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Revision 532079 of Proving the Pythagorean theorem

  • Revision slug: Web/MathML/Examples/MathML_Pythagorean_Theorem
  • Revision title: MathML Pythagorean Theorem
  • Revision id: 532079
  • Created:
  • Creator: SphinxKnight
  • Is current revision? No
  • Comment

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a 2 + b 2 = c 2 We can prove the theorem algebraically by showing that the area of the big square equals the area
of the inner square (hypotenuse squared) plus the area of the four triangles:
(a + b)2 = c2 + 4(1 2)a b a2 + 2ab + b2 = c2 + 2ab a2 + b2 = c2

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<p><math style=""> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mrow> <mrow> <mrow> <mspace depth="1ex" height="0.5ex" width="2.5ex"></mspace> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mrow> <mrow> <mrow> <mspace depth="1ex" height="0.5ex" width="2.5ex"></mspace> <msup> <mi>a</mi> <mn>2</mn> </msup> </mrow> <mo> + </mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo> = </mo> <msup> <mi>c</mi> <mn>2</mn> </msup> </mrow> </mrow></mrow></mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mrow> <mspace depth="1ex" height="0.5ex" width="2.5ex"></mspace> <mrow><mtext mathcolor="black" mathsize="12pt"> We can prove the theorem algebraically by showing that the area of the big square equals the area<br />
 of the inner square (hypotenuse squared) plus the area of the four triangles: </mtext> </mrow> </mrow> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mrow> <mrow> <mspace depth="1ex" height="0.5ex" width="2.5ex"></mspace> <mo>(</mo><mi>a</mi><mo> + </mo> <mi>b</mi><msup><mo>)</mo><mn>2</mn></msup><mo> = </mo> <msup><mi>c</mi><mn>2</mn></msup><mo> + </mo> <mn>4</mn><mo>(</mo><mfrac><mrow><mn>1</mn></mrow> <mn>2</mn></mfrac><mo>)</mo><mi>a</mi> <mi>b</mi> </mrow> </mrow> </mrow></mrow></mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mrow> <mrow> <mspace depth="1ex" height="0.5ex" width="2.5ex"></mspace> <msup><mi>a</mi><mn>2 </mn></msup><mo> + </mo> <mn>2</mn><mi>a</mi><mi>b</mi><mo> + </mo><msup><mi>b</mi><mn>2 </mn></msup> <mo> =</mo> <msup><mi>c</mi><mn>2</mn></msup><mo> + </mo> <mn>2</mn><mi>a<mi>b</mi> </mi></mrow> </mrow> </mrow></mrow></mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mrow> <mrow> <mspace depth="1ex" height="0.5ex" width="2.5ex"></mspace> <msup><mi>a</mi><mn>2 </mn></msup><mo> + </mo> <msup><mi>b</mi><mn>2</mn></msup> <mo> =</mo> <msup><mi>c</mi><mn>2</mn></msup> </mrow> </mrow> </mrow></mrow></mtd> </mtr> </mtable></mrow></mrow></mrow></mrow></mtd></mtr></mtable></math></p>
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