High School Glossary Pre-


BOARD OF EDUCATION OF THE CITY OF NEW YORK Board of Education of the City of New York

Carol A. Gresser President Irene H. ImpeUizzeri Vice President Louis DeSario Sandra E. Lerner Luis O. Reyes Ninfa Segarra-Velez William . Thompson, ]r. Members Tiffany Raspberry Student Advisory Member Ramon C. Cortines Chancellor Beverly 1. Hall Deputy Chancellor for Instruction


Ie is the: policy of the New York City Board of Education not to discriminate on (he of race. color, creed. religion. national . age. handicapping condition. marital StatuS • .saual . or sex in itS eduacional programs. activities. and employment policies. AS required by law. Inquiries regarding compiiulce with appropriate laws may be directed to Dr. Frederick..6,.. Hill. Director (Acting), Dircoetcr, Office of Equal Opporrurury. 110 Livingston Screet. Brooklyn. New York 11201: or Director. Office for o ..·ij Rights. Depa.rtmenc of Education. 26 Federal PJaz:t. Room 33- to. New York. 'Ne:w York 10278. HIGH SCHOOL MATHEMATICS GLOSSARY



~ 0/ * ~.tt Jf -taJ ~ 1- -jJ)f {it ~t ~ -ffi 'ff

Chinese!Asian Bilingual Education Technical Assistance Center of Bilingual Education Board of Education of the City of New York 1995 INTRODUCTION

The High School English-Chinese Mathematics Glossary: Pre­ calculus was developed to assist the limited English proficient Chinese high school students in understanding the vocabulary that is included in the New York City High School Pre-calculus curricu lum. To meet the needs of the Chinese students from different regions, both traditional and simplified versions are included. The bilingual mathematics teachers may also use this glossary as reference material. This is one of a of English-Chinese glossaries that is being developed by the Chinese/Asian Bilingual Education Technical Assistance Center (CAB ETAC ), Division of Bilingual Education, Board of Education of the City of New York. The project is made possible by a grant from the Office of Bilingual Education, New York State Education Department.

The following is a list of the glossary series . The Mathematics and Science glossaries will be available by the of May, 1995. The Social Studies glossaries will be available by the end of September, 1995.

The Mathematics Series:

• Integrated Mathematics (Course I) • Integrated Mathematics (Course II) • Integrated Mathematics (Course III) • Pre-calculus • Calculus The Science Series:

• High School General Science • J unior High School Science • • Biology The Social Studies Series:

• Global History 1 • Global History 2 • Global History 3 • Global History 4 • American Government • American History 1 • American History 2 For information or recommendation, contact CABETAC office, Division of Bilingual Education, c/o Seward Park High School, 350 Grand Street, Room 518, New York, NY 10002, Tel: (212) 677-0493 Fax: (212) 677-0398 . ACKNOWLEDGEMENTS

Special acknowledgement is extended to: Wenhua Reyen, Mathematics teacher at Seward Park High School for developing the High School English-Chinese Mathematics Glossary: Pre-calculus; Annie Han, Consultant of Chinese/Asian Bilingual Education Technical Assistance Center (CABETAC) for reviewing; De-Kun Yuan, word processor of CABETAC, for coordinating the typing and printing; Eva Hsien, typist, for typing; and Jennifer Fung, secretary, for designing the cover; Dr. Frank Tang, previous Director and Mr. Peiqing Yang, previous Resource Specialist of CABETAC, for coordination of the Glossary Series; and Dr. Florence Pu-Folkes, Director of CABETAC, and Wendy Yang, Coordinator/Resource Specialist for supervising the completion of the Glossary Series. Special appreciation is extended to Dr. Lillian Hernandez, Executive Director of the Division of Bilingual Education, Board of Education of the City of New York, and Carmen Perez Hogan, Coordinator of the Office of Bilingual Education, New York State Education Department. Without their , this project would never have been possible. CONTENTS

