Ancient Greek mathematician thiab philosopher. Koj Greek mathematician thiab lawv tau

Cov ancient Greeks ua ib tug zoo pab rau txoj kev loj hlob ntawm lub caij nyoog sciences: kev kawm txog zauv, astronomy, physics. Lwm yam haiv neeg nyob rau ntawm lub sij hawm, dhau lawm, muaj ib qhov nqi ntawm kev txawj ntse. Tab sis yog hais tias tus Egyptians thiab Babylonians twb ntsiab lus twb qhib thiab tshawb lub cheeb tsam, lub Greeks tau ploj mus txawm ntxiv. Lawv ho tsis nres thiab qhib tshiab horizons nyob rau hauv txawv spheres ntawm lub neej.

Greek lej

Qhov no science yog ib tug ntawm cov hiob thiab nrov. Ntawm cov hoob kawm, tus Greeks contributed rau cov kev loj hlob ntawm kab lis kev cai thiab geography, logic thiab economics. Lawv lub tsev kawm ntawv uas yog kev xav yog li ntawd tshaj hais tias txawm niaj hnub no amazes contemporaries nqe lus thiab discoveries. Tab sis kev ua lej muab ib tug me me nyob rau hauv no txoj kev uas paub txog kev.

Muaj ntau ntawm cov achievements nyob rau hauv lub teb ntawm xam yuav tsum tau sib tham hais tias muaj lawm ces nrov nrog lub Greeks. Cov neeg sau nyob rau hauv lub square, sib cav thiab li tuaj mus rau qhov kev txiav txim siab. "Nyob rau hauv ib tug tsis sib haum yug qhov tseeb" - qhov no dogma tau mus txog peb nws txij li thaum uas lub sij hawm.

Tej Greek mathematician enjoyed meej thiab hwm. Muab theorems thiab tus qauv, nws yog ib qhov nyuaj to taub yooj yim neeg qhuas nws mus rau lub sab saum toj ntawm lub pedestal, tus zoo ibyam ntawm lwm yam zoo kawg siab. Cov kev loj hlob ntawm kev kawm txog zauv raws li ib tug science tshuav npaum li cas rau Archimedes, Pythagoras, Euclid thiab lwm yam personalities, tej hauj lwm thiab nrhiav tau no tias lub hauv paus ntawm niaj hnub algebra thiab ntsuas kev kawm nyob rau hauv tsev kawm ntawv thiab universities.

Pythagoras thiab nws lub tsev kawm ntawv

Qhov no Greek mathematician, philosopher, politician, pej xeem thiab kev cai dab qhuas cov nuj nqis. Nws yug los kwv yees li nyob rau hauv 580 BC nyob rau hauv cov kob ntawm Samos, yog li ntawd cov neeg uas nws twb hu ua Samos. Raws li Legend, Pythagoras yog zoo nkauj heev thiab zoo nraug tus txiv neej. Nws yeej tsis nkees ntawm kev kawm tag nrho cov tshiab thiab cov tsis paub hais tias, nws yog tiag tiag ib tug neeg tseem ceeb kev kawm ntawv. Nws kawm tus tub hluas tsis tau tsuas yog nyob rau hauv tsev tab sis kuj nyob rau hauv Is Nrias teb, Tim lyiv teb chaws thiab Babylon.

Pythagoras, Ancient Greek mathematician thiab patron ntawm slaveholders thiab cov aristocracy. Idealist rau tus tub ntxhais, nyob rau hauv Croton, nws nrhiav tau nws tus kheej lub tsev kawm ntawv, uas yog ob qho tib si kev cai dab qhuas thiab kev nom kev tswv qauv. Clear lub koom haum ntawm lub neej txhua hnub, nruj kev cai thiab kev canons - nws cov ntsiab nta. Piv txwv li, cov mej zeej ntawm lub zej zog yuav tsis muaj ntiag tug, ua raws li ib tug neeg tsis noj nqaij noj cov zaub mov, thiab undertook tsis qhib neeg tej lus qhia ntawm nws tus kws qhia ntawv.

