Come risolvere i problemi di matematica. Logica ed euristica nel metodo matematico

254 Pages·1976·3.257 MB·Italian

by  George Polya

Colladniaa ggiornamento
e didassi
11
Titoldoe ll'oopreirgai nale
How tos olviet
Copyrigh©t 1957b y G.P olya
Copyright 19©4 b5y P rinceUtnoinv ersPirteys s
Traduzdiaolnle' idnig lese
MariSap oglianti
Primead iziitoanleia apnra1i9:l6 e7
Secoenddiaz igoinueg1:n9 7o6
Copyrbiyg ht
©
GiangiaFceolmtor inelli Editore
Milano
GeorgeP olya
Come risolvere
i problemi
dim atematica
Logiecdae urisnteimlce at odmoa tematico
FeltriEndeiltloiMr iel ano

Dallap refazailolnpaer imead izione
Und'eiag enirailseo slpveesu snog ranpdreo mbal,em an el­
lar isoludiz tiuotinpt eri o blienmtie ruvnip einzezd iigc eon iit.aà l
Puòt ratdtia rpusrnio blmeomedas ttou;tv itaas,ee sssot uzlzai ca
nostcruar ioesdei cttcàali en orsetf acomletnàt ea,ls io pruat,tt to
ses ir ieasr cies oldvaes rollsoiis , c oplr'inrsaàid ae lla rliac erca e
giodieal slcao p.eS ritmaielsip er,if eantazt etee mpoop porot,u n
possornaop presuennv tearreoe p ropreisoe rcdiezlislopo i ri­
toe lascuinai'rmepn rtonae 'alnlimeo n ecla rraetp teert utltaa
vi.t a
Quinudnii nsegndaimn attee mahtai cuan a pgorsasnidbei li­
tàO.v vmiean,ts eee gli impliese ugoehr ederi là e ziaof naeer s e­
guidreeci a lcaoisl uios it utdiefi,nn ipreàsr o ffociallr oeri on te­
rees,as rersrteai ll orsov ilumpepnot ea slcei upla'propeo rtunità
chgel siip renst.eaI nv,es ceer isvelgalice urrsàii odteàg alliu nni
proponpernodbol deim id ifficoltà aplrlocepo onrozsicoennaztee
delslcao laerl eias icuat ae rriàs ollveqe urees tpiroonpioc sotne
domanodpep uonrete,g lsia pirsàp iirnal roeri olg ustdoi u nr a­
gionamoernitgoi nale.
Anchae q uelsltou deinlct uepi i adnios utdcio ntesmopll­i
tanqtuoa locrhdaei m atemastioi ffcraue n ap articooclcaarsei o­
neN.a turalemgelpniut òse c iupsaesr ilo tasi,n ear riàg uardare la
matemactoimcuean am aetridae lqluaa ldee vrea ggiuunng ere
cerltiov edlicl oon osceec nhzpeao tdriàm entailpc iapurer es to
dopaov esro esntutleo'as mefi na.lQ euesotcac aspiuoòin nfien e
essersem arraintcsahee l 'luanhnoau nan aturianlcel inpaezri one
lam atemcaait;ni tfitae glcio,m oeg nail trraog azdzeova,en croa
scoplreis rupeeo sbsiileidti sà u ogiut s:ic omneo np uòs apesree
glpii acciil oanmop ofinncih néo nn ea vraàs sag.gT iuatttoagvliia
sarfàa cciolmep rencdheer peur no bldie mmaa temaptuiòac sa­
sumeurnea speptitpuoi acesvepo rlees enctoamuteno g ioec-o
7
Prefazioni
nig1mscto,1o ppucrheue n c oncriasgoi onammeennttapoul òed i­
veniurnee sercailztiroe tetcacnittdoaiu n ntave e locpea rtdiit a
teinsnA.v endgous taitlpo i acdeirf ea re mdaetleltmcaiaa e,g li
nond imentimcohletrroaà p idamqeusnettmaea terei caè' una
buonpar obabcihleei stsdàai venqguaa lcpoeslrau : iu nh obby,
oppuurneos trumennetlsolua pa r eosfsioopnpeu,lr aes upar o­
fessisotneeso spap,uu rneag ranadmeb izione.