Introduction ...... i

Acknowledgements ...... ii

Traditional Character Version ...... 1

Simplified Character Version ...... 30 TRADITIONAL CHARACTERS A

abridge division t1!'~~ ambiguous jtJli'lCi:;:!I!5tt abridged t1!'*~ of a periodic l!J\ljiii§t\:lJR~ abridged notation ~1iC~ amplitude of function iii§~lJR~ abridged proof t1!'Hi!~ analogue ~ltl! adjacent vertices ;ffl~rn:~ analogue ~ltl!ift:l't~ adjoining figure 1*,Mlil% analogue multiplier ~!J:ij<*~ adjoining rectangles 1*,MlJi!!% angle of inclination ~fff adjoining 1*'llil'l:JcJ3i;11ill of incidence AMfff adjoint 1*,Mltr~tl;t angle of parallelism 'J!-trfff adjusted proportionally ilml~!t{fu angle of liMfff admissible error ~iit~ anharmonic 3I:!t; IF ar.J;;:U!t;:!I!!t advance estimate ¥1ltr#tiff-tli: anticommutative property li3l:i9'

arbitrary 1ftt~tl alternative ~-0;t progression JHfjli/k~ alternative symbolism ~-W'lCi: arithmetic series :jll:j;fjli/kl!: ambiguous m~J':ti4 arithmetical series :jll:j;fjli/kj;fj, ~~~&l!:

-1 - array ~7iJ; llc*ll. asymptotically equal jtllfrttl"ll asserti Dn J!TiE asymptotically equivalent ltlilfr"lliJ associative t$15-0J.m augmented ~~J;e~ astrDid liU[;i~ automorphic i3li'iJt/li!i9 ; i3;t-!i9 asymmetrical step functiDn ~f:;Hjl}~I1':t1\pj§~ automorphic function i3 ;t-pj§~ asymptDtic It\lfra~ i3liiHIli asymptDtic apprDximation ltlilfr:i!lfrl'ti: auxiliary i\!iIi[l!!J)1!il asymptotic ltlilfrtif'11 axiom of comparison ttilR0l111 asymptotic circle ltllfrllil axiomatic 0l111S9 asymptotic series ltlilfr~llc of order ~Jf.0ll1!

- 2- B

vectors il\!i[!;]:!i bound for the lttMIi9f!!.JI!! basis vector il\!i;$:[!;]:Il: boundary f!!.; iif!!.; ii~ distribution =l:'Ii::51-~ boundary complex iif!!.fj[JB =l:'Ii:JtJEJlll. boundary f!l.tilIi biorthogonal 1!J!iE:9: boundary and minima bisecant =~jIf~~ ii~;fil!*f!l;fil!/J' block of digits -fi§.1ll:'¥ boundary of half- ¥-'¥'iliili9f!1.~~

Boolean ;tp1>liff"t1ll: bounded 1if!l.1i9

Boolean ;tp1>lif*JiJt bounded above J:1if!!.1i9

Boolean factor .:(P1>lifE§.y bounded below T1i f!!.1i9 bound f!!.; iif!!.; M1* Briggsian 1jt fflltt1ll:

-3- c

,L.'J!!£Ml comparison function tt~PEil\: center of ilIl$.tjo,L.' complement of 1m~ characteristic ~~Jit, ~~~1lii completeness jt~¥:t characteristic ~~'litl\: completeness of axiom systems characteristic ~~[ ilIl J~ 0l1BU1i:!B jt~¥:t characteristic determinant t¥~rrllJA components of a vector ioJ:lll:!B?t:!li; characteristic ~~;ff;l composite determinant ifJiX;rrjlJ;o'\ characteristic function ~~PEil\: composite matrix if JiX;[9:E: J'" characteristic root ~~m composition of probabilities i!t$if $'; characteristic vector ~ioJ:!i composition of vectors ioJ:lll:!BirJiX; circle of curvature ilIl$1liIJ of correlation ;fI'HIIl~l\: closed half-plane M~"¥'1lii coincidence 1fif,1ll:ir closed Mm;:r., coincidence 1fifl\: ~~'" coincident lines 1ll:if1l:~~ ~PEi l\: column matrix jIJ9:E:'" cologarithm I*~l\: concave downward l'!]ioJTIl9 col umn vector jlJ [ti):lll: concave upward l'!]ioJ..t!B common differcnce 0~ conchoid J:f~ common divisor 0;o/-Jl\: {!$#M common or Briggsian 'litJll~l\: conditionally convergent {!$#M commom ratio 0tt conditional probability iHH~$