Thaum kev cai ywj pheej kis mus rau ib Croton, Pythagoras thiab nws cov thwjtim tau khiav mus Metapontum. Tab sis ib tug nrov uprising raged nyob rau hauv lub nroog. Nyob rau hauv ib yam ntawm cov fights 90-xyoo-laus mathematician raug tua. Nrog rau nws mus nyob qhovtwg li thiab nws nto moo lub tsev kawm ntawv.

qhib Pythagoras

Nws yog lub npe hu rau tej yam uas nws yog nws authorship belongs rau qhov kev piav qhia ntawm cov zauv, lawv lub zog thiab proportions. Nws kuj yog ib tug ntawm cov thawj zaum uas thov hais tias lub ntiaj teb yog puag ncig, uas lub ntiaj teb tsis muaj ib tug tsab ntawv tsa suab txoj kev raws li cov hnub qub. Cov tswv yim lub hauv paus rau tus naas ej heliocentric tej lus qhia ntawm Copernicus. Txij li thaum lub tag nrho lub neej ntawm tus paub txog tau surrounded los ntawm paub tsis meej, kom dim tsis yog ib tug ntau ntawm nthuav cov lus tseeb hais txog nws cov kev ua ub no. Ib txhia ntseeg hais tias nws muaj pov thawj tus naas ej theorem. Raws li ib co lus ceeb toom, lawv paub tias nws, thiab ntau lwm yam ancient haiv neeg ntev ua ntej cov me nyuam yug ntawm kev kawm txog zauv.

Greek philosopher thiab mathematician, muaj ib tug ntau ntawm cov muaj peev xwm, thiab tsis tsuas yog nyob rau hauv lub sciences. Nws lub npe thiab cov kev ua ub no shrouded nyob rau hauv myths xwb thiab legends, thiab mysticism. Nws twb ntseeg tau tias Pythagoras tswj dab nrog ntiajteb sab hauv to taub cov lus ntawm cov tsiaj, sib txuas lus nrog rau lawv, teev cov sib ntaus ntawm cov noog txoj cai coj rau nws, yog muaj peev xwm mus twv seb rau yav tom ntej. Tsis tas li ntawd ntaus nqi mus rau nws voodoo muaj peev xwm.

Archimedes: lub ntsiab hauj lwm

Qhov no yog ib qho ntawm feem koj cov neeg sawv cev ntawm lub era, tus naas ej tus paub txog, philosopher, mathematician thiab inventor. Nws yug los nyob rau hauv 287 BC nyob rau hauv Syracuse. Nyob rau hauv no me me lub zos uas nws nyob yuav luag tag nrho nws lub neej, ces sau tau nws nto moo treatises thiab kuaj tshiab mechanisms. Nws txiv yog ib tug lub tsev hais plaub astronomer Phidias, yog li Archimedes kev kawm coj qhov chaw nyob rau theem siab tshaj plaws. Nws muaj kev nkag tau mus rau qhov zoo tshaj plaws cov tsev qiv ntawv ntawm lub sij hawm, nyob rau hauv lub nyeem cov chav uas siv ntau tshaj li ib hnub.

Nws twb dim ob peb zauv tej hauj lwm ntawm tus paub txog. Conventionally, lawv yuav tsum tau muab faib mus rau hauv peb lub ntsiab pawg.

1. Tej hauj lwm siab volume thiab cheeb tsam ntawm curvilinear lub cev thiab cov nuj nqis. Lawv muaj ib tug ntau ntawm cov pov thawj theorems.
2. Geometric tsom xam ntawm hydrostatic thiab zoo li qub teeb meem. Txoj kev tshawb no txog qhov nqi koj tshuav ntawm cov nuj nqis, hais txog lub cev txoj hauj lwm nyob rau hauv cov dej thiab thiaj li nyob.
3. Lwm yam xyuam xim ua hauj lwm. Piv txwv li, hais txog lub calculus cov nplej ntawm cov xuab zeb, neeg kho tshuab theorem tseeb tiag.

Archimedes raug tua thaum lub sij hawm lub capture ntawm Syracuse los ntawm cov Roman tub rog. Nws li ces thiaj li fascinated los ntawm cov duab ntawm ib tug tshiab geometrical teeb meem, nws tsis pom tus tub rog uas tuaj rov qab. Cov tub rog tua tus paub txog, tsis paub hais tias tus thawj coj muab qhov kev txiav txim rau txuag lub neej ntawm ib tug naas ej mathematician thiab philosopher.

