Lub keeb kwm ntawm lub Pythagorean theorem. lub pov thawj

Lub keeb kwm ntawm lub Pythagorean theorem muaj ob peb millennia. Cov ntaubntawv hais tias lub square ntawm lub hypotenuse yog sib npaug zos rau cov sum ntawm cov plaub fab ntawm ob txhais ceg, nws twb paub ntev ua ntej cov me nyuam yug ntawm tus Greek mathematician. Txawm li cas los, lub Pythagorean theorem, lub keeb kwm ntawm creation thiab cov pov thawj ntawm nws bound rau feem ntau ntawm nws yog nrog cov kws tshawb fawb. Raws li ib txhia qhov chaw, yog vim li cas rau qhov no yog thawj pov thawj ntawm cov theorem, uas twb tau powered by Pythagoras. Txawm li cas los, ib co kev soj ntsuam refute no qhov tseeb.

Music thiab logic

Ua ntej peb yuav qhia tau rau koj yuav ua li cas zaj dab neeg hloov zuj zuj Pythagorean theorem, luv luv biography ntawm mathematician. Nws nyob hauv lub VI xyoo pua BC. Hnub yug ntawm Pythagoras 570 BC. e, ib qhov chaw -. cov kob ntawm Samos. Nyob rau ib tus paub txog lub neej nws yog lub npe hu ib tug me ntsis. Biographical ntaub ntawv nyob rau hauv Greek qhov chaw yog interwoven nrog pom tseeb tseeb. Nyob rau hauv cov nplooj ntawv ntawm treatises nws zoo nkaus li ib tug zoo kawg sage, zoo hais kom ua ntawm cov lo lus thiab muaj peev xwm kom koj yaum tau. Los ntawm txoj kev, qhov no yog vim li cas lub Greek mathematician Pythagoras thiab hu ua, uas yog "haub hais lus". Raws li lwm version, cov me nyuam yug ntawm ib tug yav tom ntej sage kwv yees Oracle. Leej Txiv nyob rau hauv nws yawm hu ua cov me nyuam tub los ntawm Pythagoras.

Sage kawm nrog tus poj minds ntawm lub sij hawm. Ntawm cov xib fwb ntawm tus hluas Pythagoras thiab Pherecydes tshwm Germodamant Sirossky. Tus thawj instilled nyob rau hauv nws ib tug hlub ntawm cov suab paj nruag, lub thib ob qhia philosophy. Ob yam no sciences yuav nyob twj ywm rau kev tsom xam ntawm ib tus paub txog thoob plaws nws lub neej.

Kev kawm ntawv nyob rau hauv lub 30-xyoo-ntev

Raws li ib tug version, yog tus inquisitive hluas cov txiv neej, Pythagoras tshuav nws lub teb chaws. Nws mus nrhiav kev txawj ntse nyob rau hauv Egypt, nyob qhov twg nws nyob, raws li ntau qhov chaw, los ntawm 11 mus 22 xyoo, thiab ces twb npaum li cas neeg raug txim thiab xa mus rau tim Npanpiloo. Pythagoras muaj peev xwm tau txais txiaj ntsim los ntawm nws cov kev cai. Rau 12 xyoo, nws kawm ua lej, geometry, thiab khawv koob nyob rau hauv lub ancient lub xeev. Samos Pythagoras tsis rov qab mus txog 56 xyoo. Ntawm no, thaum cov kev cai ntawm lub tyrant Polycrates. Pythagoras yuav tsis txais xws li ib tug nom tswv system, thiab tsis ntev yuav mus rau sab qab teb ntawm ltalis, qhov uas nws tau muab tso rau Greek colony ntawm Croton.

Niaj hnub no koj yuav tsis hais rau paub tseeb seb Pythagoras yog nyob rau hauv Iyi tebchaws, thiab Babylon. Tej zaum nws tshuav Samos thiab tom qab ntawd mus tam sim ntawd nyob rau hauv Croton.

