Weaver - Lewis Carroll Mathematician

8/12/2019 Weaver - Lewis Carroll Mathematician

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ewi Crr: MthecMany people who have read "Aic's Avnture n TVonerla

an gh the Loking-Glass ar awre tat th author ws mathemta. Exatly wat was wok n themt?

i Crrollwsn't he rstclssmthemticin too? This is typicl remrk when the nm

of the uthor of Alice in Woderlandcomes up Tht Crro's rel nme wsChres Lutwige ogson n tht hismin lifelong interest ws mthemticsis firly common knowege n fctmong is literry mirer there hslong been current ompletely flse butunstoppble stor tht Queen Victori

ed Alice, iked it ske or notherbook by the sme uthor n ws sentogsons ry speci nd dr litte

book on lgebric eterminntsLewis Crrol ws so gret literr

genius tht we re ntury curious toknow the cliber of his work in mthe-mics There is ommon enency toconsier mthemtics so snge subtlerigorous dicult nd deep subject thtif person is mtemtici is f

course "gret mthemticin therebeing so to spek no sml gints hisis ery compimentry but unfortuntel not ncssrily true Crrol produce consierbe olume of writing onmny mthemticl subjects from wichwe my juge the qulity of his contributions Wht sort of mthemticin in fct ws he?

The story of his cemic creer squickl to C odson ws born i

CARRO AD AICE aea in these hotogahs fom the

ois Paish Coection in the Pinceton University ibayAice was Aice idde whom Caro had in mind when e wote

' ate she became s. e-

inad Hageaves. Aice was hotogahed by Cao imsef i

859 when she was seven yeas od. Caro was hotogahed

obaby by Reginad Sohey in 856 when e was 24. In 855 e

ad been made do and ete in mathematics t Oxfod

1956 SCIENTIFIC AMERICAN, INC


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183 a Chhir. Hat a r, had hdathr, atradth adatatrdathr. H t u d 185 at u i h u ho. t th d 185 h a v t a hor atht d a itd uh ha u a

h dti tht h aiiat d o t t h B. rt a r t al ahta h 5d h . i 1857 I 1855, at h 3, h a v hlarhithat aid th ril u o 2 oud a, ad a itd or u-d, r d, a Chrt Chh, aathaal turr h Uivri. ivd, ahlr, ll uartr Quad r 1868 utl h dd,66 ar ld, i 898 aadi lfa ivd, ou l ardo th

ro, th vr Vitria v-i o bi ad ubibraria 855; bi rdad a dao 6,a a iax, h h wa 50, binad ator of h Con Rooaort o u ard.

h v or hi ludd fav hi a i fr wr,bth a Char utwid do ada wi Carro. hr ut b authr h wr uh ad ar rbrd for o tt h tandardbibiorah o h r t 256 rint duri h ifti, ad nar900 it i a Of h 6 ar booku i rit for hidr ad abou10 dvotd o athti and loi.O ha o a aout bau it i hardt l hthr o er ndd forhildr or adu, hth othr arathai or ata. In addtion ar-rol ro ar 200 ahl About50 atd to inor aadi uarre aChr Churh, au 3 t rd a,ihr ad h ik, ad or ha 50o wd ianeou ubj ho to

ori da, ho t bwdrShakepar for oun ir, how or nni ourna, oo errori ing, rue for rkonin oa,ad o on

Of h 56 ie prned drn hilft, wre doed o aheai ad oi f e on eork for a eia of Carro'orha hold no ay odgonar a a aheaan, we oerthat h wa r of a a aher, eae ornd wh ehod of in-tion i ar bj. wro

narl to do x or den i

A EON IN REATIVITY: Te hie Qeen cries Faster faster and exains o

Alie Now yo see i aks a e rnnn can do o kee in the same ae

A EON IN OIC: Contrariwise exained the one wth his coar abeed DEE if

i was so i miht be an if i wee so it old be b as it isnt i an Thas oic

A LEON IN ARITHMETIC: Can yo do diison? asked the hite ee. Diide

oaf by a knife. Try another sbtration sm said the Red Take a bone from a do



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9 -

x

- y y''

