Isibalo esikhulu seMathematika u-Euler Leonard: impumelelo kwimathematika, inyaniso enomdla, i-biography emfutshane

Leonhard Euler - yezibalo Swiss physics, omnye wabaseki lemathematika ehlambulukileyo. Wenza nje kuphela imirhumo ezingundoqo kwaye lusetyenziswa geometry, calculus, ukusetyenziswa kunye nethiyori ye amanani, kodwa kuphuhliswa neendlela zokusombulula iingxaki ngeenkwenkwezi lokuqwalasela yaye basebenzisa imathematika zobunjineli kunye nemisebenzi yoluntu.

Euler (sezibalo): ibhayografi emfutshane

Leonhard Euler wazalwa Aprili 15, 1707 Loo Paulus Euler noMargaret Brooker ebengowamazibulo. Uyise livela uhlobo othobekileyo weengcibi, kunye iminyanya Margaret Brooker waba eziliqela izazinzulu ezaziwayo-kakuhle. Paulus Euler wakhonza ngelo xesha umfundisi kwi Church of St. Jakob. Ngenxa yenkolo, uyise kaLeonard wayenomdla kwimathematika, yaye kwiminyaka emibini yokuqala ukufunda eyunivesithi baya kwiikhosi edume Yakoba Bernulli. Emva konyaka onesiqingatha emva kokuzalwa konyana wabo, intsapho yakowabo yafudukela Riehen, Basel-dolophu apho Paulus Euler waba ngumfundisi lendawo. Apho ke bakhonza de kwasekufeni kwakhe.

Intsapho yayihlala kwiimeko emxinwa, ingakumbi emva kokuzalwa komntwana wakhe wesibini, uAnna-Maria, ngo-1708. Esi sibini iya kuba ngabantwana ababini nangaphezulu - Maria Magdalena kunye uJohann Heinrich.

Izifundo yokuqala kwimathematika, uLeonard wafumana ekhaya kuyise. Ehlabathini eneminyaka esibhozo koko wathunyelwa kwisikolo Latin e Basel, apho wahlala endlwini kuninakhulu. Ukuze kubuyekezelwe umgangatho ophantsi wemfundo ezikolweni ngelo xesha, utata waqesha wawungumkhapheli yabucala, umfundi wezakwalizwi oselula ogama uJohannes Burckhardt, umthandi neqhayiya lemathematika.

Ngo-Oktobha 1720 eneminyaka engama-13, uLeonard wangena University of Basel kwi-Faculty of Philosophy (meko ngelo xesha), apho waya kwiiklasi ezitshayelela sabaqalayo zemathematika Ioganna Bernulli, umzalwana omncinane kamfi ngexesha kaYakobi.

Euler Young ngenzondelelo waluthabatha izifundo zakhe, nto leyo kungekudala kwatsala ingqalelo ngutitshala, ngubani bamkhuthaza ukuba afunde iincwadi entsonkothileyo kakhulu abakhe bakhe, wada wacela ukusinceda kwizifundo zabo ngeMigqibelo. Ngowe-1723, uLeonard abagqibe imfundo yakhe isidanga master waza wanikela intetho yesidlangalala Latin, apho Descartes kuthelekiswa inkqubo kunye bulumko bendalo Newton.

Emva iminqweno yabazali bakhe, abhalise kwi Theological Faculty, nikela, Noko ke, uninzi imathematika ixesha. Ekugqibeleni, mhlawumbi xa ukunyanzelisa ka Ioganna Bernulli uyise wathabatha ngenxa wamnika unyana wakhe ukuba enze njongo lwezenzululwazi, kungekhona umsebenzi zenkolo.

Kwiminyaka eli-19, i-Euler sezibalo nabuganga ukukhuphisana izazinzulu ephezulu xesha, ukuthatha inxaxheba kukhuphiswano isisombululo ka Paris Academy of Sciences kwi nokubekwa ngokupheleleyo iimasti nqanawa. Ngelo xesha ke sasingahlali ubone ngeenqanawa yobomi bam, ibhaso lokuqala akukho iphumelele, kodwa waphumelela indawo yesibini ezidumileyo. Kunyaka xa kukho isithuba kwiSebe Physics kwiYunivesithi Basel, Leonard, exhaswa nomcebisi wakhe Ioganna Bernulli, wagqiba ukuba alwe indawo, kodwa walahlekelwa ngenxa yobudala babo kunye nokungabikho kukho uluhlu khorwisaka ezipapashiweyo. Xa mqondo nethamsanqa kuba yakwazi ukwamkela isimemo ye-St Petersburg Academy of Sciences, yasekwa kwiminyaka embalwa ngaphambili Tsar Peter I, apho Euler wafumana intsimi ethembisayo ngakumbi, nto leyo eyamnceda ukuze ngokupheleleyo. Indima engundoqo edlalwa Bernoulli kunye noonyana bakhe ababini, uDaniel Nicklaus II mna, nabasebenza ngenkuthalo apho.

