Table Of Content

MathemaWtoircla•d lV olum1e m>M sa • 101 V.M . Tikhomirov AmericaMna thematiScoalc iety Mathematical AssociatioofnA merica MathemaWtoircl• adVl o lu1m e Storiaebso ut Maxima andM inima V.M . Tikhomirov Transflraottmeh de Rubsy sian Abe Shenitzer AmericMaant hematSioccaile ty MathematAiscsaolc iaotfiA omne rica B.M .T I1XOMJ1POB PACCKAlhl 0 MAKCHMYMAX H MHHHMYMAX <<HAYKA». MOCKB1A9.S 6 Abe Translaftreodm tRhues sibayn Shenitzer 1991 OOA07. Matlu!SnuwhtjiCeclcvat l l'ifuaPrtiimoarny. OOA300.0 A350,1 -014.6 -01. 49-01.4 94199-90 3. LibraorfCy o ngrCeas!>t alo-giinn-gPublDiactaat ion TikhomirVolv,,t diMm i(rV ladiMmiirk hailovich), 1934- Storidebso umta ximadn dm inima/MV Tikhomirov p em Md(t hemdtiwcoarll dI.S SNI 0 55-942I6 ,) ISBN0 -8:!18-0165-1 I Maximaan dm inimd2 dCl culouf�V dirdtion3s Mathemdtiocpdtli miZdtion QA306T 55 1990 90-21246 5116'6 dc20 CIP Copyianngdr eprintInidnigv.i druca,lt doefrt sh ipsu blicatainodnn o,n prolfiibtr ..ttrcitcfison rgt hem, arep emrittetdom .tkfea iurs co ft hem aterisaulc,dh S tcoo pya chaptfeorru sei nt eachionrrg e search Permissiisog nr antteodq uotber iepf. tss.f.trgoemts h ipsu bclaitiionnr eviepw1s0,v idtehdec ustomary dcknowledgmofet nhtes ourciesg iven Rcpublicdstyi�cotmnd,t icco pyinog:rm, ultiprleep roducotfia onnym ateriatlh ipisun b clditi(oinn ­ cludidnbg:s tr,itscp tesmr)i tteodn luyn delri cenfsreo mt heA mericMaant hematiScoacli eRteyq uesftosr such permis�hsoiuolbend addrestsoet dh eA ssisttaont th eP ublisAhmeerr,i caMna them.ttSioccdile ty, PO Box6 248P,r ovidenRchoed,e l sl.0.t2n9d4 0-62R4e8q uesctasn. llbes om ddeb ye -matiolr eprint­ perm1SS1on�math.ams.org © Copyrig1h9t9 0b yt heA mericdMnd themdtiScoacli etAyl lr ighrtess erved Printiend tUhnei teSdt atoefsA merica TheA mericdMna thematiScoacli ertcyt didnlslr ights exceptth o�gcr antteodt heU niteSdi dlGeosv ernment @ Thep apeurs edi nt hibso oki s. tcid-afnrdcf ca lwlist hitnh eg uidelines cstdblitsohc cnds urpcc mrdnencden dd urability 0 Printoend r ecyclpeddp cr 109 8 67 5 43 2 009 99 89 79 69 5 Tot hMee mory ofMy D eFarri end, V.M .A lekseev TabloefC ontents Iondturction . . . . . . . . . . . . . .i x . . . . . . . . . . . . . . . . . . . . . ParOtn e. AncieMnatx imuma ndM inimuPmr oblems Tefih rsstto ry WhyD oW eS olMvaex iamnuMdmi nimum Problems? . . . . . . . . . . . . . . . . . . . . . 3 Teshc eond story The OPlrdoebslte m-Dido's Problem .. . 9. Tehti hsrtdo ry MaxiamnMadi niiNnma aet ( uOrptics) . . 1.9 Tefhu osrttho ry MaxiamnMadi niiGnme ao metry .. . .2 7. . Teh fifth story MaxainmMdai niiAnml ag aenbidrAn an alysis 37 Teshx istyth o r KeplPerro'b.sl em . 47 Teh seventh story ThBer achistochrone 55 Teehg tihsht ory NewtAoeonrd'ysn aPmriocb.al..le. .m. . 