Revision 601189 of Proving the Pythagorean theorem

Revision slug: Web/MathML/Examples/MathML_Pythagorean_Theorem
Revision title: MathML Pythagorean Theorem
Revision id: 601189
Created: May 28, 2014, 8:10:30 AM
Creator: nielsdg
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$\begin{array}{l} a^{2} + b^{2} = c^{2} \\ We can prove the theorem algebraically by showing that the area of the big square equals the area of the inner square (hypotenuse squared) plus the area of the four triangles: \\ {(a + b)}^{2} = c^{2} + 4 \cdot (\frac{1}{2} a b) \\ a^{2} + 2 a b + b^{2} = c^{2} + 2 a b \\ a^{2} + b^{2} = c^{2} \end{array}$

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<p>
  <math style="">

    <mtable columnalign="left">
      <mtr>
        <mtd>
          <!-- a² + b² = c² -->
          <mrow>
            <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>
        </mtd>
      </mtr>

      <mtr>
        <mtd>
          <mtext mathcolor="black" mathsize="12pt">
            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:
          </mtext>
        </mtd>
      </mtr>

      <mtr>
        <mtd>
          <mrow>
            <!-- We want to square the whole expression between the braces so we need to wrap it -->
            <msup>
              <mrow>
                <mo>(</mo>
                  <mi>a</mi> <mo> + </mo> <mi>b</mi>
                <mo>)</mo>
              </mrow>
              <mn>2</mn>
            </msup>

            <mo> = </mo>
            
            <msup><mi>c</mi><mn>2</mn></msup>
            <mo> + </mo>
            <mn> 4 </mn>
            <mo> &sdot; </mo>
            <!-- the area of the small triangles-->
            <mo>(</mo>
              <mfrac>
                <mn> 1 </mn>
                <mn> 2 </mn>
              </mfrac>
              <mi>a</mi><mi>b</mi>
            <mo>)</mo>

          </mrow>
        </mtd>
      </mtr>

      <mtr>
        <mtd>
          <mrow>
            <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><mi> b </mi>
          </mrow>
        </mtd>
      </mtr>

      <mtr>
        <mtd>
          <mrow>
            <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>
        </mtd>
      </mtr> 

    </mtable>
  </math>
</p>

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