OCA DIARA inted on seaate cad accomanied coies of Caos . Reades of the book wer aso fnished nine adboad contes, fo of them ed(meanig yes) and ve gay (meaig no) and invited t ay the game. Reades of

this agazine sing ennies (yes) and dimes (no) fo contes may ay ot the

concsion fom the foowing two emises: A dagons ae ncanny and A Scotch

men ae canny The to diagam is sed to state the emises; the owe one to state theconcsion In accod with Caos diections et eveything in the fo centa boxes of

the to diagam be canny (m) ; eveythig otside the boxes ncanny (m) Core

sondingy animas that ae dagons (x) wi be fond in the e two boxes; notdragons

(x) in the owe two boxes Finay animas that ae Scotchmen (y) wi be fond in the

eftand boxes; notScotchmen ) in the ghthand boxes. n ayin ot emises on the

diagam it shod be ecaed that eac of them imies its negative; .. o dgonsae cann and o Scotchmen ae ncanny On Caros advice it is best to stake ot

negative statements st. Hence a dime shod be aced in each of the two e boxes in

the centa diagam (o dagon ae canny) Reades who oceed coecty fom hee

wi end with a dime in the e eft box in the concsion diagam (A dago aenot Scotchmen) and a eny in th oe eft box A Scotcmen ae ot dagons)

atht aba a trrt ad aaltal tr

Dd lat ad t ru t Euclid and His Modern Rivls, v u a ht t harah t athat It h ha a ltat vatv, ddatd tdfd Euld aat a drv t rv ha h a

ay Dd uht rv hb that Eld ax dt,rf ad tl ly uld t bhad f th bttH v tdthat th rd ad ubr f Euldhr b rrvd Dd llfull ruld tra th trd t tat Euld aalllax, ad thr ut all h attta ly tru It , hv,rth t that a lat b ttldA New Thery of Prallels Dhlf uht t la th laalax by f h dv

Ecd nd His Mder ivls utb lad a au, dululy natd and tally urtatIt rt nth f h r alat an tar athata that th ax aalll a a lfvdt fat f atu but a a

btarly adtd ad uvabl tulat NEulda try th tvlutay u f athat ad n a t drat f Dd hlh

h ba r f th RvdDd ratd by h daal

r laatl lvd h ur t h th athatal rtH l t th a a Carll , f xal, a tralttl b alld Pillow Problems. HrDd rt 72 rblhn albra, la r ad ntryall f hh h had dut bd at ht thu l rard urd f a,and hl h a arful t utthat athat uld u t

l, h arud that t uld uth nd laantly ad rvt rrIt haratrt f h vl uatttud that h rd athatalthk, durn akful hur a ady f ktal thht, hh fr th t t ut th rt fath blahu thuht,hh dart unbdd t th t vrnt ul uhl thuht hhtrtur th th hatful r hfany that ud fa b ur

Th rbl th b hl lntary, ar rthl latd

nh t rur ral kll ntrat an lat, f t



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scrips inces his to forite puzzleswhich he no pubish One cledWhere oes the y Begin? consi-ers the ox h mn who relswestwr roun the erh h smspee s he sun wi n h hough hestre on Tues when he returnsto is srtng oin the y is now cedWenesy Where n when i th

de chnge? ogson troube mnyocils in goernment oces n teerh comnies wh coresponenceon this question which he rst pos in86. o one coud nswer i of course

\,

unil the rbitrry Internion eLine ws estblished in 884

ogson's oher forite puzzlenmed The Monkey n Weight wsqully bing to his contmporries Aweightless perfecly exible rope ishung oer weightless frictionless pulley At one en is monkey he oher weight which xctly counerbnces

the monkey The monkey strs to climbWht oes the weight o? One of theicuies in ths trcky problem is hti is not wel ene For exmple doeshe monkey jerk the rope? Or oes he be

?

TRINGLE PARDOX leads to te impossible onclusion that 64 equals 65. The square

at top, composed of 8 X 8 square units is cut into the four arts shown. These may then be

ed togeter to forthe rectangle of aparentarea 5 X 13 squareunits, shownat bottom.

