gamma William Jewell College, Liberty 7 May 1947TX Gamma Texas Woman’s University, Denton 7 May 1947WI Alpha Mount Mary College, Milwaukee 11 May 1947OH Gamma Baldwin-Wallace College, Berea 6 Jun 1947CO Alpha Colorado State University, Fort Collins 16 May 1948MO Epsilon Central Methodist College, Fayette 18 May 1949MS Gamma University of Southern Mississippi, Hattiesburg 21 May 1949IN Alpha Manchester College, North Manchester 16 May 1950PA Alpha Westminster College, New Wilmington 17 May 1950IN Beta Butler University, Indianapolis 16 May 1952KS Epsilon Fort Hays State University, Hays 6 Dec 1952PA Beta LaSalle University, Philadelphia 19 May 1953VA Alpha Virginia State University, Petersburg 29 Jan 1955IN Gamma Anderson University, Anderson 5 Apr 1957CA Gamma California Polytechnic State University, San Luis Obispo 23 May 1958TN Beta East Tennessee State University, Johnson City 22 May 1959PA Gamma Waynesburg College, Waynesburg 23 May 1959VA Beta Radford University, Radford 12 Nov 1959NE Beta University of Nebraska—Kearney, Kearney 11 Dec 1959IN Delta University of Evansville, Evansville 27 May 1960

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OH Epsilon Marietta College, Marietta 29 Oct 1960MO Zeta University of Missouri—Rolla, Rolla 19 May 1961NE Gamma Chadron State College, Chadron 19 May 1962MD Alpha College of Notre Dame of Maryland, Baltimore 22 May 1963CA Delta California State Polytechnic University, Pomona 5 Nov 1964PA Delta Marywood University, Scranton 8 Nov 1964PA Epsilon Kutztown University of Pennsylvania, Kutztown 3 Apr 1965AL Epsilon Huntingdon College, Montgomery 15 Apr 1965PA Zeta Indiana University of Pennsylvania, Indiana 6 May 1965AR Alpha Arkansas State University, Jonesboro 21 May 1965TN Gamma Union University, Jackson 24 May 1965WI Beta University of Wisconsin—River Falls, River Falls 25 May 1965IA Gamma Morningside College, Sioux City 25 May 1965MD Beta McDaniel College, Westminster 30 May 1965IL Zeta Dominican University, River Forest 26 Feb 1967SC Beta South Carolina State College, Orangeburg 6 May 1967PA Eta Grove City College, Grove City 13 May 1967NY Eta Niagara University, Niagara University 18 May 1968MA Alpha Assumption College, Worcester 19 Nov 1968MO Eta Truman State University, Kirksville 7 Dec 1968IL Eta Western Illinois University, Macomb 9 May 1969OH Zeta Muskingum College, New Concord 17 May 1969PA Theta Susquehanna University, Selinsgrove 26 May 1969PA Iota Shippensburg University of Pennsylvania, Shippensburg 1 Nov 1969MS Delta William Carey College, Hattiesburg 17 Dec 1970MO Theta Evangel University, Springfield 12 Jan 1971PA Kappa Holy Family College, Philadelphia 23 Jan 1971CO Beta Colorado School of Mines, Golden 4 Mar 1971KY Alpha Eastern Kentucky University, Richmond 27 Mar 1971TN Delta Carson-Newman College, Jefferson City 15 May 1971NY Iota Wagner College, Staten Island 19 May 1971SC Gamma Winthrop University, Rock Hill 3 Nov 1972IA Delta Wartburg College, Waverly 6 Apr 1973PA Lambda Bloomsburg University of Pennsylvania, Bloomsburg 17 Oct 1973OK Gamma Southwestern Oklahoma State University, Weatherford 1 May 1973NY Kappa Pace University, New York 24 Apr 1974TX Eta Hardin-Simmons University, Abilene 3 May 1975MO Iota Missouri Southern State University, Joplin 8 May 1975GA Alpha State University of West Georgia, Carrollton 21 May 1975WV Alpha Bethany College, Bethany 21 May 1975FL Beta Florida Southern College, Lakeland 31 Oct 1976WI Gamma University of Wisconsin—Eau Claire, Eau Claire 4 Feb 1978MD Delta Frostburg State University, Frostburg 17 Sep 1978IL Theta Benedictine University, Lisle 18 May 1979PA Mu St. Francis University, Loretto 14 Sep 1979AL Zeta Birmingham-Southern College, Birmingham 18 Feb 1981CT Beta Eastern Connecticut State University, Willimantic 2 May 1981NY Lambda C.W. Post Campus of Long Island University, Brookville 2 May 1983MO Kappa Drury University, Springfield 30 Nov 1984CO Gamma Fort Lewis College, Durango 29 Mar 1985