65 ParTtw o. MethodsS oolfu toifoE nx tremal Problems Tehn isnttohr v WhaiatsF unc.t.i.o.n..? . . 81 Teht esnttohr y Whaiatsn E xtrPermoab.ll. e m? 93 Teeh elnsettrho rr ExtreFmuan cootffi oVOnansre i able 99 viii CONTENTS Teht wseytl oftrh Extroefm aF uonfMc atnViyao rneissa .b l ThLea grParnignec iple . . . . .1 0.9 . . . . . Tehti hernsttteho ry More PSroolbvlienmg . . . . . 1.1 9 . . . . . . . . Tefhu orstteoernyt h WhaHta ppLeanitetendhr T e h eooEfrx yt remal Problems? . . . . . . . 1.4 3. . . . . . . . . . . . . Tehl satsotr y MorAec curaDa itseclu.ys.,.s ..i..o.n . 179 Biiobg.lr aphy 187 Introduction In ldeiai fitcl oyin ss nteacnettscloshy ao roybs eeps otts h(seoi pbtlei mal) soluAtt ireomne.nn udmoobusfesu rp c rho balreiimenssc e o naonmidin c s technIosnlu cocaghisy te.fs ru ieesqn utsletyfro ue lst omora tt hematics. Inma thetmhasett iuocdfmsy a, x iamnumdmi nimum bpegraonb lems av elroytn igam geio nf,ca tt,w entcye-nfitavugeroF i.oae rl s o tnigm e thweernreoe u noirfwma oyfts a cpkrloibnflgrofie nmdsei xntgrT ehmea . firgsetn meertaholiof nd vse isoatnnsi dgo alotueftx itorpner bmolaewlme sr e create3d0y 0e aaabrgoasoutt ,th t ei omfte h fero matofim oant hematical analysis. Theibnte ccalmteeha caret r stpaeiocnpi tailm pirzoabtlieaom ns play crurcoiiltanehl n ea tsucriaeSlnp ceecsii.wfit ac fsauo lntldhy ma,at n y laws of enc aabtnedu errfirmvos eod- c"avlalreipdar tiinocAnicapcllo ersd.i"n g ttoh persien gciivapenlcnyeo sl,lo efac dtmiiosns ibwlheda itsm totiino­ns, guitshhaeec stm uoatloi fom nea c hasnyisoctrael lmio ,fge hltec,at ricity, fluagi adas,n,s d o iotsnh i,at t maxmiimniiizzcmeeessr q tuoaarin nt ities. Somceo ncerxettrpeerb molaewlmh soc,so en dteernfitrv otemhsn e a tural sci(etnbhcreea sc hipsrtoobNclehewrmtop,onr neo' basln oedtm h,we errse) , posetdhe enao dtft hsee tveeencnetnyht.T u hre tnose oeltdvh eea sse , welmla noayts ph reorb olgfee mosmm eetcrhyaa,nn pdih cysls,eit dco s ,t he creoaftn ieaobw nr anch ofa nmaatlthychasaetimtm seoa k tnbioecaw asnl thcea locvfua lruisa tions. Thien tednesvievleoo ftp hmceea nltco ufvl aiurastc ioonuntesfid ron abotuwctoe ntMuarnioyef s fi.tn hesesc ti eonft eitishgtehs at nede nth nienteceenntthtu oroikie nsp patrrhotiac sne dsts,h, be be yg ionftn hiinsg cenitsuter eyam,ise tf dh eye xhhaatduh set etdo pic. Buittt nu erodut th tahtwi asns o tc atsThehen.e e eodfps r acleti.if cal espeicenic aolnlaoynmt die ccsh ngoarlvioetsg noeye p ,wr obtlhceaomtus l d nobtes olbvyte hodel m de thOondhesa t.dao d vaInwtca ens.e cessary tcor eana etfiwee olfmd a theamnaatlikycnsaoaiwl"ssn c n, ov aenxa lysis," invotlhsveti uondfgy c fonuncvteaixnoc dno sn vexp reboxltermesm.a l ix

