Toán học và tuổi trẻ Số 154 (2/1987)

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Toán học và tuổi trẻ Số 154 (2/1987) sau đây trình bày về có thể làm Toán sinh động hơn được không? Đường cong Peano; điểm đặc biệt của họ đồ thị hàm phân thức; toán học và đời sống - tính các chỉ tiêu thời gian trong xây dựng. Mời các bạn tham khảo.

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Nội dung Text: Toán học và tuổi trẻ Số 154 (2/1987)

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f: 1,.*- I j l l t,]l grinrr" - 6c{r r -- 5 : l} silr'i' * r1"*{;-}i$ (e f{'r + !) erlng *h{$re'$*uA { ehu h}, **u sS th$p ph&e n r:ra i'{,r,) s{ /(a- * 1} Sugs it{'t a6i ti6p, k =0, t1,"" {3) --- [,u*$+Zi;r, +t ' 'uh*u trorg:bibu tii6:r thsp p&&r e&a sS e,'su3' tr f(a') =i(,u + I ). Ms u 'thu, a na)'qllehring tb L .,'* -(3 +{:/rS1}8. Asws' ,t f,..,'({} kh6tg od m$t gi* tri sdo efia n o lf, sd v6i P l,il g6e cd sinP = {l - {'i }/3' t'+\' ph rro ng tria h tiI r']ro cd I he aghiSrn NhQn rtt: T{t e& .a* ioi gi&i gtii tdi diu c6 |(t). (2)" (3) vr (,t) f, ttr6*g atru e{eh 1, aou$ IAp lrr$n cS* c{t }:$n 'iftdn rit: C*.e hao :\grrYGn Cing Dia |G:* tai : eds t}*i tl*ng v&.t.hi$u e h$t ch€' .Nop turir),' N.r7ug 0 ls ss bf,t lir', thi it tiah en{t cila i(.r }, vt}i :r G {G, +:a) ta- c6 : Sr,5 ra 0>(ri? - or2 ui..r ', = !,'2' f x: ^ li \- : griyirr t"itng Ddo'' -\ig'r.'/Fn Bira "-\ = I'i{r + u} I u"*-;;J s ,\lrdn ;rdJ (){11t11il tlatg, }'rlug6r 'l'a Dnng' Bt)i ' {hnnh An' ,r'(.i') ;n; tlai \rdn !'lwrtlt, it*uugiit'!"hanh littdtt, Plult'n r.:,f1,r -+ ,lri {)a$nh ?;1u, -iIr.i Tizdi Sop, llainq Q;ttrttt'3.-i-1r"e , Sy - =4 3+h ||.t1;tc I/oon, lI'rin Xiriirz .:\-Id-li, 7-d IlDng Sun, }."guy\n YiQl 7't;nug *6 i,bi giAi rt)t' < _.+- /(.r t /rr. ,r_il ll r+ft Bei .+ ! 5l j Giri; phuo tt4 I ritth : (d.p.*.m) :'*- . '. ?7r-:i.rs{"1'- Sriilt,t' 72, '.\ KEt qu&r tr{n rin dtingg' n6u f 0} t-0 hhfiug Lrii girii.- +{re i,dt*t Br.ta ?-urin r''& Ii'ii;r -f irrln ,v Thq* v'Sv h*m sd l'(,r) = t * rE t.h&a inis iliEa ' ,\,.&dn. i'ip 11 !rrirng Pf fU Le Qrrt l:';*n r'& PTfll * 1 )'0' vd kien *riu nai 1,'6n, rrhr*g /($)p11':r:C{St 1} 7 -l'igt trislt dfr rho dirrii dqug: |l.t-|i.t 'vir -'- 'r + lr'r tl{Ie Si4u fi&rrt 14i phuong ' dun rliQtr t6ug kiri.r;fi{i' i"*): ' ' * . 27**u,ru * Ssin;J-'=' 1fr(aiat.?: e*",,sa'x) ?) f * c6 {h} l}rdy 6sv ii - h*'r* }6i' n&n ' ++'*?e ,:sa.r - 12*inE:r: { (Ssin:r'* }?*ae3'r') = 0 1"i.1 > S. 3"4 t:ti:g. *e'- ri'b .*h-",og -minlt khi.xg .str'. (li[ o S Scos2"r. - 2siu.r') (3' os'.1 r ?ri, .u) ", q{i*h nay nh$ s[ A F (0 ': :* ' 'X{n * c)l = /(tl * )')'u +'li;-v) { l't,t +.- .o (:lcusr.r'* tsin.r') (.q.nu?*' i Sstrne: * {} - I { (r - a');t,ri + itf(Y) : o (3s!r,*,r. * ?slns * 3) igsin?a' $slne,1!) r) - = ' s) 38in*r*?sifi-I, * 3s0€'sitrr p tY lS - 1) 3 l-\t'l t-(g'ttt" -f 2.{'r. /i = 0, :il'"' !l6u )a r' thi * I r' -.e* "- * + 24'r. {1, r7 ! .;'=" l : il. *l ." (1i J :_:.f {y-:-,.r) -1/i.rr < J!-) - /(*j} . r,Oi .r fr+ gdc eir,z l" i" I + { lt-r ll. ".,i :1 . ri