Pythagoreans

Lub keeb kwm ntawm lub Pythagorean theorem muaj feem xyuam rau txoj kev loj hlob uas tsim los ntawm lub Greek philosopher ntawm lub tsev kawm ntawv. Qhov no kev cai dab qhuas-koom cov kwvtij nkauj muam qhia kev ua raws li kev ua neej, kawm zauv, geometry thiab astronomy, twb koom nyob rau hauv txoj kev tshawb no ntawm lub philosophical thiab mystical sab ntawm lub xov tooj.

Tag nrho cov me nyuam kawm ntawv qhib lub Greek mathematician ntaus nqi mus rau nws. Txawm li cas los, lub keeb kwm ntawm lub hauv paus chiv keeb ntawm cov Pythagorean theorem yog ua txhua yam los ntawm ancient biographers tsuas los ntawm ib tug philosopher. Nws yog assumed hais tias nws tau muab lub Greeks cov kev txawj ntse tau nyob rau hauv Npanpiloo thiab tim lyiv teb chaws. Muaj kuj yog ib tug version hais tias nws yeej nrhiav tau lub theorem rau lub ratios ntawm ob txhais ceg thiab lub hypotenuse, tsis paub txog lub achievements ntawm lwm haiv neeg.

Pythagorean Theorem: keeb kwm ntawm foundations

Nyob rau hauv ib co Greek qhov chaw piav kev xyiv fab ntawm Pythagoras, thaum nws muaj peev xwm los ua pov thawj rau hauv lub theorem. Nyob rau hauv Honor ntawm qhov kev tshwm sim, nws kom nws cov neeg txi rau cov gods nyob rau hauv daim ntawv ntawm cov pua pua ntawm cov bulls, thiab ua lub tsiab peb caug. Ib txhia kws tshawb fawb, tiam sis, tus taw tes rau lub impossibility ntawm xws li ib txiav txim vim qhov xwm ntawm tus Pythagoreans views.

Nws yog ntseeg hais tias nyob rau hauv lub treatise "hais", tsim los ntawm Euclid, tus sau muab pov thawj ntawm cov theorem, tus neeg sau ntawm uas yog tus yawm Greek mathematician. Txawm li cas los, qhov no saib yog tsis txaus siab los ntawm tag nrho cov. Yog li ntawd, txawm tus ancient philosopher Neoplatonist Proclus taw tes qhia tawm tias tus neeg sau ntawm lub saum toj no nyob rau hauv lub "Principia" yog nws tus kheej pov thawj ntawm Euclid.

Txawm nws yog, tiam sis cov ua ntej mus npaj ib tug theorem uas tseem tsis Pythagoras.

Ancient tim lyiv teb chaws thiab Babylon

Pythagorean theorem, uas tseem ua hauj lwm nrog cov dab neeg uas tsim nyob rau hauv tsab xov xwm, raws li cov German mathematician Cantor, twb paub li thaum ntxov raws li 2300 BC. e. nyob rau hauv Iyi tebchaws. Cov ancient inhabitants ntawm lub reign ntawm lub Nile Valley vaj ntxwv Amenemhat kuv paub koob pheej ntawm lawv 3 ² + 4 = 5 ^{² ².} Nws yog assumed tias nrog kev pab los ntawm ib tug peb tog nrog sab 3, 4 thiab 5 ntawm cov neeg Iyiv "hlua natyagivateli" hlua ces kaum.

Paub theorem ntawm Pythagoras nyob rau hauv Npanpiloo. Nyob rau av nplaum ntsiav tshuaj yos los ntawm 2000 BC thiab ntaus nqi mus rau lub reign ntawm King Hammurabi, sab ib approximate muab xam los ntawm cov hypotenuse ntawm ib txoj cai daim duab peb sab.