St. Petersburg (1727-1741): a ukunyuka meteoric

Euler wachitha ubusika ka 1726 e Basel, ukufunda nokwakheka amalungu ukulungiselela ekwenzeni imisebenzi yabo kulindeleke kule Akhademi. Xa efika e St. Petersburg wasebenza isalamane, kwacaca ukuba kufuneka azinikele yesayensi zemathematika. Ukongeza, yi Euler kwakufuneka ukuba bathathe inxaxheba isigqibo-iimviwo kwi yeCadet lweSizwe, kunye nokucebisa uRhulumente kwimiba eyahlukeneyo lwenzululwazi nobugcisa.

lula uLeonard ingaguqulwa ezintsha iimeko ezimaxongo ubomi kumntla Europe. Ngokwahlukileyo namanye amalungu bezinye iintlanga akhademi, ngoko nangoko waqalisa ukufunda ulwimi Russian yaye ubuchule ngokukhawuleza ngeendlela ezibhaliweyo ngomlomo. Kangangexesha wayehlala Daniel Bernoulli yaye abahlobo kunye Christian Goldbach, uNobhala obungesosigxina the Academy, namhlanje eyaziwa ngokuba ndisaya ayilungiseki le ngxaki bayo, kuyo naliphi inani 4, angamelwa isiphumo etsala ezimbini. Imbalelwano omkhulu phakathi kwabo, yinto ebalulekileyo yembali zenzululwazi kwinkulungwane XVIII.

Leonhard Euler, impumelelo kwimathematika okukhuphileyo enyamekile nodumo ehlabathini lonke waphakamisa sakhe, kubanjelwa Academy of kwiminyaka yabo kakhulu nemveliso.

NgoJanuwari 1734, watshata Katarine Gzel, intombi umzobi Swiss, owafundisa kunye Euler, baza bafudukela kwikhaya labo. Umtshato weza ukuba zikhanyise abantwana-13, apho ke, ezintlanu kuphela ifikelele ebudaleni. Owamazibulo, uJohann Albrecht, naye waba kwezezibalo, yaye kamva wanceda uyise emsebenzini wakhe.

Euler akazange usizi. Ngowe-1735, waba wagula kakhulu yaye phantse wafa. Ukuze yoncedo omkhulu zonke, wabuyisa, kodwa emva kweminyaka emithathu emva uyagula. Ngeli xesha, esi sifo ixabise yena iliso lasekunene, nto leyo ebonakala gca phezu zonke enemifanekiso yabantu izazinzulu ukususela ngelo xesha.

Ukungazinzi kwezopolitiko eRashiya, nto leyo eyenzeka emva kokufa Queen Anna Ivanovna, Euler kwanyanzeleka ukuba ushiye eSt Petersburg. Ngokukodwa ekubeni isimemo esivela Prussia uKumkani Friedrich II ukuza eBerlin nokunceda ukwakha i Academy of Sciences apho.

NgoJuni 1741, Leonard kunye nomfazi wakhe uKatarina, uJohann Albrecht oneminyaka eli-6 ubudala kunye noCarl oneminyaka ubudala evela St. Petersburg ukuya Berlin.

Jobs in Berlin (1741-1766)

Kumadabi eSilesia Frederick II iye elinye izicwangciso ngokusekwa yale Akhademi. Kwaye kuphela ngo 1746 ke ekugqibeleni kwasekwa. Waba umongameli Pierre-Lui Moro de Maupertuis kunye Euler wamiselwa umlawuli we-Mathematics yeSebe. Kodwa phambi koko, akazange ahlale bengasebenzi. ULeonard wabhala amanqaku zenzululwazi malunga 20 ezinde 5 ezinkulu yaye wenza iincwadi ezingaphezu kwama-200.

