Yuav ua li cas nrhiav tau ib tug sab ntawm ib txoj cai daim duab peb sab? Tsim ntawm geometry

Lub ob txhais ceg thiab lub hypotenuse - sab ntawm ib txoj cai daim duab peb sab. Thawj - qhov no yog qhov feem uas yog nyob ib sab mus rau ib tug txoj cai kaum sab xis thiab lub hypotenuse yog tus coos ib feem ntawm cov duab thiab yog opposite lub kaum sab xis ^90. Pythagorean daim duab peb sab yog hu ua ib sab ntawm uas yog lub ntuj tus xov tooj; lawv ntev nyob rau hauv cov ntaub ntawv no yog hu ua "Pythagorean triples".

Iyiv daim duab peb sab

Rau tam sim no tiam tau kawm geometry nyob rau hauv daim ntawv nyob rau hauv uas nws yog qhia nyob rau hauv lub tsev kawm ntawv tam sim no, nws tau tsim ob peb centuries. Nws yog suav tias yog tseem ceeb rau cov Pythagorean theorem. Lub sab ntawm daim duab peb sab (lub cev yog lub npe hu mus rau tag nrho lub ntiaj teb no) yog 3, 4, 5.

Ob peb uas tsis paub nrog cov kab lus "Pythagorean ris nyob rau hauv tag nrho cov lus qhia yog muaj sib npaug." Tab sis nyob rau hauv qhov tseeb, Theorem suab yog: c ² (square ntawm lub hypotenuse) = ² + b ² (lub sum ntawm cov plaub fab ntawm ob txhais ceg).

Cov mathematicians daim duab peb sab nrog sab 3, 4, 5 (pom, m thiab r. D.) Yog tus "Iyiv '. Nws yog nthuav tias voos kheej-kheej ntawm lub vajvoog uas yog inscribed nyob rau hauv ib daim duab sib npaug zos rau ib tug. Lub npe tuaj txog nyob rau hauv lub xyoo pua V BC, thaum cov neeg Greek philosophers mus rau tim lyiv teb chaws.

Thaum constructing lub pyramid architects thiab surveyors siv piv ntawm 3: 4: 5. Cov chaw kho mob tau txais proportionately, zoo-nrhiav thiab dav, thiab tsis tshua muaj tsaus muag.

Yuav kom tsim ib txoj cai lub, builders siv txoj hlua uas tus ntawm 12 fastened. Nyob rau hauv cov ntaub ntawv no, qhov yuav tshwm ntawm constructing ib txoj cai daim duab peb sab yog nce 95%.

Tej yam tshwm sim ntawm koob pheej ntawm lawv cov nuj nqis

• Cov mob lub nyob rau hauv ib txoj cai daim duab peb sab thiab ib tug loj sab uas yog sib npaug zos rau cov tib yam nyob rau hauv lub thib ob daim duab peb sab, - tus indisputable kos npe rau ntawm koob pheej ntawm lawv cov nuj nqis. Noj rau hauv tus account tus nqi ntawm cov ces kaum, nws yog ib qho yooj yim los ua pov thawj hais tias tus thib ob mob ces kaum kuj sib npaug zos. Yog li, lub duab peb ceg yog cov tib nyob rau hauv lub thib ob feature.
• Thaum daim ntawv thov lub ob daim ntawm txhua lwm yam tig lawv kom lawv yuav tau tshaj, tau ua ib tug ceskaum daim duab peb sab. Raws li cov khoom teejtug uas yog ob tog, los yog es, lub hypotenuse yog sib npaug zos, raws li zoo raws li lub ces kaum nyob puag, thiab yog li ntawd cov nuj nqis yog tib yam.

Raws li cov thawj feature nws yog heev yooj yim mus ua pov thawj tias lub duab peb ceg yog tseeb sib npaug zos, raws li ntev raws li lub ob me me thiab ob tog (ie. E. Lub ob txhais ceg) yog muaj sib npaug rau txhua tus lwm yam.

Cov vajvoos peb sab yog zoo tib yam rau lub hauv paus ntawm II, uas nws essence lus dag nyob rau hauv kab zauv ceg thiab ib tug mob kaum sab xis.

Thaj chaw ntawm ib tug peb tog nrog ib txoj cai lub

Qhov siab, uas yog nws txo qis los ntawm txoj cai lub, cais lub daim duab mus rau hauv ob sib npaug zos qhov chaw.