Description:
Throughout the history of mathematics, maximum and minimum problems have played an important role in the evolution of the field. Many beautiful and important problems have appeared in a variety of branches of mathematics and physics, as well as in other fields of sciences. The greatest scientists of
ebook img

Stories About Maxima and Minima PDF

200 Pages·1991·2.04 MB·English
by  V. M. Tikhomirov
Save to my drive
Quick download
Download
Upgrade Premium
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Stories About Maxima and Minima

MathemaWtoircla•d lV olum1e m>M sa • 101 V.M . Tikhomirov AmericaMna thematiScoalc iety Mathematical AssociatioofnA merica MathemaWtoircl• adVl o lu1m e Storiaebso ut Maxima andM inima V.M . Tikhomirov Transflraottmeh de Rubsy sian Abe Shenitzer AmericMaant hematSioccaile ty MathematAiscsaolc iaotfiA omne rica B.M .T I1XOMJ1POB PACCKAlhl 0 MAKCHMYMAX H MHHHMYMAX <<HAYKA». MOCKB1A9.S 6 Abe Translaftreodm tRhues sibayn Shenitzer 1991 OOA07. Matlu!SnuwhtjiCeclcvat l l'ifuaPrtiimoarny. OOA300.0 A350,1 -014.6 -01. 49-01.4 94199-90 3. LibraorfCy o ngrCeas!>t alo-giinn-gPublDiactaat ion TikhomirVolv,,t diMm i(rV ladiMmiirk hailovich), 1934- Storidebso umta ximadn dm inima/MV Tikhomirov p em Md(t hemdtiwcoarll dI.S SNI 0 55-942I6 ,) ISBN0 -8:!18-0165-1 I Maximaan dm inimd2 dCl culouf�V dirdtion3s Mathemdtiocpdtli miZdtion QA306T 55 1990 90-21246 5116'6 dc20 CIP Copyianngdr eprintInidnigv.i druca,lt doefrt sh ipsu blicatainodnn o,n prolfiibtr ..ttrcitcfison rgt hem, arep emrittetdom .tkfea iurs co ft hem aterisaulc,dh S tcoo pya chaptfeorru sei nt eachionrrg e search Permissiisog nr antteodq uotber iepf. tss.f.trgoemts h ipsu bclaitiionnr eviepw1s0,v idtehdec ustomary dcknowledgmofet nhtes ourciesg iven Rcpublicdstyi�cotmnd,t icco pyinog:rm, ultiprleep roducotfia onnym ateriatlh ipisun b clditi(oinn ­ cludidnbg:s tr,itscp tesmr)i tteodn luyn delri cenfsreo mt heA mericMaant hematiScoacli eRteyq uesftosr such permis�hsoiuolbend addrestsoet dh eA ssisttaont th eP ublisAhmeerr,i caMna them.ttSioccdile ty, PO Box6 248P,r ovidenRchoed,e l sl.0.t2n9d4 0-62R4e8q uesctasn. llbes om ddeb ye -matiolr eprint­ perm1SS1on�math.ams.org © Copyrig1h9t9 0b yt heA mericdMnd themdtiScoacli etAyl lr ighrtess erved Printiend tUhnei teSdt atoefsA merica TheA mericdMna thematiScoacli ertcyt didnlslr ights exceptth o�gcr antteodt heU niteSdi dlGeosv ernment @ Thep apeurs edi nt hibso oki s. tcid-afnrdcf ca lwlist hitnh eg uidelines cstdblitsohc cnds urpcc mrdnencden dd urability 0 Printoend r ecyclpeddp cr 109 8 67 5 43 2 009 99 89 79 69 5 Tot hMee mory ofMy D eFarri end, V.M .A lekseev TabloefC ontents Iondturction . . . . . . . . . . . . . .i x . . . . . . . . . . . . . . . . . . . . . ParOtn e. AncieMnatx imuma ndM inimuPmr oblems Tefih rsstto ry WhyD oW eS olMvaex iamnuMdmi nimum Problems? . . . . . . . . . . . . . . . . . . . . . 3 Teshc eond story The OPlrdoebslte m-Dido's Problem .. . 9. Tehti hsrtdo ry MaxiamnMadi niiNnma aet ( uOrptics) . . 1.9 Tefhu osrttho ry MaxiamnMadi niiGnme ao metry .. . .2 7. . Teh fifth story MaxainmMdai niiAnml ag aenbidrAn an alysis 37 Teshx istyth o r KeplPerro'b.sl em . 47 Teh seventh story ThBer achistochrone 55 Teehg tihsht ory NewtAoeonrd'ysn aPmriocb.al..le. .m. . 65 ParTtw o. MethodsS oolfu toifoE nx tremal Problems Tehn isnttohr v WhaiatsF unc.t.i.o.n..? . . 