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NE Delta Nebraska Wesleyan University, Lincoln 18 Apr 1986TX Iota McMurry University, Abilene 25 Apr 1987PA Nu Ursinus College, Collegeville 28 Apr 1987VA Gamma Liberty University, Lynchburg 30 Apr 1987NY Mu St. Thomas Aquinas College, Sparkill 14 May 1987OH Eta Ohio Northern University, Ada 15 Dec 1987OK Delta Oral Roberts University, Tulsa 10 Apr 1990CO Delta Mesa State College, Grand Junction 27 Apr 1990PA Xi Cedar Crest College, Allentown 30 Oct 1990MO Lambda Missouri Western State College, St. Joseph 10 Feb 1991TX Kappa University of Mary Hardin-Baylor, Belton 21 Feb 1991SC Delta Erskine College, Due West 28 Apr 1991SD Alpha Northern State University, Aberdeen 3 May 1992NY Nu Hartwick College, Oneonta 14 May 1992NH Alpha Keene State College, Keene 16 Feb 1993LA Gamma Northwestern State University, Natchitoches 24 Mar 1993KY Beta Cumberland College, Williamsburg 3 May 1993MS Epsilon Delta State University, Cleveland 19 Nov 1994PA Omicron University of Pittsburgh at Johnstown, Johnstown 10 Apr 1997MI Delta Hillsdale College, Hillsdale 30 Apr 1997MI Epsilon Kettering University, Flint 28 Mar 1998KS Zeta Southwestern College, Winfield 14 Apr 1998TN Epsilon Bethel College, McKenzie 16 Apr 1998MO Mu Harris-Stowe College, St. Louis 25 Apr 1998GA Beta Georgia College and State University, Milledgeville 25 Apr 1998AL Eta University of West Alabama, Livingston 4 May 1998NY Xi Buffalo State College, Buffalo 12 May 1998NC Delta High Point University, High Point 24 Mar 1999PA Pi Slippery Rock University, Slippery Rock 19 Apr 1999TX Lambda Trinity University, San Antonio 22 Nov 1999GA Gamma Piedmont College, Demorest 7 Apr 2000LA Delta University of Louisiana, Monroe 11 Feb 2001GA Delta Berry College, Mount Berry 21 Apr 2001TX Mu Schreiner University, Kerrville 28 Apr 2001NJ Gamma Monmouth University, West Long Branch 21 Apr 2002CA Epsilon California Baptist University, Riverside 21 Apr 2003PA Rho Thiel College, Greenville 13 Feb 2004VA Delta Marymount University, Arlington 26 Mar 2004NY Omicron St. Joseph’s College, Patchogue 1 May 2004IL Iota Lewis University, Romeoville 26 Feb 2005WV Beta Wheeling Jesuit University, Wheeling 11 Mar 2005SC Epsilon Francis Marion University, Florence 18 Mar 2005PA Sigma Lycoming College, Williamsport 1 Apr 2005MO Nu Columbia College, Columbia 29 Apr 2005MD Epsilon Stevenson University, Stevenson 3 Dec 2005NJ Delta Centenary College, Hackettstown 1 Dec 2006NY Pi Mount Saint Mary College, Newburgh 20 Mar 2007OK Epsilon Oklahoma Christian University, Oklahoma City 20 Apr 2007HA Alpha Hawaii Pacific University, Waipahu 22 Oct 2007NC Epsilon North Carolina Wesleyan College, Rocky Mount 24 Mar 2008

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CA Zeta Simpson University, Redding 4 Apr 2009NY Rho Molloy College, Rockville Center 21 Apr 2009NC Zeta Catawba College, Salisbury 17 Sep 2009RI Alpha Roger Williams University, Bristol 13 Nov 2009NJ Epsilon New Jersey City University, Jersey City 22 Feb 2010NC Eta Johnson C. Smith University, Charlotte 18 Mar 2010AL Theta Jacksonville State University, Jacksonville 29 Mar 2010GA Epsilon Wesleyan College, Macon 30 Mar 2010FL Gamma Southeastern University, Lakeland 31 Mar 2010MA Beta Stonehill College, Easton 8 Apr 2011AR Beta Henderson State University, Arkadelphia 10 Oct 2011PA Tau DeSales University, Center Valley 29 Apr 2012TN Zeta Lee University, Cleveland 5 Nov 2012RI Beta Bryant University, Smithfield 3 Apr 2013SD Beta Black Hills State University, Spearfish 20 Sept 2013FL Delta Embry-Riddle Aeronautical University, Daytona Beach 22 Apr 2014IA Epsilon Central College, Pella 30 Apr 2014CA Eta Fresno Pacific University, Fresno 24 Mar 2015OH Theta Capital University, Bexley 24 Apr 2015GA Zeta Georgia Gwinnett College, Lawrenceville 28 Apr 2015MO Xi William Woods University, Fulton 17 Feb 2016IL Kappa Aurora University, Aurora 3 May 2016

Documents

Contents€¦ · Contents Kappa Mu Epsilon National Ofﬁcers 3 ... Murray Klamkin’s Duality Principle for Triangle Inequalities 10 Daniel Sitaru The Problem Corner 15