Nangona isibakala sokuba Euler wenza imisebenzi emininzi - unoxanduva Observatory kunye neegadi zezityalo, ukusombulula abasebenzi kunye nemiba yezemali ababandakanyekayo ekuthengisweni achaza, besenza mthombo bengeniso Academy, singasathethi ke iiprojekthi lobuchwepheshe kunye nobunjineli ezahlukeneyo, ukusebenza kwayo imathematika ayiphazamiseki.

Kwakhona, oko akuyi kakhulu aphazanyiswe kwihlazo ngayo igunya kokufunyanwa umgaqo intshukumo incinane, leyo yaqhambuka 1750s yokuqala, yafunwa yi Maupertuis ukuba umngeni sisazinzulu Swiss kunye academician asanda kunyulwa uJohann uSamuweli Koenig, ukuthetha athetha ngayo Leibniz wabhalela yezibalo uYakobi Hermann. Koenig wayesondele Maupertuis izimangalo zokuveza. Xa wacelwa ukuba avelise incwadi, akaba nako ukuyenza loo nto, yaye Euler wabelwa ukuba kuphanda ityala. Ukuba akukho uvelwano kwintanda-bulumko Leibniz, ngenxa yokuthethelela umongameli yaye emangalela König lobuqhophololo. Ingongoma ukubila yafikelelwa xa uVoltaire, owazeka icala Koenig wabhala uvuthondaba kubuhlungu, lampooned Maupertuis kunye Euler basinda. Umongameli wacaphuka gqitha kangangokuba washiya eBerlin kamsinya, Euler kwaye kwafuneka ukuba sijongane, de facto ekhokelwa yi-Academy.

sesayensi ekhaya

ULeonard waba mkhulu kakhulu kangangokuba sathenga Estate Charlottenburg, namadlelo basentshona eBerlin kaThixo, enkulu ngokwaneleyo ukuze kuqinisekiswe ukuhlala obutofotofo unina ongumhlolokazi, lowo kuziswa eBerlin ngowe-1750, isiqingatha-udade bonke abantwana bakhe.

Ngowe-1754, wamazibulo uJohann Albrecht ngengcebiso Maupertuis eneminyaka engama-20 kwaye kunyulwa Berlin Academy. Ngowe-1762, umsebenzi wakhe perturbations ze umzila ezinomsila kume yeeplanethi lawongwa ngebhaso le St. Petersburg Academy, leyo yena nabalandeli Alexis-Klod Klero. unyana wesibini Euler kaThixo, uCarl, wafunda amayeza e Halle, kwaye eyesithathu, Christoph, waba ligosa. Intombi yakhe Charlotte watshata intshisakalo Dutch kunye nodadewabo omdala Helena ngowe-1777 - ligosa Russian.

King agile

Relationship Isazinzulu Frederick II kwakungelula. Oku lunemiqathango inxenye kwi umahluko omkhulu okulahlekiswa kunye bulumko Frederick - a abanekratshi, ukuzithemba, ezintle nehlekisayo lokuxoxa, kukho sympathizer le-French yiEnlightenment; sezibalo Euler - kumProtestanti obulula, eyingqondi, ungowomhlaba kunye ozinikeleyo. Enye, isizathu mhlawumbi kubaluleke nangakumbi ingqumbo ULeonard ukuba akazange intsika umongameli Berlin Academy. Le ingqumbo ikhule kuphela emva kokuba sokuhamba Maupertuis kunye neenzame Euler ukuze ugcine iziko udlule, xa Frederick wazama umdla isitulo kamongameli Jean d'Alembert Leron. Le yokugqibela, enyanisweni, weza Berlin, kodwa kuphela ukuba uxelele uKumkani malunga disinterest wakhe Share Leonard. Friedrich alihoywa ukuze nje icebiso D'Alembert, kodwa wathi washo ngokwakhe intloko yale Akhademi. Oku, kunye nezinye iintsilelo ezininzi uKumkani, ekugqibeleni, kukhokelele kwinto yokuba biography of yezibalo Euler wajika elibukhali umva.

Ngowe-1766, phezu kwazo zithintelo yinxalenye kumkani, wamshiya eBerlin. ULeonard iye yavuma isimemo ka uCatherine II ukubuyela eSt Petersburg, apho ndamkelwa umva ngokusesikweni.