L'uatorriec olre'dpao icnac ueig leirs at eundtuen,os u tdente
unp op'r esusnota,un oimdaatuo n g rande ddeisc iodmeprrieon ­
derleam atemaetl iafic scaia S.ir ecaòda scolctoanrfee rleensz­e,
sel ibtrein,dt icò a pilrere i soluezdii f oanteits ip o;es ptpiuurnea
domanldota o rmensteamvpapr ie:u " fS,l ar isoluèz sioodndei ­
sfaceen steem bersaa ;tm taac omèep osbsiilien venutnaarr ie­
soluzsiiofftnaaet? quesetsop erimentoe da apffpaacsroceni ­na
Sf,
formael rleal at;mà ac omseip ossosncoo ptrialicr soee ?c ome
E
potrieodi a,s olion,v entares cooppprtuiurrtecetò i o?" .O ggi
l'utaoirnes emganetam atailcla' uint;iàe vgelpriens sao, a lmeno
spercah,qe u alcduensiou osit udepnitupi e rspsiicp aocnigl ae
stedsosmea ned tee ndtiai p paglaar ep rcouporrsiii.aPt ràoprio
sforzannodnso oslit dainc toom prenldare irseo ludziqi uosentoeo
queplr oebml,a maan cihm eo ticvhihe a nncoo ndoatltlsoac elta
did etermmientaotddiiir isoluez sipoineeg aandad lot qriu seti
motiev qiu setmie to,ld i'utaogrieu nas sec rivqeuersetl oi b.r o
Eglsip ecrhaee s ssroaà u tislieaag ilnis egcnhadene tsii dsevrii­no
luppnaerpier opsrtiu deln'btiailn ietrlài solpvreorbels eimaaig li
studmeingtliei doa rt iu tctoil ocrhoie n tendano lsepe rcoo­ndare
priien clinazioni.
Quetsol ib,cr hosei p ropodnipe r esptaatrriec oaltatreen zione
allees igednezgselt iu deen dteigin lsie gndainmt ait emcaadt,oi ­
vrebabnec hien terecsoslaocrrheoes io ccupdaenlovl ieee d ei
mezzdiir iceer cdias cotpaeS.rif afttion teesrsèep iue stedsio
quanstipo o sismam agiLnoas rtee.ss psazoi roi sersvuagiti oo rna­
lies ulrliev iasigt ieo cdhiei n igmisèt iincdaid zeilocl icaro stanza
chei,nr ealstidà e,d imcoal ttoe mpalol rai soludzipi roonbel emi
chneu lhlaan naco h vee decroeln av ita cpaOr.la ttarilde e siderio
dir isolqvueersoetq ou eqlu esinidtiop endendtaeom genvniat ne­
taggmiatoe ricailròei ,fl eutntcaeu riopsiiputr ào founnda an,e lito
ac omprenldeve ireeed i m ez,zl iec auesdei p rocedidmeelnltei
risoluzsitoe.ns is e
Quesptaeg isncer,ii tnut neos i tlpei uttcoosnitcsomo a,s em­
pliiclpe i pu ossib,is loenof ruitltdi o u nl ungep or ofosntduo­
dio demie toddiir isoluTzailosent eu,.dc ihoale cuni autodrei-
8
Prefazioni
signanioln ocmoen e urisotgginico anè, modat;u tvtieaas ­
di di
soh au ng lorpiaoasstsoeo ,f r osuen,f ut.u ro
Sutdianidm oe topdeirl ar isoludzeipior noemb ils,ei s copre
una ltarsop edtetloml aat emcaaSt.ii l,am atemahtadi uceva o l:t i
las ciesnezvaed riEa u cliqduea sleacd o 'lat.rN oe'llasseeut­to
è
clideesosc aia ppaurneas ciesnzitase ma,td iecudatvta;im an ella
pratsiirc iav eulnaas ciesnpzear nitlma,eei nudtt.iQ vuaesdtuie