Lub sab ntawm ib txoj cai daim duab peb sab thiab nws cov theem nrab yog yooj yim paub los ntawm txoj cai: lub nruab nrab, uas yog so rau hauv lub hypotenuse yog sib npaug zos rau cov ib nrab ntawm nws. Square nrhiav nrhiav tau nyob ob leeg nyob rau hauv lub Heron lub mis, thiab cov kev paub hais tias nws yog sib npaug zos rau ib nrab ntawm cov khoom ntawm tus lwm ob sab.

Cov khoom no angled daim duab peb sab ces kaum ntawm 30 ^o, 45 ^o thiab 60 ^o.

• Nyob hauv ib lub kaum ntse ntse, uas yog sib npaug zos rau ^txog 30, nws yuav tsum tau nco ntsoov tias opposing sab yuav ua ncaj rau 1/2 ntawm lub loj tshaj plaws tog.
• Yog hais tias lub kaum sab xis yog ⁴⁵ °, ces tus thib ob mob lub kuj ⁴⁵ °. Qhov no qhia tias daim duab peb sab yog ceskaum thiab nws ob txhais ceg muaj sib npaug.
• Cov cuab yeej ntawm lub kaum sab xis ⁶⁰ lus dag nyob rau hauv lub fact tias peb lub-degree angle muaj ib qho kev ntsuas ^ntawm 30.

Lub cheeb tsam no yog yooj yim paub los ntawm ib qho ntawm peb cov qauv:

1. los ntawm lub qhov siab thiab sab uas nws ntog;
2. Heron lub mis;
3. nyob rau hauv sab thiab lub kaum sab xis ntawm lawv.

Lub sab ntawm ib txoj cai daim duab peb sab, los yog es ob txhais ceg sib nyob rau hauv ob tug sib txawv heights. Yuav nrhiav tau cov thib peb, nws yog tsim nyog los xav txog lub resulting daim duab peb sab, thiab ces los ntawm lub Pythagorean theorem los xam yuav tsum tau ntev. Nyob rau hauv tas li ntawd mus rau qhov formula muaj tseem yog ob zaug rau hauv cheeb tsam piv thiab qhov ntev ntawm lub hypotenuse. Cov feem ntau qhia cov menyuam kawm ntawv yog cov thawj, vim nws yuav tsum tau tsawg dua suav.

Theorem thov mus rau sab xis daim duab peb sab

txoj cai daim duab peb sab geometry muaj xws li kev siv ntawm tej theorems raws li:

1. Pythagorean theorem. Nws essence lies nyob rau hauv lub fact tias cov square ntawm lub hypotenuse sib npaug rau hauv lub sum ntawm cov plaub fab ntawm lub ob sab. Nyob rau hauv Euclidean geometry, qhov no piv yog tus yuam sij. Siv cov mis mos yuav, yog tias muab daim duab peb sab, piv txwv li, SNH. SN - lub hypotenuse, thiab nws yog tsim nyog los nrhiav tau. Ces SN ² = NH ² + HS ^2.
2. Cosine theorem. Tshab xyuas lub Pythagorean theorem: g ² = f ² + s ² -2fs * cos lub therebetween. Piv txwv li, muab ib tug daim duab peb sab DOB. DB paub ceg thiab hypotenuse UA, koj yuav tsum nrhiav tau cov OB. Ces mis yuav siv sij hawm rau hauv daim ntawv: OB ^{2 2} = DB + UA ² -2DB * UA * cos lub D. Muaj peb txim: mob-angled ces kaum ntawm lub daim duab peb sab yog, yog hais tias tus sum ntawm plaub fab ntawm lub ob sab ntawm lub square rho peb ntev, qhov tshwm sim yuav tsum muaj tsawg tshaj li zero. Lub - obtuse, nyob rau hauv uas cov ntaub ntawv, yog hais tias tus qhia yog ntau tshaj pes tsawg. Lub - kab nyob rau ntawm xoom.
3. Sine theorem. Nws qhia tau hais tias cov kev sib raug zoo ntawm ob tog mus rau lub tawm tsam cov ces kaum. Nyob rau hauv lwm yam lus, qhov ratio ntawm lengths ntawm lub sab opposite rau lub sine ntawm cov ces kaum. Nyob rau hauv daim duab peb sab HFB, nyob rau lub hypotenuse yog HF, nws yuav muaj tseeb: HF / txoj kev txhaum lub B = FB / txoj kev txhaum lub H = HB / txoj kev txhaum lub F.