Ntawm 3,700-xyoo-laus Babylonian av nplaum ntsiav tshuaj, tus kws ua lej hauv tebchaws Australia pom tias yam twg yuav yog qhov piv txwv qub tshaj plaws ntawm kev siv cov duab geometry. Cov ntsiav tshuaj, hu ua Si.427, suav nrog cov phiaj xwm phiaj xwm uas qhia txog ciam teb ntawm qee yam khoom.
Cov ntsiav tshuaj tau raug tshawb pom nyob rau xyoo 19th xyoo pua Iraq thiab hnub tim los ntawm Old Babylonian era ntawm 1900 thiab 1600 BCE. Nws tau muaj nyob ntawm Istanbul Tsev khaws puav pheej Archaeological kom txog thaum pom los ntawm Dr. Daniel Mansfield ntawm University of New South Wales.
Mansfield thiab Norman Wildberger, tus kws tshaj lij ntawm UNSW, tau tshawb pom yav dhau los lwm lub Babylonian ntsiav tshuaj uas muaj lub ntiaj teb cov laus tshaj plaws thiab meej tshaj plaws cov lej trigonometric. Lawv xav thaum lub sijhawm uas cov ntsiav tshuaj muaj lub luag haujlwm zoo, tej zaum hauv kev tshuaj xyuas lossis tsim lub tsev.
Plimpton 322, ntsiav tshuaj, sawv cev rau lub kaum sab xis sab xis siv Pythagorean peb npaug: peb tus lej tag nrho uas cov lej ntawm thawj ob sib npaug sib npaug ntawm peb-piv txwv, 32 + 42 = 52.
"Koj tsis tuaj nrog trigonometry los ntawm kev ua yuam kev; koj feem ntau ua qee yam ua tau, " Mansfield piav qhia. Plimpton 322 txhawb nws kom nrhiav cov ntsiav tshuaj ntxiv los ntawm tib lub sijhawm uas muaj Pythagorean peb zaug, uas thaum kawg coj nws mus rau Si.427.
"Si.427 yog hais txog ib daim av uas muag," Mansfield piav qhia. Cov ntsiav tshuaj cov ntawv cuneiform, nrog nws qhov sib txawv ntawm cov npoo uas tsis pom zoo, piav qhia thaj tsam nrog thaj av marshy, ntxiv rau hauv threshing pem teb thiab pej thuam nyob ze.
Raws li Mansfield, cov duab plaub uas qhia pom thaj chaw muaj qhov sib txawv ntawm qhov ntev sib xws, cuam tshuam tias cov neeg tshawb fawb nyob rau lub sijhawm pom cov txheej txheem los tsim cov kab sib dhos kom raug dua li ua ntej.
"Koj muaj cov neeg ntiag tug sim txheeb xyuas seb lawv thaj av thaj tsam nyob qhov twg, ib yam li peb ua niaj hnub no, thiab tus kws tshawb fawb tawm los, tab sis tsis txhob siv cov cuab yeej GPS, lawv siv Pythagorean peb zaug. Thaum koj nkag siab tias Pythagorean peb npaug yog dab tsi, koj kab lis kev cai tau ua tiav qee yam ntawm kev ua lej, " Mansfield piav qhia.
Peb Pythagorean triples muaj nyob hauv Si.427: 3, 4, 5, 8, 15, 17, thiab 5, 12, 13 (ob zaug) thiab kwv yees tus lej Greek Pythagoras ntau dua 1,000 xyoo. Nws yog ib qho piv txwv paub ntawm daim ntawv OB cadastral thiab ib qho ntawm cov khoom qub uas paub zoo tshaj plaws.
Cov neeg Babylonians tau ua haujlwm hauv paus 60 tus lej, uas yog piv rau peb sau sijhawm li cas niaj hnub no, ua rau nws tsis tuaj yeem ua haujlwm nrog cov lej tseem ceeb ntau dua tsib.
Si.427 tau tshawb pom nyob rau lub sijhawm ntawm kev loj hlob ntawm cov cuab yeej ntiag tug, raws li kev tshawb fawb luam tawm hauv phau ntawv xov xwm Foundations of Science. "Tam sim no peb paub qhov teeb meem Npanpiloo tau sim daws, nws rov hais dua txhua cov lej ua lej los ntawm lub sijhawm no," Mansfield piav qhia.
"Koj pom kev ua lej yog tsim los kom tau raws li qhov xav tau ntawm lub sijhawm." Ib qho ntawm Si.427 uas cuam tshuam rau Mansfield yog tus lej sib deev "25:29" - sib npaug li 25 feeb thiab 29 vib nas this - sau ua cov ntawv loj ntawm lub ntsiav tshuaj sab nraub qaum.
"Puas yog ib feem ntawm kev suav uas lawv tau khiav? Puas yog ib yam uas kuv tsis tau pom dua ua ntej? Puas yog qee yam kev ntsuas? " nws piav qhia. "Nws ua rau kuv chim siab vim muaj ntau ntau txog cov ntsiav tshuaj uas kuv nkag siab. Kuv tau tso tseg los txiav txim seb tus ntawd yog leej twg. "