Close insection of the rectangle, however shows that the ange of inclination of the hy-

potenuse of each triangle is not qute the same as that of the slantig side of the tetragon

next to its shortest side. The extr "squreunit is ctually spred out in the resulting open

sace between the upper and loer arts of the ectangle. Carroll generalized this ara-

do in n lgebric eqution tht yields the dimensions of ll the possibe squres tht cn

be cut in the same paradoxical fashion; for example squares with sides 21 and 55.

gin puling on it ery genly n if show oes he minin he pull?

n ll of ogson's mhemticwriing it is eient ht h ws no importn mhemicin As we heseen in geomery his ies were olfshioned een for his ime in he robbiiy problem cied h fied to grsphe principle of insucien reson; in

gebr he once wroe in his notes: tht (x + y2) is lwys he sum of twosures seems true but unproble Iook hm some time o rcl the fcfmir to ny highschool suent ofeemenry gebr th (X2+y2) x+y)2+ (Xy)2 In clcuus his con-cep of inntesims ws he wholyconfuse one tht these were ueershowy qunities h noninnite nonnie n so nonzero isnoes recor such logicl monsrosiess nnesim uni innity unimnium nite fcion e nonersn he bsc concept of thelimitng proce in the ccuus s is in-ice by he remrk in his notes: Thenoton h becse rible mgn-tue cn be proe as nearly equal to xe one s we pese i is thereforeeq is to my min nstsfcory swe on redce he ierence n neernnhe

ut before we write ogson o s mhemicin we ms consier hscontributons to form logic ey hf

of his mhemticl wrings were in hiselhe mos impont wee The Game

of Logc ublishe in 1886 n n xpnsion of i 1 yers ter ino longen somewht more serious book ceSybolC Logc: Par Eleentary. nhese works Crro eeoe he useof scheme whch h rst ben ino-uce by the Swiss mhemicneonhr Euer in 1761 It inoes theeesenton of ses of similr proposi-ions by sp igrms [see page ]togeher with symbolic ngug for

rnsing he digrms bck ino erbsttemens The exmples he inentefor he use of he meho were chrcteristicly cler n musing

For insnce from the premises:

Al rgons re uncnnyAl Scotchmen re cnny;

he erie the comforting concusions:

All rgons re notScochmenAll Scotchmen re notrgons

Another exmple of the un he hdwith simpe logic is the following (de



6/15

RLABTY

Dependable perforanc is quarter-ntuy rtion at Moorola

the world' lagest xcsiv mnfactu lctnic upen.

Under sbcoc Cvai, tl enginered for elabty, and

is now poucing th gudan unt Navy

lleaher antarcraft issil the "Tere

Pstion pn t qua Engn and Phycit

M &

V . aboao: Phi rz oa a iri ir



7/15

FILRAO NWS

MAN RKAN FR element. Inuse, subconic feromagnet prcestck ke cps n photo

Mg v vv

A stcky servo vlve he hydru conro system for Mch oe-pus rrme scky usness deed!

Ye Cuo eneers recely encounteredjust suh prolem Submicronc wer prtles wel elow the sze rne o covenonl lers the empertures nd pres

sures nvoved ontmnted he hydrulud. These y prcle the servo vveused errt operto d stblty

o' ezed orous ro e

oves h role removn erer res ro d er e l re o-Je re heode ve ee desed o de % d o MIL-05606 dru o

drd K lter o porous 316

tness seel re lso ve omplee rne o stndrd AN 623 zes oropero o 350F Smr lers for use to

9F nd vrey o up ynder dds shpes re so vle.Ask your loc Cuno representtve or

he ts on verste hhstrehhh-temperture corroson-resstt K or rr or dustrl ters Orwre Cuno Enneeri Corporton ou Ve ree Merde Co 5

F! d w N 8!

AUTOKlE (1,.t") eKlN r. rtr_)FlOKlN Ir.. j) OO-KlN rm st.ss sti

0=1Aj 3 6 7 13& 3 ( .Jf SO 2 r t b 4 af1 6 - 0 S 0 2 J 2 : 3

3 8(

' : 6 b l . .1 z J-:. k r

MNEMONIC AID was worked out by Carrol t facilitate his reollction f nmbers

First he associated certain consnants with the digits. In his tale, it is apparent that "b

and c the rst consnants go with 1; q (for quarto) and f go with 4 etc. Given number h woud incorporate its consonants in an appropriate word or phras ths 545coud be vice f glee. He wod x the hrase in hs mind by incorporaing t in a rhym

ing verse of tw or four lins. Then if he remembered he verse he could recall the nmber.

du ousio ro h iv riss

" was os absurd o ou or i! ou ih hav ow, ou had a ss ha od saiors vr ik ru!

"Bu I houh, as h was u o ours. . . .

"A u of i idd! Su!"ou a a su if ou i.

