Pythagorova věta - důkazy

Eukleides
Eukleides, Základy, kniha I, věta 47, přeložil Fr. Servít 1907[br]V pravoúhlých trojúhelnících je čtverec nad přeponou roven součtu čtverců nad odvěsnami.
[list][br][*] Čtverec FBAG nad odvěsnou má dvakrát větší obsah než trojúhelník FBC, jelikož mají společnou strana FB a shodnou výšku.[br][*] Trojúhelníky ABD a FBC jsou shodné dle věty sus.[br][*] Obdélník BDLJ nad odvěsnou má dvakrát větší obsah než trojúhelník BDA, jelikož mají společnou strana BD a shodnou výšku.[br][*] Dokázali jsme, že čtverec FBAG má stejný obsah jako obdélník BDLJ (Eukleidova věta o odvěsně).[br][*] Dle stejného postupu je i obsah čtverce ACKL stejný jako obsah obdélníku LECJ.[br][*] Celý čtverec BDEC rovná se součtu čtverců FBAG a ACKL.[br][/list]
Důkaz 2 - tangram
Důkaz 3 - indický matematik Bhaskara II, 12. st. n. l.
Nejprve sestrojíme čtverec se stranou c, potom sestrojíme libovolný vrchol pravoúhlého trojúhelníka s přeponou c a vytvoříme jeho tři kopie nad zbývajícími stranami. Pokud náš trojúhelník nebyl rovnoramenný, vznikne uvnitř čtverce malý čtverec se stranou [i]a-b[/i]. Dopočítáním úhlů v trojúhelnících dokážeme, že jsou jeho úhly pravé. Odtud přerovnáním, nebo pomocí algebraického zápisu plyne:[br][br][math]c^2=4\cdot\frac{1}{2}ab+\left(a-b\right)^2=a^2+b^2[/math][br][br][img]data:image/png;base64,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[/img]
Důkaz pro rovnoramenný pravoúhlý trojúhelník
[center][img]https://is3-ssl.mzstatic.com/image/thumb/Purple123/v4/52/da/99/52da9907-cafb-a748-c82a-407afc0caaa4/source/256x256bb.jpg[/img][/center][br][url=https://www.geogebra.org/m/bxwt8wes]Pythagorejský tangram[/url] můžete použít k důkazu Pythagorovy věty pro rovnoramenný trojúhelník a ke spoustě dalších rébusů podporujících porozumění obsahům rovinných útvarů. Inspirující je pro žáky vytvořit učební pomůcky ve formě skládaček a vytisknout je na 3D tiskárně. K tomu můžete použít přímo GeoGebru, [url=https://www.sketchup.com/]SketchUp[/url], či [url=https://www.tinkercad.com/]TinkerCAD[/url].
Více informací o důkazech Pythathagorovy věty:[br]R. Hašek: [url=https://www.geogebra.org/m/tbprzxgq]Perigalův důkaz Pythagorovy věty[/url], online materiál na serveru Geogebra[br]František Kuřina: [url=http://mdisk.pedf.cuni.cz/SUMA/MaterialyKeStazeni/PublikaceKnihy/KurinaMatematikaARU.pdf]Matematika a řešení úloh[/url], České Budějovice, 2011[br]Martin Vinkler: [url=https://www.geogebra.org/m/PWzD4WKR]M - Pythagorova věta, Eukleidovy věty[/url], GeoGebraBook[br]Michal Čučka: [url=http://is.muni.cz/th/79355/pedf_m/Diplomova_prace.pdf]Pythagorova věta a její důkazy[/url], diplomová práce, Brno 2007, s. 26-30[br]Cut the Knot: [url=http://www.cut-the-knot.org/pythagoras/index.shtml#27]Pythagorean Theorem[/url] [br]Pink Cree, Š. Voráčová: [url=https://www.geogebra.org/m/hysvwuqu]Pythagorean tangram[/url], online materiál na serveru Geogebra[br]Pauline K: [url=https://www.geogebra.org/m/gd37pfvj]Pythagoras: Based on Bhaskara's Proof[/url], online GeoGebra materiál[br][url=http://www.realisticky.cz]realisticky.cz[/url]: "[url=http://www.realisticky.cz/ucebnice/03%20Matematika%20Z%C5%A0/02%207.%20ro%C4%8Dn%C3%ADk/08%20Mocniny/21%20D%C5%AFkazy%20Pythagorovy%20v%C4%9Bty.pdf]Důkazy Pythagorovy věty[/url]" studijní materiál pro základní školu, záložka Učebnice, Matematika ZŠ, 7. ročník

Information: Pythagorova věta - důkazy