-4- conic ::.iJ;:i!!l!£il9; ~ii(til9 consistency of

conic projection ::.iJ;:i!!l~:iQ:~j ~i't:nf!€ B9.jtj?§ i't

~~fti!!l!£; ::.iJ;: i!!l~ consistent *~?§il9; -3&B9 ; ~*Jfil9

conic with center 1H.'::.iJ;:i!!l~ constant 1il"~$Jf! 'i'.\:

conic without center 1!IH,'::.iJ;:i!!l~ continuity iI!L;jf'l1:

conical ~rn:~ :i!UftiiEi~

conical function ~ii(tfEJ~ convergence 4k~

conicoid ::.iJ;:i!!lllil convergent ~B9

conjugate angle ~iWii:ffl convergent t!ldli:j~{iiJil&~

conjugate arc ~iWii3JR convergent sequence t!kMJ~

conjugate axis ~iWii*iIi conversion vlJJff<:1ff!€

conjugate conics ilic;@1 ::.iJ;: i!!l!ilb ~iWii::.iJ;:i!!l~ convex domain 6f,:;Jt

conjugate ~iWiii!!l~ convex region 61!llf,:;Jt

conjugate ~~~i!!l~ convexity ~i1

conjugate ~iWii.®!'i!!lllil coplanar vector ~llilJoJ :lIi:

conjugate imaginary ~iI!iiliffimi coprime ::S:~mi

conjugate lines ~iiIi:K~ core tt".'

con.iugate lines in a conie counterexample 5. 1f~

critical point 1l.'I;ffi.~ conjugate matrice ~iWii[i'ie JF,;;: cross line iE3C~ conjugate of function fEJ ~il9~iWii crystallographic j;S.'Ulllf conjugate pail's ;l\

cubic polynomial .:::iJ;:$Jf!'i'.\:

-5- cubic =:tXanW curve of distribution ?tWGan*,' cuboid i't::lf'.l cycloid :atE~~, m~ curvature anlf< cyclotomic !a Il!I curvature invariant anlfhelix ttw~U curvature of graph h'ilJJBIi'J an$ cylindrical projection Il!Itttlt~

-6- D

De Moiver's Theorem ,**Jl;~JJ. determinant fJ'l1J'i'\:~

decreasing VzQ(1;t determinantal fJ'l1J'i'\:i¥J

decreasing function }I(1;ti>.i§J!!: determinantal expansion :fi'l1J'i'\:JiUll

decreasing sequence T~ffl1J diagonal JIft!:¥:J!!:

decreasing series }I(1;tmJ!!: diagonal element JIjjj:n;'~

deductive lJl;:~iil!lt of matrix ~~il9Mtl!:

degenerate critical point i!Htl/li;,\\t!!\'j direction ang les :ff 101ft!

ilHt=lJ;:: iIll~ direction coefficient :ff1oJ%~

degenerated curve il!itilll~ direction component :ff1oJ?t-i!:

degree of freedom I1l El3 Jl :ff1oJ~5l\

demand matrix 1\\l'*~i!f direction :ff1oJl!:

denumerable OfJ!!:i¥J direction vector :ff1oJ1oJi!:

denying premise ~:iEiltrJ!i! directrix ~~~

dependent random event .#!1&JlJi'iiltil'H'f discontinuous function ~ilILfii>.i§J!!:

dependent J!I!.~J!!: disjoint ~.#!3Ci¥Jffl1J

Descartes' rule of signs 'lti" 5l'.IE~ ~m.llU {tt'L, ~Hll'!.ill!ill1J

determinate rr:9U'i'\: displacement of n unites to the left

determinant divisor fJ';9IJ'i'\:IZ5l'f determinant factor fJ';9U'i'\:IZ5l'f distinct elements ~f5Jil9:n;~ determinant of coefficient :¥:l!:fJ';9IJ'i'\: distinct limits ~f5Jil9 ;j!U~ determinant of transformation ~~fJ'l1J'i'\: IDf~tt;~Jl;~it

~ 7- divergent ~a9 double- angle t;l1iflt][~3t divergent arbitrarily large ~1i!l:¥tiff]!:* double ratio 3i:tt, ~f~f'il tt ~1i!l:t&~

-8- E

eccentric angle lIll,L.':fil dl1l,L.':fil escribed circle ~tIJ I!lI eccentric circle JIi~'L.'lIl] Euler circle ~1lLl!ll eccentricity JliH.'*, i\ll,L.'* Euler's equation 1ilk1JL:/J~ eight -leaved rose curve J\..1iIflj!(~til)l even function 11ll PEi1!t element of matrix Ji!11\11895i;Jli' excircle ;>I-Wli elliptic ;Jffilll]ll