A I ow s uls ar al d ad h ik ru i ahi!

"W h, us [o saiorsJ

Ausi s Crro's as owr, h wr hr hia oriia or rooud. I his oral wrso oi, as i or h raid rsou osrvaiv. Th Briish li

ia R. B. Braihwai has od ouha Carro "did o a h doriha has do so u o siif radioa foral oih irraio o uivrsa roosio as o ivovih xis o s subjr. Thuso Carro h sa "A fros haju or ha 2 ro oud ssri id h xis of rosha ju or ha 2 .

Na h d his i, howvr, Carroll did a o rl oibuio i ha h iud srius hii s ai

i ils h h

brs A, B d C. 1 A is ir so i hlavs h sho B has o o wh hi.2 Al hr ao ave oehr,si h hir sho woud b .Now wh hs wo riss usa a ssuo a s is osus. us assu ha C os ou.Th i foows ha A os ou, Bsas b ris 2. Bu b ris 1 i A os ou, B os ou oo. Thusur assuio ha C os o has do a ouso w ow o b as. h assuio is as ad hC a' o ou. Bu his is oss, oC obvious a o ou wihou disobi ihr of hs sros. C i

a o ou whvr A sas i. Thussri rasoi fro aar osis riss ads o wo uuorador ousios.

Brrad Russ rd aroudh diu b sai ha h sa

"f A os ou h B s o ou is o orador o h sa ha"I A os ou he B us sa . rus h a boh b joi ru oh odio ha "A sas . Bu hisis h sa as arui ha hr is odisar bw h sa bo oiiia ha "If h Rubiswi his wi irov, ad h s b ohr oiia ha "If hRubias wi, his wo iov. Nihr oiia would b saisd liia's ssur ha iisior woud oh hir sa

s ru. h aradox has l s or olied



8/15

C123 BECMB

PV OUNDING

SS: Combat Test Problem 3000 Ibs. OverloadFF : Power Failu

SS: Sccessf

a recent test for the Air Force, th archid prove the value thrust assst i meeting mergency enine coniions!

A was equippe wit o aircd 4 je ngn oae to achieve ros weigh 4 ou pounds verla.

Durin takeo an climb both et r peratd o ovie ouns contiuous thrust in ition o thtwo psto enines. t eet wheels were o egroun an moment ater at a spee o nots oe

roeller wa eathereFro ths tao positon th cimbe ou at eet per minute - provin again its big job capabty an

aaul vrality, heihtene b et umentatio o giveextra power an extra saet an emerec.

Dvo f Farchld Engne an Arplane Crpr

H'ILD



9/15

ntroeaneCH2

nto etane

ntropropaeHCHCH22

ntoopaneCHCH2CH

w

Y.I.

n esn y y o logcnsin pe pblse e Bitis ounl Md. Te connng iscssionis eience o te neest wic stlltces o s logicl pzzle As Bwite obsees Coll ws plog-ing eepe tn e knew is mnws emee by n mble logi

wc e ws ble to bing to fllconsciosness explici ciicsm tis tis tt mkes is Smbol ogso specil s csl pzzlesso on

t wol b o ste bee tnBitite oes in ese wos teconlsion of te mter Te Reeenogson ws ll conscientios ncpble tece of elemny mte-mtis Lewis Croll ws in tntlz

ingly else n excellent n nconscosly ee logcin Bt wen ete o ppc logc e on in pope oessonl wy ws onlymoeely sccessl ws wen ele logic n loose tt e emonseis te sbtlety n e n fc o fll mese o is se s logi-

cin we mst look into WonlnAlice n e compnions e oftenbeen oe n books on logic n plosoy P. EB Join in is eligtfl book The Phlosophy o M BOt-Od ROssll eles eil on Collo emonste e key noons of logicTe smlng o Coll's itositywic ollows is tkn om tt book

Logcins e for ges strgglewit teoes o ienty s wen isone jsie in syng "X is ienticl

PILLOW ROBLEM hlpd Carroll ndr insomnia throgh a night in wolst himslf th task of framing nd soling sch prolms iho ping a mrk on ppr

ntil morning. hn h wold writ it p in th orm sow hr, wth th otio

"thoght ot and th dat dtrmind by hthr h sold it for or afr minigh

Carrol plishd som of ths roms in ook for othr insomniacs h mnscrirrodc r is on o a nmb illow prolms in th or's collcion



10/15

A D PA M I S O by Drtr of R, ockhd Mise

Ectn cnra to e of d . Draa prvme i reur aer; re acr t ro ans lctroic s ic an no ye

He t he M Sstm so a aware f qumn. W k elc-r s exn gtst rl i te a u,

lonic g, is b c y w lste wh up rmnc ad rlabl.Ts te for r t Pat hq wl nt e reqn e Exprnc in d-n g alifctonfor epest chal. ygivngt bs pnib lty tocet ad ngnr,wear ing to ypmpasi ont new lec.