ffi'j ;V-! a I !-ri:;l'r':'' Choll * 0.tlli vd rrpi ti€n:t&t l:(,r:):(flreo, dinh fi8t1 := C*1 ( gde r:hqo c6 iaatr tuong #ug'vudng -\i -% t t'/,,1 * r/J:\ \i-'r-:'--l-\-/* nghiu i!a* h&rrr,) :+ i"{.i I ( . N, A t ,, a-:'" .v 1{y J{,a{J = CAl, * dS' vr}e l&'p}r&n gi{s vr}a lh{e,,xu{t Iir dudns /'...1 lt//. pirAi li'r -+ cao e&a 4'"-- " - - Liyi,{ Iit:) *it * iifiyt t ir'I,' * i1 **; 'l:El 1A trung tuydn cii.e e\ esr .{&F "tn,s*g, - --.. : vA blng e6.elr JSni ttrorg ly ia cir .+ f,'ff = B:IL tg 3'/ : 3'.1r, thea 6iE tpiatla'r * 8.1{t r"6y 'il'ff *-*q'}J * rl q4*! il€a .., ,'- fryl * {(.t'\ t \g t ,? --r-*-..-=.* ' 1"+y r1(.r) ' < l':{g}' ! eqnh 1.8 sa ,lf;"+ CIl vrta I& Su{ng .ph4a gi*.e. v** l$ Su*ng.qno cia A,{EC =} AkEC :.'1, Tr) d$ siljr re f"(a.) rist cli&u tEng trC* [0i rls & C. i &'Jrdi.r e3r:, {.(e }:q:r'-g*i b&i li$n fii&i thco f&t **t e(r; * r l''(;r) * ,'(c), ts co i rihiIrr rf,th t'l.Ae nhsil . r dBu d(:ng. ,: i rr*.8 9-(_.i)' =' r:/'i:ui - f{t} *: e{:r:} -il --:-' 9 -r' BAi ?11 5t r:tw JECD td lu gtatlbico crle dittit khdng ndm trln ?n}t r|.u'dng tran. Gr2i. A'B'C'B' {,i. ttr- gitle c6 e
.: --:-- ---+\ TuongtE C'l-r'.{'*x*C.6'1 F-q : .. v6i I. {tti a* J tr.r)Eg v6i I; ihi .\'rrtng r6i I/. -1----: lt6u ?' khdag trrtng voi Ii thi ? &_ agoii vSog . -/\ lrt)n drrrlng kinh B/r' v& aim troug doln Ml. *rf'{,'r e iz d.:lDC I,9 I e6 ltl LB.y ntn lu0u t'6 -1,\'( N-*. Do d6 -4.'I)'C'lt'ctag I& tu.gi6c i&i i-h6ng aQi Gr-rl .ar, fff, B) t& hluh ebisu vrr0ng g6e efie tidp e uqo. C&og r$y tn..i4i. ro -4'B'e "I;" 16 tir A, II , b 'ltn r!u&-rrg th&rg Cri te e6 ddr = llllt ' gt&* tSt v& hra. nile -{"8", dB etng vu6ng 66e v& Oli=(I}.rlr* AAll,12-rdti&rlg rru&g Utoh crla .r&i 6'I}''s&n A"B'-fl,{,?. Tuong tV B''t:"llE{) hinh thaug Htt $tB.l. Yfly Afl =t{Ui w aAr*EBr st C",1'//Cl . D* dS c{c lam gi{s ,,l".&"C'r va rdc dlfrb" Tu itd dtitm ?.dlug:.-x6,0 Sinh (i.=K] 18Lr illEg'.itqng. L{p lu4'4. iuong !? 1a.e&ng e* y& .{N*,{IJ: l& l6a nh$r; 'c{e eSy tern'gt*t dbng dq*g -'i' ,'t.'1,:l' vi -1 Lr(.': 2. Cdcll rlqrlg: Yli. I hE '--r.'!{:Di efu.rng -tt. 81 aa: F':c"i)" va ac.p; -{n's"ri" sa '1.}9IJ. sr5 re IA hinh ehi:du /vudng g6e e fra -1 vi B t€x Cii I .l r:+ al -lrit-li,t"a ir'6"1."'o" dbng dang. L6y A l.