Mathematics and the Wonders of Creation by James Nickel B.A., B.Th., B.Miss., M.A. Copyright 2008-2009

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Mathematics and the Wonders of Creation

byJames Nickel

B.A., B.Th., B.Miss., M.A.

Copyright 2008-2009www.biblicalchristianworldview.net

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Creational Harmony

• Connections with the reality of Creation.– The Physics of Motion (free fall, projectile,

planetary orbits, springs, heat, etc.)– Quadratic Equations.


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Creational Harmony

• Poetry of theorems.– The internal structure of thinking.– The meter and rhyme of logic.– The elegance and beauty of proofs (Pythagorean

Theorem, the infinitude of primes, the Fundamental Theorem of Arithmetic, Algebra, and the Calculus, etc.).


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Creational Harmony• Unity in Diversity.

3.14 (from geometry to infinite series to probability).

e 2.718 (from interest compounded continually to stunning interconnections in advanced mathematics).

(from quantum mechanics to alternating current electricity to the beauties of fractal geometry).


i 1

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Copyright 2008-2009

www.biblicalchristianworldview.net

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Stunning Wonder!


ie 1 0 Drum roll ………………………………..

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Creational Harmony

• The person of Christ is the source of:– Rationality.– The interconnected wonder of Creation.

• In Him, all things interconnect (the wholeness of harmony)!


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One Example of Harmony

• The Golden ratio captures the essence and the spirit of creational harmony.

height

base

Golden Ratio = base/height = 1 5

1.618033989...2


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Golden Ratio

• Sometimes this ratio is referred to as the ratio of the “extreme to the mean.”

ExtremeGoldenRatio

Mean

where is the Greek letter “phi.”


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Mean/Extreme Ratio

a b aa b

a b

a + b


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Mean/Extreme Ratio

aa b

b

a b aa b

b b bb b


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Mean/Extreme Ratiob( 1)b b

b

21

b b bb b

1


2 1 0

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Mean/Extreme Ratio

1 1 4( 1)

2

2b b 4ac2a

1 1 4

2

2 1 0 Apply the Quadratic formula


1 51.618, 0.618

2

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Amazing Connection

• 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, …

• What is the pattern?


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The Pattern


1, 1, 2, 3, 5, 8, 13, 21, …

1+1=2

1+2=3

2+3=5

3+5=8

5+8=13

8+13=21

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Fibonacci Sequence

• Named after the Italian mathematician Leonardo Fibonacci (1170-1230).

• He introduced the work of al‑Khowarizmi and the Hindu-Arabic positional/decimal system to Christian Europe.


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Fibonacci Sequence• He discovered this sequence

by studying the population of rabbits and the genealogy of bees.

• More creation connections: seeds of a daisy head, pine cone and pineapple scales, seeds of a sunflower.


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Question

• 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, …

• Let Fn be the nth term of the sequence.

• What happens to the ratio Fn+1/Fn as n gets larger and larger?


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Answer

n Fn+1/Fn n Fn+1/Fn

1 1/1 = 1 7 21/13 1.615

2 2/1 = 2 8 34/21 1.619

3 3/2 = 1.5 9 55/34 1.618

4 5/3 1.67 10 89/55 1.618

5 8/5 = 1.6 11 144/89 1.618

6 13/8 = 1.625 12 233/144 1.618


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Limits

n 1

n n

Flim 1.618

F


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Johannes Kepler (1571-1630)

• “Geometry has two great treasures: one is the theorem of Pythagoras; the other the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.”


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Kepler’s Confession• Kepler also stated that when doing

mathematics, he was “thinking God’s thoughts after Him.”


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The Golden Rectangle

5 1

Begin with a SquareDivide the Square into two equal partsDraw the radius of a circleExtend the base lineDraw a portion of a circle Complete the Rectangle, which is GoldenL 1 5

1.618W 2

2

1 1

5

2

By the Pythagorean Theorem:

12 + 22 = 1 + 4 = 5

The length of the red line is 5

The yellow rectangle is also a Golden Rectangle!L 2

1.618W 5 1

5 1

2


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Why?

2 1 525 1

2 5 1

5 1 5 1


Conjugate

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Why?

2 5 1

5 1

2 5 1

5 1 5 1

2 1

5 1

4

2


1 52

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12

34

5

6

End with the perfection and wondrous beauty of a Logarithmic Spiral!

Start with a Golden Rectangle


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Point O is the center of the Spiral

The Center Point of the Logarithmic Spiral

A

B

C

D

O

Draw Diagonals AB and CD

AMMB

CNND

Amazing!

M N


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Marvelous Unity in Diversity

O

J

K

The Logarithmic Spiral is also called an Equiangular Spiral for this reason.


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Fractal Geometry

Logarithmic Spiral!Copyright 2008-2009


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Chambered Nautilus

• Logarithmic Spiral in God’s creation.• Note how mathematics conforms exactly with the

handiwork of God.Copyright 2008-2009


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Conclusion

• Man can think mathematically and the physical creation reflects mathematical patterns because of a common Creator.


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Conclusion

• Mathematics is an unique tool of wonder.


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Conclusion

• Studying mathematics in a Biblical way will lead us to better worship and adore our Faithful God!


Documents

Mathematics and the Wonders of Creation by James Nickel B.A., B.Th., B.Miss., M.A. Copyright 2008-2009