MISL SYTEI DVON resch and engirst fLOCKHED IRFT P VAN UYS C .



11/15

BRH

10S1alamO

los

The cyclotron shown abov s one of the many typs

of advd rsarh quit n s at Los Alamos.

his vib gy i s dsigd to aclrat

high isiy bs of th hydogn ad hlim

sos

ot s id g of oportunts

to d rs ad dvo k i th filds f

Physis, Chis, Mtllgy Mis, Compt

g ad Egiig

If you tstd lig o abot careeopotuntis at os Alaos i-

DEPARTMENT OF SCIENTIFIC PERONNEL

Division

)aamosf THE E!J:oratory

L L X

with Y, or "X is the same as Y, or "Xs Y"? Ths matter was entrely e toCrols ttle friends:

Th dy s th same length asanhing tat s the same lenth as" (Sylve n Bruno)

Bruo observed that hen theOther Proessor lost hmsel, heshoul shout 'He be sure to harhssel cause he coulnt b faro" Sylvie n Brno)

Most logicians-and most of the esof us for that matter-hve to b eryrful about precson n detonsad about the onfusing overlap ben what words denote n what heyonote But this ws not a matter ofouso on the other sde of the LookinGlass:

Tweedle dum and Tweedledewere, in man espects, ndstnguishabl, Ale, alking alongthe o, notced that whenevrthe road dided thre we sur obe to ngerposts pontn hsame ay, on marked O WEEDEDUS OUSE nd the ot OE OUSE O WEEDEDEE

I do blieve, sad Alie tlast, tht they n th samehouse! '

When us wo, Humty

Dumpty sad in athe soune,t means just wt I oos o mean-neithe or or ess

The queston is, sad Al,whthr you c ke words mndierent things

The question is, sad HutyDumt, hih is to be mstthats all"

Extemely subtl nd intriat probems in moden mathematcl ognge on the qustion hether rxsts any such thing as univesa sso all possble tings But even the Gnat

had that one gured out The Gnt hadtol Alie tha the BreadndButterFly lves on wek tea wth rem in it

Supposing t couldnt nd anysh sugstd

Ten i would d o ous!Bu us a y

oftn, i kd outuyI y ans s

(hgh h kg

o yz

\



12/15

CNIG GLASBULET FORPE9L WH

f--: CORNING GLASS WORKS, 49-4----."

Please send Ih maeria checked belOw.Crystal Street, Corning NewYrk IJusraed booke "GI d ' . ass an You" ,Bul/ein "Proper S I es e ected C .

Bul/ein B.

ommrca Glasswar au acture a Deign C , Nam

ommercial Glassware , Tile MKE THIN S Company I, A.ddres

Hw mak a -allyIn the syringe behind the needle, whichyour dentist wields so defl, is a neatly prepackaged dose of anesheic.These con tainers are glass tubes soppered a boh ends.

We call hese painkiller packages"cartridges;' and fashion man y of them of a brand glass he specic glasssed goes under the somewhat undraatic name of glass No 7740

While the itle may be lacking imaginative quality, he glass is no. Conider, for a star, the fac ha he glasscarridges must be made o close insdeoutside tolerances because (a) rubberstoppers must t snugl isie a ()the carridge iself needs esle ealy in

the dentiss hypo or syrngeThese close s demand re polshingthe ends (so tey wont chip) wihout impairing dimensional tolerances-quite adelicate operation for mass prouction.