Kwakhona, St. Petersburg (1766-1783)

Amoyika yaye baqubuda kwi nesikolo kwinkundla uCatherine sezibalo omkhulu Euler wasebenza sithuba ophambili kakhulu yaye Iimfundiso eyanikelwa ayinikwa elide kangaka eBerlin. Enyanisweni, wadlala indima yokuba inkokeli ngokomoya, ukuba intloko yale Akhademi. Ngelishwa, Noko ke, impilo akayi yonke into waya kakuhle. cataract iso sasekhohlo, eyaqala ungenakuwuxhalabela naye Berlin ukuba inobungozi kakhulu, yaye ngo-1771 Euler wagqiba kwi uqhaqho. Ekugqibeleni kwaba ukubunjwa ithumba, abatshabalalisa phantse ngokupheleleyo umbono.

Kwangaloo nyaka, ngexesha emlilweni enkulu eSt Petersburg, waphuka indlu yakhe ngomthi, kunye Euler phantse uyimfama ayikwazanga atshiswe ephila kuphela Bulelani kokuhlangula yobuqhawe Peter Grimm, yomsebenzi wezandla evela Basel. Ukuze abancede, uKumkanikazi sele zabelwe imali ukulungiselela ukwakha ikhaya elitsha.

Elinye igalelo enzima engakuqondi Euler ngo-1773 xa eswelekelwe ngumfazi wakhe. Emva kweminyaka emi-3, ukuba baxhomekeke abantwana babo, watshata ixesha yesibini umsakwabo enesiqingatha, uSalome uAbhigali Gsell, (1723-1794).

Nangona zonke ezi ziganeko ezibulalayo, sezibalo Leonhard Euler enikelwe kwinzululwazi. Eneneni, malunga nesiqingatha umsebenzi wakhe yapapashwa okanye wazalwa eSt Petersburg. Phakathi kwazo kukho ezimbini "ethengwa 'yakhe -". Algebra "" Iileta kwi Princess isiJamani "yaye Ngokuqhelekileyo, akaba nako ukuyenza ngaphandle kokuba unobhala elungileyo kunye noncedo sobugcisa kubonelelwa, phakathi kwezinye izinto, Nicklaus zinani, a compatriot ye Basel kunye nomyeni elizayo umzukulwana ka Euler. inxaxheba kwinkqubo yokuthatha unyana wakhe uJohann Albrecht. Le yokugqibela kwakhona wenza njenge Iiseshoni Academy stenographer apho ingcali yenzululwazi, njengelungu epheleleyo omdala, kwafuneka ukuba sesihlalweni.

ukufa

Sezibalo omkhulu Leonhard Euler wabulawa zestrowuku-18 Septemba 1783 xa edlala kunye nomzukulwana wakhe. Ngomhla ukufa zayo ezimbini ezinkulu zileyiti kwafunyanwa ifomula ezichaza ukuba andize ngebhaluni, ngoJuni ogqibeleleyo-5, 1783 eParis, abazalwana Montgolfier. Le mbono waphuhliswa kwaye walungisa ekupapasheni uJohann, unyana. Kwakuyinto yokugcina ukuba sisazinzulu, eyapapashwa ngo-1784 Memoires umthamo. Leonhard Euler kunye namagalelo bakhe kwimathematika kangangokuba kakhulu ukuba amanani amanqaku elindele ithuba lazo kwiijenali zemfundo, iye yapapashwa iminyaka engama-50 emva kokufa sisazinzulu.

umsebenzi Scientific e Basel

Kwithuba elifutshane Basel Euler igalelo zemathematika kwakulula ukuba ezigoso isochronous kwaye efanayo, kwakunye umsebenzi kukhuphiswano umvuzo Paris Academy. Kodwa ke kunzima iphambili kweli nqanaba yaba Dissertatio Physica de Sono, bafake ukuxhasa ukutyunjwa kwakhe esitulweni wezenzululwazi kwiYunivesithi Basel, kuhlobo kunye nokuhanjiswa isandi, ingakumbi, isantya isandi kunye nesizukulwana izixhobo zomculo.