-9- F

finite progression;fj"~~~ focal ellipse !Iii..Jfili!lJ finite sequence ;fj"~Ill~JU focal !Iii.'¥lil! finite series' ;fj"~Ill~~ focoid J:fi!i!lJ!l'.'i five -leaved rose curve .li1i!*ljli:;i6*,'i! folium ~7f;itill: focal axis ;l(\\iJili formal axiomatics 7f;i5t0Jll!* focal !lii.S!; of occurrence i:lHll.1:l\~ focal eire! e !Iii. ffilI function of dispersion 0-IiHj§~ focal conic !Iii.!!iIi='1:l\!lIJtill: fundamental direction vector &4:ioJ:fil: focal ;\\'J~

- 10- G

Gaussian Elimination itli)[email protected]*i'! geometrical series ~{i;yf;11~; ~ ltj,ll.~ genera tor i!ttilll; ~JiJI;:7G geometry of the llltiili ~{i;y geometric ~{UJ"V-:BJ~ greatest lower bound ~Ar,w. ~{UJf;11~ ~» geometric projection ~{UJ:tlC~

-11- H

half- angle identities ¥flJtli:~A heterogeneous ::t:t.'Il-(j9, ~~ , .

homogeneity ~tt ~;f!lJm~ homogeneous ~tt[S9]; ~&; ~S9 harmonic progression ~;f!l~tt homogeneous equation ~&1f~ harmonic ratio ~;f!llt homogeneous linear equation ~~~~ ' I1:1f:mA harmonic series ~;f!l~tt ~ljM.l'(tilli ~;f!lBi§~ hypothetical models ~l!ltmA helicoid !.-l'(!i1iiIi

- 12- I

icosahedron:::: +WIlf induction hypothesis l\il~{1

- 13- intermediate convergent opr"jq\>:~ inverse ci ,'cular function Bi:'::=:1'il~l\:

by central difference Inverse matrix i2![J;EJIliI1

inverse rotations ~~$; Bi:$1j: intelTelationship *~1iF;jiJi* inverted sequence J$lf, Bi:lf intersection of solution sets !i¥~Z3( iiJiJl![J;EJIliI1 ~~; ;;r:~it; /F~li irreducible over F :trF1ff;/FiiJMJ

. invariant under :fjjf.$/F~:lii:

- 14 - J

joint occurrence 1jjjiiS- HEll. -l'j,:i!ll.iS-; ~i1I.i1l.,g.

Lagrange's interpolation formula linear correlation ~'I1#l~

~i1lfli{1[i'1< lattice ill- linear minimization ~'I1~/Ht leading §Jjj linear relation -iJ;:: ~1*; ~i1~f*: least limit :liluH']~& Jituus )!Ui\J!l!~ lenlniscate ~~~ local maximum ftjJl!1I~* limit t~~& logarithmic function t-t~jjj§!Itt limit of function jjj§~Il-J~~& t-t~t~~ limit of sequence ~ ;9 IJ B9 tO)jF>& lower bound T!Il- line of curvature iIII$~ Ioxodrome #4!¥f~ line of reference W~~; ~~; [1i:J~

- 15 - M

m - fold factor m:m~A mixed - product lIf:fl"tJii' major axis -fi;$iIi monotone decreasing ¥WlJjlglJl\i matrix jiE '*; Jt ffi.;J\1 monotone function ¥WlJiElt matrices jiE~( ~lZ ) monotone increasing ¥WlJjIg!i!1 matrix algebra [~I'!JI:q;:1-tJltt monotone sequence ¥ro;;rlf'?u matrix equation jiE~:1J~A multiple factors &:;~'f matrix of coefficients *lZjiEf>$: multiplication of j'j',?UA*1! minor axis !liJiIi multiplication of vectors ioJ:iii:*1! minor of a de terminant 'ffi,?UA multiplicity of wot t~89flll'; *Nil9:m~

- 16 - N

n-dimensional ni.