&m tArs drsrlg vdaf trr)a g6a ktnh b) GiA s&.B'r' *dt -qf tgi Ii {irung ol}rn i*a dl1+l?Sl. e,*.t':t*ltgt l/. \'F roag tren dnoc{ kiah CC,r. Tr4s B'l-r' rc dish ahiEu slrrr}ng {1? Fble #ff tiEg; x*e fi) & 3.. Srdrg rhieg nI *&t duorg ' e:::-;h{ra --/) t&i '- -4{i Khi .+ dd ''e trda dusng kinh.AB & If, ndi i{ v6i "4 elt g, ,lB'fi = ."ttl . iedr/lsinlr: O'li * .1r. aos$ilqrislJ. . * .t T'a cs djBm # *&n :dung. y0 3" Ctui'ng nti;rh; Goi rrt lA hinh.chiFu ru5:r$ 0'{i' = l?;; - dn I gdc e.ia a) iga L'8. 1'a co 0(./1 = t.li.llt .r- BB1lr2 = a 4 ..^ {,1,{r * B^Bt)l? qsl /)1 nIm rrtr dLrdrng trda =r .{r-' sia (D + 8,, } eian ein,B dunng kinh E/./. V5r {!u*ng troR EA! ltr6n tzdp Tiien6 try rtlo .:9idoqa, CO'. MFr [h6c lir0n cd .1I thu$c c ..1'= I I)'E'' etn G' + ,fr cung Cl) vA thoo eh*ng rnlqh &- phdu phAe tieh i t t,sia ,{' . sinE' lhi.S1'li l6n ohSt. Do'iI6 rt. Biitt luirrr: t)hi tsirr !uCo c6 rtrQt trgh;+Er hinh duy ah6t. A"'{"' :1 { ,t*t t-% *ruG*fr.iofr+il I I{i$a nhi$r: lr&u .{r lu&a cd m$t lghi$m binh I sin,{ tin ,8 els C rin l) I dr,iy pkdt Afi. Te sE thi ra ti6l il*dug tir*ng . gg!lcfi s€ kh
E r .j (?) Y&i ei&i t .s : :. .., .!l i.,: :i]* I dur!*g !rtng tic i'g, rE, .,rsi,.rg 1ri {u-t biifi lti rtlz r:i.r: drrdn.q thing tg ehr:* tlrillg r, cirEl:r c,it*.r.,, jrnr;' ri,jr ti?i1; t&* t.r!,: mtrl rtri. ildu butru ,-tity rc ' 1& {X) tu *6 ijrr}aS lhi,r,g .r.s r:irt'rr Jiirf j,'jri r,ri t!'i i;lt: I.t,tiitrtt..lR(. 1) ii,lltt n di$nr oria -\'rr" ii,ri,rq tr,r:t j.ql-: ,jh!r:r .r::-!, i j,: i ) diBm cria r*4 \,s it lh.',t pi'{:i I} dti;ir 1r*ns se !.i,i tti,it: {,; ir* /1ri 7'nrij .t,.rr, itr.{ p'I-Tll l t-, n ()iruc lr:iin thi x$ gr,r&*g Hgei). d6 khsng **rx trt;r 1,r, du*q6 ihirig ,,.o--2 e}rba (n * 1l) dibltr e,i+ -{r .,.r! i{ nh5i c6 i.r. * 4 iliErt ,X6t n'r${ tat* gi*u r:(> ba r.s:lh ri lr 1'. p;;.!111 1-.11 trr.llg s$ ilfr !ri:&rg s*ln trea l-n rilig fthr! "i ;r,-h,in !:,lir *1i tij;i) r, i{nr rro d,*;; iir}E ta:rr le 1,..," 6ut?::g th,{*g J-s -.:' lx,,nj *hria {r:* in ?j: i:a; iirl l* / -;..'- *" rlilnr s$a -Ys rS $'t nliSt ir tlc * ::in/?li *ibx: ,,r'-. tr'!'l r; *,il s.i, l-rl (;; .-...r , lrnag 16 drl kl,l1t# rrin-i,.$n hu' .:rj. r::.:ir:lri,.;rr.p u{} i,,r -- ,;i if * }) il * r] qi tl aag gA6 lrcrt{ r'..4r, r$lri;-6g li:;i*;i i..,. j.**t" ,,, .i I-"*lsrr]+r.i]* d,i r;?i: ).-i hj+; jFri iir r.,j: t !**--r:::*1"r-*"t I g- t I "t: :: rL-. ^Ji,a-- 17 eAe dr0m e'.ia -1.-.. itt c{. : \ ,j 3? ixnl > n'r t* - 2) -.i-(r -:-{} * ..; n$n ta od r' :] r-i t.ar'l S i, ltt * irr - :,1i,';,'t1) * *{::) g:::5m;g, -trrV rs : ,fi ;i] '::, ';';,", iigrl : I* titi,ri r1l1n {i} 'ril ! A-i- r:cli iri dj,tr+ ,1$1.1.tr_,.ir ir4* ihi (r) \ P s(n). i.l i ,'l: * ..r. * in .* '1 1',tT BAy gi*, btng ph:t,rrE ijhtFj qui :r1p llr** e.r ta *€ eh&:rg [$ r*ng t-ni r,-rrii fl ]:i.t ki e]6* t*n I -t;'l + i,il - i:^1 -t I + $S -f i),1 .+ lgl ieQl i4p'ir1rp -trn'th5:r er*lr {i}, it} "i& e{i L,] * g{n}. 'i'h&t r{,r:, v