Ixesha St. Petersburg lokuqala

Phezu kwazo nje iingxaki zempilo ezifunyanwa Euler, ikhula kwimathematika, ISAZINZULU akakwazi kodwa libangele wothuka. Ngeli xesha, ukongeza kwimisebenzi esisiseko kwi ukukhanda, ingcamango umculo, kwakunye bokwakha yomkhosi wamanzi, yena ubhale amanqaku 70 engezihloko ezahlukeneyo uhlalutyo zemathematika kunye nethiyori inani iingxaki ezithile physics, ubucukubhede kunye neenkwenkwezi.

imiqulu emibini "Mechanics" yaba sisiqalo kwesicwangciso ezihlala zihleli uhlolo olubanzi zonke iinkalo ukukhanda, kuquka ubucukubhede lwamaqumrhu eqinileyo, bhetyebhetye yaye ilastiki, kwakunye ulwelo ubucukubhede izikhakhamela.

Njengoko kubonakala inowuthi-books Euler, ukanti e Basel, wacinga lukhulu malunga umculo kunye nokwakheka zomculo kwaye uceba ukubhala incwadi. Ezi zicwangciso ziye kuvuthwa eSt Petersburg kwaye kwanika ukonyuka kuye yabasebenzi Tentamen, eyapapashwa ngo-1739. Le mveliso iqala ngengxoxo yohlobo isandi xa intlokoma kwamasuntswana zomoya, kuquka ukusasazwa kwayo, zomzimba ingqikelelo yezandi zezizukulwana umsindo izixhobo umtya kunye nomoya.

Undoqo umsebenzi imfundiso iziyolo okubangelwa umculo Euler wadala ngokumisela ngezandi lekhefu, ukulele okanye ulandelelwano amaxabiso ngamanani, ubungakanani ekulelona "ukuthandeka" lobume somculo: inowuthi inqanaba, kokukhona uyolo. Lo msebenzi wenziwe kwimeko umbhali oyithandayo diatonic sawo chromatic, kodwa kwakhona ukunika ingcamango epheleleyo zezibalo of Isimo (zombini yamandulo mihla). Euler akazange kuphela wazama ukuba umculo ube nenzululwazi ngqo: Descartes, Mersenne, yaye wenza okufanayo kuye, njengoko D'Alembert, kunye nabanye abaninzi emva kwakhe.

I ezimbini-volume Scientia Navalis - sesibini isigaba sophuhliso kwalo ubucukubhede enengqondo. Le ncwadi ichaza imigaqo kwaye kuphuhlisa lizama theory hydrostatic of intlokoma kunye namaqumrhu-ntathu ukuba emanzini. Umsebenzi iqulethe nokuqala ubuchwephetshe bokuba eziqinileyo, leyo kamva crystallizes encwadini Theoria Motus corporum solidorum seu rigidorum, imbali wesithathu enkulu ubucukubhede. Umqulu wesibini e-worldwork theory isebenza ngeenqanawa, imikhumbi kunye navigation.

Okumangalisayo kukuba, Leonhard Euler, impumelelo kwimathematika leyo kweli xesha olungathethekiyo, waba ixesha namandla ukubhala umsebenzi iphepha-300 kwi arithmetic aphantsi ukusetyenziswa kwizikolo eziphakamileyo eSt Petersburg. Lithamsanqa abo abantwana bafundiswa isazi omkhulu!

umsebenzi Berlin

Ukongeza kula manqaku 280, abaninzi kuzo ebaluleke kakhulu kweli xesha sezibalo uLeonard Euler wadala uthotho azibhala zenzululwazi bomda.

Ingxaki brachistochrone - fumana iindlela leyo ekhomba oshukunyiswa kwenqwaba womxhuzulane ukusuka kwenye ingongoma-moya nkqo ukuya kwenye kweli xesha lifutshane - umzekelo yokuqala ingxaki owadalwa uJohann Bernoulli function search (okanye curve), nto leyo uzilungisele ibinzana analytical ngokuxhomekeke function. Ngowe-1744-m, ngoko ngo-1766-m Euler izibalo kangakanani le ngxaki ngokudala isebe elitsha lonke zezibalo - "calculus na iinguqulelo".

imbali ezimbini ezincinane phezu trajectories-langa enomsila kunye ngokukhanya, wabonakala malunga 1744 no 1746 kwiminyaka. Le yokugqibela yi umdla yembali, kusukela waqala ingxoxo malunga amasuntswana Newtonian kunye nethiyori otshangatshangiswayo ukukhanya Euler.

Xa imbeko ukuba umqeshi wakhe, uKumkani Frederick II, uLeonard wajika lo msebenzi ubalulekileyo ballistics eliNgesi Benjamin Robins, nangona bagxeka "Mechanics 'yakhe 1736 Wongezelela, Noko ke, izimvo ezininzi, explanatory notes kunye nezilungiso, ngenxa ethi "zokudubula" (1745) ngu volume-phindwe 5 ngaphezulu yokuqala.