Napierian logarithms i31t.~~; llMtfiW~~ nonoverlapping ~;t§3I:T~.g. nephroid 11l'JI!l~ non vertical lines ~f¥1i:1i:~

Newton's method 4'-~~ distribution 'Ijt~:7H!jc non - degenerate circle 'Ijt!!\ll!!l normal curvature itlill$ non - degenerated curve 'Ijt!!\llilllil!: normal probability distribution 'ljtfi1Hli\$:5Hlc non coincident lines ~£.g.'ffrl1lt nth nlJ\m; nondecreasing ~lJi!\\ j>il9 null fu nction :ll)': i'Ei~ nondecreasing convergent sequence null matrix ~~I~

numerical determinant ~'¥rr31ti;;:t

- 17 - o

odd function ;;ri'Eif!!: orthogonal component iE)i:7T:iIi: odd - numbered term ;;rf!!:Ji!! orthogonal cone iE)i:i.f£OO one - side limit from the right iE)i:~f~

orthogonal vectors iE)i:{i;]:!i opposite in signs ~$t;fll& orthogonalization iE)i:1t order ilii orthonormal vectors iE)i:JiH\'I{i;]:!il: order of a determinant 1T11j:a:89~l\' orthorhombic >J.4JrdU\.89 order of a matrix [~§:Jr>Jll~l\' oscillatory series jJiHJ~r< oriented direction ~ {i;]F§'ill~ outer product 5'1-ff./ orthogonal iE)i:89 , J¥:flj 89, ~*89 g~Jf;lil!: orthogonal iE)i:~

- 18 - p

parabolic curve ~!w']Bl!i.ilI! polar curve lICMlBl!i.ilI!; Ml~fi!?Bl!i.ilI!

parameter ~$:; ~~:ll!: polar distance MlR§:

~!/!!::n;§1'i't polar equation :joJl:n;§1

partial su m W{;t;fIJ polar form Ml%'i't; i'iil!M

pericycloid fflIlllt~ polar form of fJlttl¥.JtoJl'i't

periodic changes ~WJ~1t polar normal to]lt;:i.ilI!

~WJfEitt polar radius ~*:j![

perform successively J!ll~Jl!!~ pole Ml;toJl!!!li

matrix j![~iiE/!f; :fj1.9'ViiE/!f polycylinder $1!!li1

component ¥][:$Hii: polydisc $I!!ltl:

perpendicular component of a vector polyhedral angle $llififl

fOJii:B~¥][:5t:!il: polyhedral convex cone $llif6i!£

shift ;tMt polyhedroid $llifff.

point of increase i!'l!!!li polynomial function $J1i:'i'tfEi$:

point of inflection f31!!!li; &:~!!!Iii ~Bl!!!!Ii $J1i:'i'trsMiIt;: point sphere JI1li,* polynomial over the F polar ~i¥.J; :joJllliJ; Mli.ill! FlHl J: $ Jj'i[ T-I: polar angle :jo]:flI portion of a series ~AttB9W17f polar axis ~*iIi preceding term litrJ1i: polar coordinates Ml~t~ preserve validity 1l%1i1;;r-:~ polar coordinates in the plane 3fllifMl~ti!? prime linear factor -lX'ltIEl'f; i.ilI!'I11tIEl'f

- 19 - prime linear polynomial over C principal vector :t1ii):Ill:

C'Pi391Jt-~~ probability distribution lilli¥:5Hic primitive function ~iillitt production matrix fj!(J;§:li-'l1 principal axis .i:*m progression t'&t/< principle of inference t!EJlll.~Jlll. projective geometry tQ::\ll?~ji1f .i:m proof by contradiction TiIlilll'SJlI!; 1Ji.illl'1! principal value of arcsine 1Ji.lE~iillitt.i:m provide a counterexample ~-1Ji.{9tl

- 20- Q

quartic Iilll'lz quintic equation lil'lz}j~ quintic lil'lz quintuple space li~F.!j

- 21- R

radical axis ;ffi!.$iIl; ~;m;~iIl reduced matrix 1IlHt~jilj1 radical center ;ffi!.,L,; ~;m;'L' reducible over F :(EF't'ftffll radical cirel ;ffi!.1!!J reduction ~~0J't; ftfll\0J't radical exponent ;ffi!.:fi1f!l: regression line i!!!l~il:~ rank :f9i regular matrix iEJlu~jilj1 random experiment l!iiH(l!iPt~ relative maximum or minimum random variables 11Ji:11!\~f!l: #ll!iM:kli!tM/J\ rank of a determinant 1l';9uJ'til9:f9i relative maximum point #ll!iM:k1!\5 rank of matrix ~jilj1i¥J:f9i relative minimum point #ll!iM/Nlli rigid body IiIltllll relatively prime #ll!iK1!l: reciprocal function illJiii§~t Kjjtiii§f!l: theorem i*J'tJEllll rule with left end points resoluble PJII'I-; PJII'I-~