Archimedes pab mus rau txoj kev loj hlob ntawm lub caij nyoog sciences

Txhua tus me nyuam yog me ntsis txog cov no zoo heev daim duab txij high school. Leej twg yog nws, lub ancient Greek mathematician, qw hais tias "Eureka"? Lo lus teb rau lo lus nug no yog yooj yim - yog Archimedes. Raws li cov lus dab neeg, tus huab tais kom nws mus nrhiav tau tawm - cov tseem kub ua nws crown jeweller los yog lav, diluting nws nrog rau lwm cov hlau. Xav nyob rau hauv qhov teeb meem no, Archimedes nteg nyob rau hauv ib tug da dej lawm ua tus sau nrog dej. Thiab ces nws tshwm sim rau nws ib tug startling foundations: tus nqi ntawm cov kua uas yog poured tshaj lub ntug ntawm lub tub, tseem ntim dej moog los ntawm nws lub cev. Thaum ua no nrhiav, nws qw tias tag nrho cov paub cov lo lus "Eureka". Ancient Greek mathematician nrog no exclamation dhia tawm ntawm da dej thiab khiav tsev, nyob rau hauv lub buff, zuj zus mus sau nws foundations.

Tsis tas li ntawd, Archimedes, ob txhiab xyoo ua ntej lub foundations ntawm integrals tau los mus laij lub cheeb tsam ntawm ib tug Parabolic ya. Nws qhib lub ntiaj teb no tus xov tooj "pi", ua pov thawj hais tias tus piv ntawm ib lub voj voog lub cheeb thiab qhov ntev ntawm qhov ib ncig yeej tib yam nkaus rau tej geometric duab. Nws tsim lub thiaj li hu ua Archimedes 'ntsia hlau - qhov chiv keeb ntawm cov niaj hnub aircraft thiab nkoj propellers. Ntawm nws cov tau ntuav thiab lifting machine. Cov pub leejtwg ntawm creation ntawm nws "caws nplaum daim iav", los ntawm txoj kev uas tau muab los ntawm tus yeeb ncuab ships, kom txog rau thaum tam sim no, soj ntsuam tsis tau qhia cov hnub.

Euclid

Feem ntau ntawm nws lub sij hawm nws ua hauj lwm nyob rau hauv cov suab paj nruas tej hauj lwm, qhia lub secrets ntawm mechanics thiab physics, nws kawm astronomy. Tab sis ib feem ntawm nws tej hauj lwm tseem muaj nplooj siab lej: coj mus mloog ob peb proofs thiab theorems. Nws pab mus rau txoj kev loj hlob ntawm no science yog ib qhov nyuaj rau overestimate, raws li Euclid lub chaw ua hauj lwm los ua lub hauv paus rau lwm zaum, uas nyob ntau centuries tom qab nws.

Yuav ua li cas yog lub npe ntawm tus ancient Greek mathematician leej twg sau tau ib tug zoo-paub xyuam xim muab tso ua ke ntawm lub "Start", muaj raws ntawm 15 phau ntawv? Ntawm cov hoob kawm, Euclid. Nws muaj peev xwm npaj lub ntsiab lus ntawm geometry, muaj pov thawj tseem ceeb theorem txog lub sum ntawm cov ces kaum ntawm ib tug daim duab peb sab thiab lub Pythagorean theorem. Raws li nws lub npe yog txuam nrog rau cov kev qhia txog kev tsim kho ntawm kev polyhedra, uas niaj hnub no muaj peev xwm yuav qhuas txhua tus ntxhais hluas mathematician ntawm geometry qhia. Euclid sab txoj kev ntawm kev qaug. Nws tau txais Newton thiab Leibniz sab ib txoj kev uas muab xam: ib thiab differential.

Thales

Qhov no Greek mathematician yug nyob ib ncig ntawm 625 BC. Rau ib ntev lub sij hawm nws nyob tim lyiv teb chaws, thiab twb zoo mob nrog rau tus kav ntawm lub teb chaws, tus huab tais Amasis. Lus dab neeg muaj nws hais tias nws ib zaug xav tsis thoob vaj ntxwv, ntsuas qhov siab ntawm lub pyramid xwb nyob rau hauv loj ntawm nws cov duab ntxoov ntxoo.

Thales yog suav hais tias yog txwv zeej txwv koob Greek science, ib tug ntawm xya paub qab hau cov txiv neej uas hloov cov me nyuam yaus ntawm kev txawj ntse. Historians ntseeg tau hais tias Thales yog thawj los ua pov thawj yuav tsum muaj theorems ntawm geometry. Piv txwv li, hais tias inscribed nyob rau hauv ib lub voj voog lub yog yeej ib txwm ib tug ncaj kab, vajvoog inch faib tau ua ob sib npaug zos qhov chaw nyob rau hauv lub ces kaum ntawm ib daim duab peb sab ceskaum nrog lub sib npaug zos hauv paus, tag nrho cov ntsug ces kaum yog zoo tib yam, thiab ntxiv mus.