Khej thiab Tuam Tshoj

Lub keeb kwm ntawm lub Pythagorean theorem yog kev cob cog rua nrog lub ancient civilizations ntawm Is Nrias teb thiab Tuam Tshoj. Treatise "Xuan Zhou lis-Jin" muaj cov lus qhia uas Iyiv daim duab peb sab (nws sab txog li 3: 4: 5) tau paub nyob rau hauv Tuam Tshoj raws li thaum ntxov raws li nyob rau hauv XII. BC. e. thiab mus rau lub VI. BC. e. kev kawm txog zauv ntawm lub xeev no paub cov kev hauv daim ntawv ntawm cov theorem.

Siv cov kev faib ntawm txoj cai lub daim duab peb sab siv Iyiv tau piav nyob rau hauv Indian treatise "Sulva Tseeb Duantais" yos los ntawm VII-V cc. BC. e.

Yog li, lub keeb kwm ntawm lub Pythagorean theorem rau lub sij hawm ntawm yug me nyuam ntawm cov Greek mathematician thiab philosopher mus rov qab ob peb puas xyoo.

pov thawj

Thaum lub sij hawm nws lub neej theorem yog ib tug ntawm lwm geometry. Keeb kwm ntawm lub pov thawj ntawm cov theorem ntawm Pythagoras, tej zaum pib nrog kev saib xyuas ntawm ib tug equilateral txoj cai daim duab peb sab. Nyob rau nws hypotenuse thiab sab yog lub tsev squares. Lub ib tug uas "loj hlob" nyob rau lub hypotenuse, yuav muaj xws li plaub cov vajvoos peb sab uas yog muaj sib npaug mus rau tus thawj. Lub squares rau lub cathetus li muaj ob tug duab peb ceg. Tej yam yooj yim duab sawv cev kom meej meej qhia tau hais tias lub validity ntawm cov assertion formulated rau hauv daim ntawv ntawm tus naas ej theorem.

Lwm yam yooj yim pov thawj combines geometry nrog algebra. Plaub zoo tib yam cai-angled cov vajvoos peb sab nrog sab ib tug, b, c yog twv thiaj li mus ua ob squares: txheej sab nrog (a + c) thiab cov inward sab nrog. Yog li ib tug me me rau thaj tsam ntawm lub square yog sib npaug zos rau ^2. Lub cheeb tsam ntawm lub loj los laij los ntawm cov sum ntawm cov cheeb tsam ntawm ib tug me me square thiab tag nrho cov vajvoos peb sab (lub cheeb tsam ntawm daim duab peb sab, peb rov qab, yog muab xam los ntawm cov mis (A * B) / 2), piv txwv li ² + 4 * ((A * B) / 2), uas yog sib npaug zos rau ² + 2av. Lub cheeb tsam ntawm lub loj square yuav xam nyob rau hauv ib tug txawv txoj kev - raws li cov khoom ntawm ob sab, uas yog, (a + b) ^2, uas yog sib npaug zos rau ib tug ² + ² + 2av. Nws puv tawm:

thiab 2av + ² + ² + ² = 2av,

thiab ² + ² = s ^2.

Muaj ntau ntau variants ntawm lub pov thawj ntawm no theorem. Saum toj no lawv ua hauj lwm thiab Euclid, thiab Indian kws tshawb fawb, thiab Leonardo da Vinci. Feem ntau ancient sages coj drawings, piv txwv uas yog nyob saum toj no thiab tsis txhob muab tej lus piav qhia, lwm yam tshaj li sau ntawv, "Saib!" Lub simplicity ntawm geometric proofs muab muaj yog ib co paub lus thiab tsis yuav tsum tau.

Lub keeb kwm ntawm lub Pythagorean theorem, sau ua ke nyob rau hauv ib tsab xov xwm dispels lub tswvyim hais ua dabneeg hais txog nws cov hauv paus. Txawm li cas los, nws yog ib qhov nyuaj rau xav txog tej yam uas lub npe ntawm tus poj Greek mathematician thiab philosopher puas xav tsis txuam nrog nws.