resolution of vectors riiJ:lIi:1i97J-1I'I­ rectangle rule with 't'1!\5~W~ resolving vector 7J-lI'I-riiJ:lIi: rectangular array ~jilj1;9U d~J1jilj1;9U reversion of a series ~f!l:il9jjtlili: rectangular matrix ~jilj1 revolution @],' recurring series lJi!jJ.ll!~,1H!t root of multiplicity K K'ill:;ffi!. ~(J't);~~;~J.ll! roster of the elements of a set recursion formula ~~0J't; ~~0J't ;9IJ t±l ~ 't' 5G~ recursive ~~il9 rotating coordinate axes :Iiii"JilitJfill recursive definition ~~JE}i!iS; ~1fEJE~ rotating cylinder :Iiii"ttlll

- 22- rotation about the origin tlIiRWli:at€n row rank ff:tl< row matrix ~~ row vector fff1;J1ii; row 1n1l!~

- 23- s

same orientation P15E1oJ shift to the right lol;(:;ft Ml:l:dl&:!i!b ~rt>J:I: shifting ttfli: scalar mul tiple Ml:l:t~* simplicity of notation ~$!tM{{:; scalar multiple of a vector rt>Ji:~!1e:l:**~ Simpson's rule *f!tl~i't Mlii*i't lE~tllt scalar product of vectors /aJ:!il:%:l:B~jlHi11 sinusoid iE~Q:lllIt~ scale equation t~1l!':nf,l; R1l!':nf:!t skew ~4; flil#4 schematic diagram ~~, ~ii~, m1}~ sliding vector ffi")JJ1JIBJI: self - orthogonal El nX:lE'X: spiral ~!Rti!t; ~*ti!t semimajor axes $i'Hlk spiral of Al"chimecles /iiiJi!iP!i.HH$!iil: semiminol" axes $TJi*~ square array lE/H~?" 'J semiperimeter $JlH'.t 'Ji p+':' separating point %iiUJ; square matrix of order :np~11l.l' sequence ff~IJ standard l~~~ series NH$: standard 1Jl\~ili:lii': fiHttllH~ ,*+.iFl"ilil~1Ji!; serpentine ~JF!iil: stochastic matrix IIJ1H1Hep~ serpentine curve 'rt'i!:ti!t straight line method ~.g..~ sextic ;;,;rxti!t,;;,;rx straight line of in finity ~Pl>!][ti!t sextic equ3tion t\JJ:1j~ su bdete rm j nant 1'"[l'i'?"1JJ:i'\

- 24 - subinterval -r[;&r., superior limit ..till\! subsequence -rJfJU; tl1l1Jl-JfJIJ symmetric equation :l\tftll;IJ~ su bseries -rt&f< symmetrical determinant :l\tftllDJUA su btend (5f:; J§;; jIj ~ ):I(j-1oJ (5Jl.\l!1i;:l\tjlj ~) synonym 1iiJ~~lt subtense 5f:;:l\ti& synthetic tf,il'; il'nlZ succeeding term ~-l1i: tf,il'Mti'ii: sign :;jtjf-p1'f~; i!l!:l:lO~ synthetic - tf,1Sf-\;~( i'ii:) summation symbol :;jtjf-p1'q:~

- 25 - T

plane {jJJilj ~W!f/:; f$:!j)\ tangent vector {jJioJil!: transposed matrix f:lllll':j

- 26 - u

uncertainty relation ::t:iEtlIiI-W­ uniform divergence -f<~1t\: unconditional convergence _1ll

- 27- v

variation of sign :fq='llt 1££ Venn diagram x~iilI vector angle f!iJ:lll:fi> vertical upward ~:itf!iJJ:i¥.J;;/J vector inner product f!iJ:IltJilffl virtual asymptotic line 1Ei.Wil!r~ vector product f!iJ:li!:ffl virtual circle 1Ei.1m f!iJ:Ilt~"" variation ~:lt; ~~ of particle J1t~(lJl!!lj:!j)U

- 28- x

x approaches c x~~c


zero matrix ~j;g~ zero polynomial ~~lJl;t

- 29 -