Thales muab ib tug qauv, raws li uas cov vajvoos peb sab yuav nco ntsoov ua tib yam, yog hais tias lawv yog zoo tib yam rau ib tug lub ntsej muag thiab lub ces kaum uas nyob ib sab mus rau nws. Nws kawm tau li cas los mus txiav txim qhov kev ncua deb mus rau lub nkoj sailing deb los zwj ceeb cov vajvoos peb sab. Nyob rau hauv tas li ntawd, nws ua ib tug ob peb discoveries nyob rau hauv astronomy, txiav txim rau lub caij nyoog lub sij hawm ntawm lub equinoxes thiab solstices. Nws tseem yog tus thawj meej xam lub caij ntawm lub xyoo.

Eratosthenes

Qhov no yog nej ib tug ntau yam duab. Nws yog fond ntawm txoj kev tshawb ntawm qhov chaw, thaj discoveries, kawm hais lus, hais lus lem thiab keeb kwm cov txheej xwm. Nyob rau hauv lub teb ntawm algebra thiab geometry, nws yog lub npe hu rau peb raws li lub Greek mathematician, ua tus foundations nyob rau hauv lub system primes. Nws tsim cov "cib ntawm Eratosthenes", ib qho kev nthuav txoj kev, uas txog thaum tam sim no qhia nyob rau hauv tsev kawm ntawv. Tsaug rau nws, koj muaj peev xwm tshau los ntawm cov primes ntawm tag nrho cov. Cov nuj nqis yog tsis muab lwv tawm, raws li nws yog hnub no, thiab tau raug chob rau tag nrho cov duab. Li no lub npe - "sab cib".

Eratosthenes yog tau ntawm nws tus kheej tsim mezolyaby - ib tug ntaus ntawv rau kev daws teeb meem raws li nyob rau hauv cov kev cai ntawm mechanics Delian teeb meem txog cov doubling lub voos xwmfab. Nws muaj peev xwm ua ntej ntsuas lub ntiaj teb. Thaum pom tias qhov ntev ntawm lub terrestrial meridian, nws deduced qhov ib ncig ntawm lub ntiaj chaw - 39 txhiab 960 kis lus mev. Tsis ncaj ncees lawm tsuas yog ib tus menyuam yaus 300 kis lus mev. Eratosthenes yeej zoo heev daim duab ntawm lub sij hawm, tsis muaj nws tau kawm txog zauv yuav tsis muaj nyob rau hauv nws cov ib txwm daim ntawv.

Geron

Qhov no Greek mathematician nyob rau hauv lub xyoo pua thawj BC. Cov ntaub ntawv yog approximate, raws li lub caij nyoog pov thawj txog nws lub neej tuaj rau peb hnub heev me ntsis. Nws yog lub npe hu hais tias Heron yog fond ntawm cov kev cai ntawm physics, mechanics, muaj nuj nqis tau ntawm engineering science. Nws yog nws leej twg tsim thawj tsis siv neeg lub qhov rooj, ib tug puppet ua yeeb yam, ib tug turbine sails, ancient "taximeter" - ib tug ntaus ntawv rau ntsuas txoj kev, nws tus kheej-them phom thiab hneev tua tav toj.

Ib tug ntau ntawm nws ua hauj lwm twb mob siab rau thiab kev ua zauv. Nws coj tshiab geometric qauv, tsim txoj kev xam xyuas geometric duab. Geron tau tsim ib tug zoo-paub mis, npe hu ua tom qab nws, uas koj yuav xam lub cheeb tsam ntawm ib tug daim duab peb sab thaum koj paub tias qhov ntev ntawm nws sab. Tom qab nws tshuav ib tug ntau ntawm tes sau phau ntawv nyob rau hauv uas tsis tau tsuas yog nws ua hauj lwm, tab sis kuj cov kev tshawb fawb ntawm lwm zaum tau tso tawm kom pom. Thiab qhov no yog nws loj tshaj nqis. Los ntawm cov ntaub ntawv peb paub hnub no hais txog Archimedes, Pythagoras thiab lwm yam nto moo mathematicians, tau ua cim ntawm lub era thiab tau yeeb koob ancient Greece rau tag nrho ancient ntiaj teb no.