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Science & Technology
My Pythagorean Theorem proof
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<blockquote data-quote="iooqxpooi" data-source="post: 19133" data-attributes="member: 30"><p><strong>My Pythagorean Theorem proof</strong></p><p></p><p><img src="http://img.photobucket.com/albums/v26/iooqxpooi/PYTHAGPROOF.bmp" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p> </p><p>Remember that (z-s)+s=z, that might help.</p><p> </p><p>Ok, I just realized that you can't see the math...</p><p> </p><p>Well, the box in the middle is a square, with side b. The large triangles have side c and are isosceles. The trapezoids have bases 2a/sqrt3 and a/sqrt3 with height a/sqrt3. With 2 congruent trapezoids. Thus...</p><p> </p><p>2(Atrap)=(Atr+Atr')-Asq</p><p>2(1/2)(a/sqrt3)(2a/sqrt3+a/sqrt3)=(c^2/2+c^2/2)-(b^2)</p><p>a/sqrt3(3a/sqrt3)=c^2-b^2</p><p>3a^2/3=c^2-b^2</p><p>a^2=c^2-b^2</p><p>a^2+b^2=c^2</p><p> </p><p> </p><p><img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite38" alt=":)" title="Smile :)" loading="lazy" data-shortname=":)" /></p></blockquote><p></p>
[QUOTE="iooqxpooi, post: 19133, member: 30"] [b]My Pythagorean Theorem proof[/b] [img]http://img.photobucket.com/albums/v26/iooqxpooi/PYTHAGPROOF.bmp[/img] Remember that (z-s)+s=z, that might help. Ok, I just realized that you can't see the math... Well, the box in the middle is a square, with side b. The large triangles have side c and are isosceles. The trapezoids have bases 2a/sqrt3 and a/sqrt3 with height a/sqrt3. With 2 congruent trapezoids. Thus... 2(Atrap)=(Atr+Atr')-Asq 2(1/2)(a/sqrt3)(2a/sqrt3+a/sqrt3)=(c^2/2+c^2/2)-(b^2) a/sqrt3(3a/sqrt3)=c^2-b^2 3a^2/3=c^2-b^2 a^2=c^2-b^2 a^2+b^2=c^2 :) [/QUOTE]
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