aspestotnnioa tiin siaelmlseat emsastae mca;am tai,i nu nc erto
snesos,ip uòd irceh iesl e codnide os èsp ii rue ncte:el am atema­
ticians tantaus cennedplir o,sc sedoe al slufao rmoan,zen ionè
maisa ttpar eseenstuaartiae nteimnqe unsettmeoo dnoé a glsuit­
detnin,éa gliin sengtnniaé,a lp ubblicsop encozinaa. tl oiz
Ilc ampdoe' lelruistpirceas emnotlpatl eiccoin nensism:ia toe­
matilcoig,,ip csciiol,oe gdiucaet poerris ifinloo spoofis sotnio­
i
guardarne vari rami codmeel slcseip eecnchzieefi ci dei domini
essrii stpievtamecnotlet i.v La'unatoorpee,er tfmteantceo nscio
delploasb siildiitu àn ac ritdiapc aar dtiec olocrhoen onc on­
dividloesn uooe p in,i openr ionfdoamecnotneps eavodleepi r opri
lim,it tiieandea vanzqauersets ao lpar ecis:a ezgilhoianu ena
granedsep erideirn izusazo ilodnipi r oblee dmiii nsegnamento
delmlaat emaat viacrliaiv e.ll i
Glsit easrsgio mternattiqt uasitr aia nrniorp eisniu nv olume
piaum pieop articolcahrleea 'gugtioharatie on a nimdois crive­
ree p ubbliqcuaarnet o . prima
Univedris itSàt a1n afgoors1dt9,4o 4 .
Dallpar efoanzeai llsae ttirmias tampa
Sono fdeipl oitcreeir c onodsiec sesrereri eu sacm iatnot ene­
res,i pau rienp arutne,ap roemssfao rmautnlae lplrae fazione al­
lap riemdai z:i odniue evo luImdniu ctainoAdnn alionMg ayt he­
matieP cast toefrP nlsa usIinbflee,rc ehncecos etuiitsciolmn ioo
recenteM altaehvmtoairaoc nsPd l ausRiesbaolne,i s nogniols e­
guito pdreelmlepeso sseit nHe owt oS alIv.te
Zuri3g0oa ,g os1t95o4 .
9
Prefazailloans ee coneddzaii one
Quessteac oneddai ziporneesa e,on lttar qeu almcihge liora­
men,tu onan uovqau arta "pPraorbtlees muig,g erimenti, risolu-
.
. ,,
ZlOfil.
Mentrei nce orrals aos tmapa qduise tead iziuosnde ,u no
stud(idEou catTieosntaSilen rgv Pircien,c eNt.Jo .nv;,." Tim"e,
18g iug1n59o6) c hsee mbarvae arvea nzaaltcouo nseesr vaziino ni
prospiot-oe ssneo nc ostituiusncano onvoip teàri lp ubblico
speciaatloiz,ze rmtaae mpcoh fe osseesrposr eei sn termini com­
prensai tbuit:l ti. i"l. a.m atemagtoidcdeae ll'ionncoerdreit o
esserleam atemreinapo o polarcea rdresilcelorala a. s.Itf. iu ctau ri
insegnantia d iemtpeasfinrt aadnraollp alr ei cmel aeslseim e.n.t.a ri
E cosefs rsiit oranlaslnceou opleiern segandau rnean uova gene­
raziaodno ed ialrase t emsastae "r.i a
Specrhole ap r eseendtiez idoenset,ia ndua ntapa i aum pidiaf ­
fusipoonsec,so an vinqcuearlecd uenlioe titc ohrle am atematica,
oltardee sseurneos trumeinntdoi spepneslrai 'bnigleeg needr ià
ogncio noscsecnziae nptiufiòec ssae,rs et imoleadin ntoel rtirvee ­
laruen 'iavtidtteàls lpoi rdii ptroo fovnaodlroe .
Zuri3g0og ,i ug1n95o6 .
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