81 Teht esnttohr y Whaiatsn E xtrPermoab.ll. e m? 93 Teeh elnsettrho rr ExtreFmuan cootffi oVOnansre i able 99 viii CONTENTS Teht wseytl oftrh Extroefm aF uonfMc atnViyao rneissa .b l ThLea grParnignec iple . . . . .1 0.9 . . . . . Tehti hernsttteho ry More PSroolbvlienmg . . . . . 1.1 9 . . . . . . . . Tefhu orstteoernyt h WhaHta ppLeanitetendhr T e h eooEfrx yt remal Problems? . . . . . . . 1.4 3. . . . . . . . . . . . . Tehl satsotr y MorAec curaDa itseclu.ys.,.s ..i..o.n . 179 Biiobg.lr aphy 187 Introduction In ldeiai fitcl oyin ss nteacnettscloshy ao roybs eeps otts h(seoi pbtlei mal) soluAtt ireomne.nn udmoobusfesu rp c rho balreiimenssc e o naonmidin c s technIosnlu cocaghisy te.fs ru ieesqn utsletyfro ue lst omora tt hematics. Inma thetmhasett iuocdfmsy a, x iamnumdmi nimum bpegraonb lems av elroytn igam geio nf,ca tt,w entcye-nfitavugeroF i.oae rl s o tnigm e thweernreoe u noirfwma oyfts a cpkrloibnflgrofie nmdsei xntgrT ehmea . firgsetn meertaholiof nd vse isoatnnsi dgo alotueftx itorpner bmolaewlme sr e create3d0y 0e aaabrgoasoutt ,th t ei omfte h fero matofim oant hematical analysis. Theibnte ccalmteeha caret r stpaeiocnpi tailm pirzoabtlieaom ns play crurcoiiltanehl n ea tsucriaeSlnp ceecsii.wfit ac fsauo lntldhy ma,at n y laws of enc aabtnedu errfirmvos eod- c"avlalreipdar tiinocAnicapcllo ersd.i"n g ttoh persien gciivapenlcnyeo sl,lo efac dtmiiosns ibwlheda itsm totiino­ns, guitshhaeec stm uoatloi fom nea c hasnyisoctrael lmio ,fge hltec,at ricity, fluagi adas,n,s d o iotsnh i,at t maxmiimniiizzcmeeessr q tuoaarin nt ities. Somceo ncerxettrpeerb molaewlmh soc,so en dteernfitrv otemhsn e a tural sci(etnbhcreea sc hipsrtoobNclehewrmtop,onr neo' basln oedtm h,we errse) , posetdhe enao dtft hsee tveeencnetnyht.T u hre tnose oeltdvh eea sse , welmla noayts ph reorb olgfee mosmm eetcrhyaa,nn pdih cysls,eit dco s ,t he creoaftn ieaobw nr anch ofa nmaatlthychasaetimtm seoa k tnbioecaw asnl thcea locvfua lruisa tions. Thien tednesvievleoo ftp hmceea nltco ufvl aiurastc ioonuntesfid ron abotuwctoe ntMuarnioyef s fi.tn hesesc ti eonft eitishgtehs at nede nth nienteceenntthtu oroikie nsp patrrhotiac sne dsts,h, be be yg ionftn hiinsg cenitsuter eyam,ise tf dh eye xhhaatduh set etdo pic. Buittt nu erodut th tahtwi asns o tc atsThehen.e e eodfps r acleti.if cal espeicenic aolnlaoynmt die ccsh ngoarlvioetsg noeye p ,wr obtlhceaomtus l d nobtes olbvyte hodel m de thOondhesa t.dao d vaInwtca ens.e cessary tcor eana etfiwee olfmd a theamnaatlikycnsaoaiwl"ssn c n, ov aenxa lysis," invotlhsveti uondfgy c fonuncvteaixnoc dno sn vexp reboxltermesm.a l ix

Description:
Throughout the history of mathematics, maximum and minimum problems have played an important role in the evolution of the field. Many beautiful and important problems have appeared in a variety of branches of mathematics and physics, as well as in other fields of sciences. The greatest scientists of
See more

The list of books you might like

Upgrade Premium
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.
DMCA & Copyright: Dear all, most of the website is community built, users are uploading hundred of books everyday, which makes really hard for us to identify copyrighted material, please contact us if you want any material removed.
Copyright @ PDFdrive.to, 2022 | We love our users