I-volume ezimbini "Intshayelelo uhlalutyo omncane" (1748), ingcali yezibalo Euler uhlalutyo ukubeka njenge uqeqesho ozimeleyo, lushwankathela abaninzi ezifunyaniswe yakhe endle lwe thotho ongapheliyo, iimveliso engenasiphelo namaqhezu baqhubeka. Uqala umsebenzi umbono ocacileyo amaxabiso yokwenene kwaye zintsonkothile kwaye igxininisa indima engundoqo uhlahlelo inani le e, kobudlelwano kunye nemisebenzi lwe logarithm olusezantsi. Umqulu yesibini lunikezelwa geometry analytical: thiyori ezigoso-aljibra kunye nemigangatho.

"Calculus umehluko" liquka iinxalenye ezimbini, owokuqala leyo unikezelwa ekubaleni lweeyantlukwano nomahluko, kwaye eyesibini - imfundiso amandla series summation ifomula kunye nenani elikhulu imizekelo. Apha, koko, kunegama eprintiweyo Fourier series.

Umthamo ezintathu-"calculus Integral" yezibalo Euler kuqwalaselwa quadrature (m. E. uniko unless) imisebenzi cebetshu neteknoloji ukuze ndibazise umehluko zibalo yomgama, inkcazelo eneenkcukacha thiyori umehluko zibalo linear ngayo ukuze yesibini.

Kuyo yonke le minyaka e Berlin, yaye kamva uLeonard sasifunda ngokukhanya zejometri. amanqaku neencwadi bakhe isifundo, kuquka omkhulu abathathu-volume "Dioptrics" yaba imithamo ezisixhenxe Opera Omnia. Ngumxholo ophambili kulo msebenzi ukuphucula izixhobo ezisebenzisa ezifana ngeeteleskopu kunye iimikroskopu, ukucombulula indlela aberration chromatic kwaye ungqukuva ngenkqubo oluntsonkothileyo lens uzalise iziselo.

Euler (yezibalo): Facts umdla kwexesha St. Petersburg yesibini

Yayilixesha kakhulu onemveliso, ngexesha apho sisazinzulu iye yapapashwa amaphepha ngaphezulu kwe 400 kwizihloko sele sitshilo, kwakunye geometry, theory amathuba kunye manani, mapping, kwaye imali yomhlalaphantsi ukuba abahlolokazi kunye nezolimo. Kubo lungahlulwa-hlulwa zibe azibhala amathathu kwi-aljebra, ithiyori kweNyanga kunye nenzululwazi yomkhosi wamanzi, kwakunye kwithiyori amanani, intanda zendalo kunye dioptrics.

Apha kwafika omnye 'kunazo "lakhe -" Algebra. " Igama yezibalo Euler bahombise lo msebenzi phepha-500, nto leyo sibhalwe injongo kwingqeqesho kukufundisa i abaqalayo ngokupheleleyo. Yena abhale incwadi ukuya ngumfundi oselula, lowo weza nayo bevela eBerlin, yaye xa wagqiba ukuwenza umsebenzi, waqonda lonke yaye ndakwazi ukucombulula ngokulula kakhulu iingxaki aljibra ebhekiswa kuye.

"Imfundiso yesibini iinqanawa" Kwakhona yakhelwe abantu abangenalo ulwazi lwemathematika, ezizezi - oomatiloshe. Ngoko ayimangalisi into yokuba umsebenzi sele umbulelo yimpumelelo kakhulu izakhono ezimangalisayo yayisetyenziselwa lombhali. Minister of the Navy kunye Finance French Anne-Robert Turgot ekwakucetyisenwe ngazo uKumkani uLouis XVI ukuba ukuba bonke abafundi kwizikolo zaselwandle kunye zokudubula ukufunda imbali Euler kaThixo. Kusenokwenzeka ukuba omnye wabafundi kwaba uNapoleon Bonaparte. nkqu ukumkani uhlawule 1,000 engange izibalo ilungelo ukushicilela umsebenzi, uKumkanikazi uCatherine II, engafuni ukuba kukumkani, uye kabini imali, kwaye sezibalo enkulu Leonhard Euler Ukongezelela wafumana 2000 engange!