Pythagoras ntawm Samos, zoo dua lub npe hu ua Pythagoras, yog tus neeg Greek tus kws tshuaj thiab cov kws txawj lej uas nyob ib puag ncig 2.500 xyoo dhau los. Nws tau hais tias yog lub luag haujlwm rau kev tshawb pom thiab ua pov thawj kev sib txheeb ntawm qhov loj me ntawm ob sab ntawm txoj cai ntawm cov duab peb sab thiab thaj chaw ntawm cov plaub fab, tau tsim qhov sib hu ua Pythagorean Theorem, suav hais tias yog ib qho kev tshawb pom loj hauv kev ua lej.

Txheem ntsiab lus

Saib xyuas cov ntsiab lus ntau

Ua ntej saib ntawm Pythagorean Theorem yog dab tsi tiag, cia peb nco ntsoov tias daim duab peb sab yog dab tsi thiab qee cov ntsiab lus ntxiv. Ua raws:

  • Hauv geometry, ib daim duab peb sab yog ib lub duab peb ceg uas muaj lub kaum sab xis, uas yog, lub kaum sab xis uas ntsuas 90º (degrees);
  • Hauv daim duab peb sab xis yog tsim los ntawm ob tog thiab hypotenuse. Lub hypotenuse yog lub sab sib txawv nrog lub kaum sab xis thiab tsim cov ntu loj tshaj plaws ntawm daim duab peb sab; Ob txhais ceg yog sab uas tsim txoj cai kaum sab xis.
  • Xam xyuas thaj chaw ntawm ib lub xwmfab yog ua tiav los ntawm sib npaug ntawm qhov ntev ntawm ob sab. Yog li ntawd, yog sab = a, peb muaj thaj tsam = axa = a².

Pythagoras

Theorem

Pythagorean theorem hais tias: "Hauv txhua daim duab peb sab txoj cai, lub xwmfab ntawm qhov ntev ntawm hypotenuse yog sib npaug ntawm cov xwm txheej ntawm qhov ntev ntawm ob txhais ceg."

Cov theorem no tseem tuaj yeem hais txog kev sib raug zoo ntawm thaj chaw. Yog li, theorem hais tias: "Hauv txhua daim duab peb sab xis, thaj tsam ntawm lub xwmfab uas nws sab yog qhov hypotenuse sib npaug sib npaug ntawm cov cheeb tsam ntawm cov xwmfab uas nws sab yog ob sab."

Rau thawj lossis thib ob nqe lus ntawm Pythagorean theorem, peb muaj cov qauv hauv qab no:

c² = b² + a²

qhov c sawv cev qhov ntev ntawm lub hypotenuse, thiab a thiab b sawv cev qhov ntev ntawm lwm sab ntawm ob sab.

Kev siv ntawm Pythagorean theorem

Raws li peb tau hais ua ntej, Pythagorean theorem raug suav hais tias yog ib qho kev pom loj ntawm kev ua lej. Vim li cas thiaj hais li ntawd? Dab tsi yog qhov kev siv ntawm qhov theorem?

Nws yuav yog tias tsis muaj lwm txoj kev sib raug zoo geometric zoo li ib qho uas siv hauv kev ua lej xws li Pythagorean theorem. Piv txwv li, hauv Cartesian Geometry, uas tau siv dav hauv Science thiab Engineering, txhua qhov kev suav nrog kev sib txuas trigonometry thiab kev sib txheeb ntawm thaj chaw siv cov theorem ua lub hauv paus.