The glass tube must be capable ofbeing sterilized without undue srain orbreakage it must be chemcaly iner soi neither adds o nor tracs from thequality of its cones And the carridgesmus be economical as, in the interests ofsterility, they are used once and discarded

S far, s good This brandglass 7740 meets all the countsandthen some It a glass tha's easily

formed into intricate shapes, by variedmethods, including inexpensive, onepiece molding

Fo mos general purpose use, No7740s reluctance o iterfere wih chemicals is without peer. Is unusual thermalexpansion coecie (33 x 10 between and 300 .) gives it a better than ghing chance with the temperatures encounered in a wide range of design problems

nd certainl of importance, the facha coutless custoerconceived projects have is prot worth

e recommend fo you reading Blleti B83, ropertie eece erc Glasre ihe pge ee ll ele e

rty '; Zone---------____ -SIale I------------_.glasses (o. 740 included), data onmechancal properes, thermal sresses,hea transmission, and elecrical andcemical characteristics. Free Mucheasier ith the coupon.

Say ay ... ca adadl felecive maneuvering of rays in thevisible specrum has raditioally been

one of he roles that glass plays with considerable success.Now comes another improvement in

his eldone that adds comfor andsafey to your motoring and, conceably,some valuable facts to your les on glassuiliy s the new sealedbeam headlight hich reduces the hazards of drivingat ight and in the fog

The glass les and reecor of he newheadlight, sealed togeher hermeicall,are designed to reduce sray ras, to cocenrae more light-furher ahead ohe high beam ad o he right of heroad on the low beam

ounds like a simple achievemen, butt took several years to accomplsh andinvolved sgnicant conribuions ofauomotive, lighing, and orning glassengineers workig togethe on lens design, reector design, and lamen design Corning now makes hese prismaticlenses and the reecors for several headlight manufacturers, one of hom evenincludes three algnig knobs on his lens,which contribute to easier and morepositive focusing

-PRISMATCEFAG

PN

ALUMIZEDEE1NOIA OOU

The ne sealedbeam headligh illustates how you can enginee glass oaneuver light ino places where i doesthe most good It also illustrates highperfection in hermetic sealingglassoglass and glasstomeal The ealedbeamheadlight is as airtig as lamp bul

Yo a glea more aou the atred exten o engineere glas com

plishments, in elds, rom a attractive little prime called lass and ouWell gladly send you a copyfree

Or, Bulletin 84: Maufacture andDesign of ommercial lassware onents follow he itle, oering suggesonsfor maching esign to knon advanages(as well as limitatios) of various processes. The coupon will bring them to yourdrawng board or desk

T b ay?Heres a quiz hat may get you przesgalore in the form of money made (orsaved) This is a matching game, aimeda showg you how one usrigh ornng glass handles a dicul problem

Wrie the number of te appropriaeglass in he box following each descripion

Proecs lightsensiive substaces romwayward and annoying angsroms onducts elecici and provies uniform heaing surface Protects against radiation eects aseectively as concree is nobrownig

has desi of 33 an be used wih intermitent temperatures o 1200 has thermal coecie of expansion o 8 x 10 per Absorbs visible light from tungsen lament (200 K) but transmis ifrared 1 VYOR brand lass No 7910

2 Lo ctinic lass

3 orning ode No 8362 lass

4 orning E lass

5 VOR brand lass No 7950Correct answers: s t S 'v 'z

And thats us a stat heres alsoribbon glass that outperforms mica glassthats brickwall thic or eggshll thinglas ha handles metaleating acidswithout ill eects glass tha copes withalmost any form of radiat energglasshat improves performance o and enadds beauty to many any, manyprducts

Jot down your mos vexing prolema we'll le yo no i ne ourlasse can hel o sle

G G W

6



13/15

'p

INERTAL AVGOImmediat opennD8 for

Supeisoy and ta

ositions as well a8 o

Snio Einee

Eniees ad

oct Engin

expience n:

YSTEM EVALUATIONGYROSCOP ICS

DIGI OMPUTESCEROMETERS

ELEMETRYGU IDNCE YSTEMS

TABILZ NG DEVICESERVOMCHNISM

OMATIC CONROLHERODYNAMICSOPTIC

NVIRONMEN EARCH

ARMA, rcognized for is ccomishmnt n th ld

of navigatin and control. is ladr n th

deveomnt of Intial Navigation This nw systm

deas soel with sac tim and accration

actg indepdenty of xtrnl nunc

Ceatie nginring of th highst orde is quid

to eeo comonents making Inrtial Nvigation

ossbe: accleromtrs to measur cceetion;

integato8 to convrt this nfoaton nto vocity

a dstc gyos to ovde dictional rfence

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15/15

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Weaver - Lewis Carroll Mathematician