s, ' t dl girii I {e*e. .\rguydn Yan Pho4g i6plg r}riy'&a :* rlg{:.rcis '.'r ,Sxl:r t slssll'* {:lsis -- 3r)/3 x 2Sl9; i.e'13 - I (t) ' . I 1{{t k}rAir " s63.!Nea *5seB" S1S*'3} (:} ''': -Jt ,.t. ] ,. (1)'i'a : : 1r! (e) ta qd ESh -:,?"r'13''=S/ts - 3ce en 7J:3 # 5,,{J i*r J. E S/Jl }rr_r, Sgg}t -,{/'!1. }fl*dn :srdl : Ba-" s6 e6* hq.a k6 th4ru dufrng thing song song v& rr dgng tlnh ch6t vE lt' IQ dlgn rieh s&e' tem giAe dbag dqng 6b eh*rg rl 'rntrli s&e# ag*ili'ggn. H$i eG b4u Bhqlg.sai I&m khi tish to*n. Ri€eg ban ;Yi Le : ?'1i (11 ly I ' Ta c6 5i4gs r* PT1H f{4. N$i. &r:tole;.ciaar} sii' drnq g!nh lf S. .Gei Snelt.* 39., i\{er:elar.tu s€u ctl lei 6t&i,ag[n ggn han c&. MC-="2Btl3 * Srmc * }SiJ I o S.n".*3S/3^lr nAi $/1.{.&: Clle *&t: sd lg ahi6u lr'vA n L,4p' l,ai di-v od |r;.i o* lrif nhu atu i . t !u,ir tirr'r ll:{t I ,'iiia l' :Lu .'t ilrrq: lbr.r:ng iri ar v& drr 1A il' Broe th+? j: e hia ,(' 'r r1*1 thr; n deire thu'ong iX a; ri du i{ r; ivji:ij. ' Tinh tbrg ur * cl + ... * oo' r,Op fis6! c{rrrrcs ' I Dd *)*t Thriiii : ' S&i I$54ittho ttr+t ptra'ng kE 6 vu$ng ttau ffi&i -6,15,t: iho'c ) I, J?!, n I$ cde sd tU vi. II[y tier tI*&ng tron c6 bAn klnh ltln:sh6{ uhi6n' Chfrng nr:nh rfrog: cht 8i gua e.{e Sinh g vr,6ng m{ khdng e{t . ozd.ra *. t b n(6ra*1),,rc ** cin*1i/E). mQt eqnh blnl: vu{lng eAo e&. ' Ta Vdn TV Y# flin& IIda tsdi ?itia : Cirung rniub riag r,6i n:6i 0
rr-'q- n1 .: EAi L,} 1[54: Ch*iig r*inti n'S*g rridi-r t(i f& .t*t.q,** ni tri rri* *;.1 phfurg (R) g*a J/ e'dt Oc, c6e gde niri di{n cria rn*t g6c ianr di$n iA rih.qn, {ly, O: i4n lrsoi i4i .4, B, C. thi sAe €6,: t;l'irr;1 r'f1 1 rO r0n; nLqn. Chinh rAe h6: ui trl ;:fia lF) dt : a') 't'&n6 E.i! + O,B */0* r,:h* nli&t . ' \ , fr) fenI c6s l,in!r p:.]1ro'nS e{* egni'r eria lum 'S&i L?l 15..{ : Cirr,'nr''it j:ri* ts:* riigr: ha :tr}t gi*:, .'lHC' n'ti nlif,t vudng ft,1t;- Ilitm -ii .'d r!l,iir ii ti-rtrg goc dt' \...: , $r1o ?rlrellg Giorig : fl "'*" trl * 12'.* *11 L ,r* - !") ,t, ..!:i,i T riin .1$a! r hiiu F,.*p tr3 . 1.-fhrrng nrinh l")l{ lr}rr lh'.r'y I, flliu"ng n1iuh r*ne s,/ri n:r,i F. { la lrrfiu c6: * 3n;{,, i.,;i},i2 lL-,,;1',.jJ - i.rr,,4 , ! i,.5 3i?p * i)r + I + [l - I{1]' -- i}aj rir,:d},i l15 ':l- CiAi lrhrrtrng iri*ii : v6i bSt k! trl
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