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Geometric Proof of the Sum of Squares by Christina Martin Math 310, Fall 2012

Geometric Proof of the Sum of Squares by Christina Martin Math 310, Fall 2012. a 2. + b 2. a 2. = c 2. b 2. -Begin with two squares of arbitrary size, a 2 and b 2 . Stick them together to form a hexagon. a 2. b 2.

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Geometric Proof of the Sum of Squares by Christina Martin Math 310, Fall 2012

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  1. Geometric Proof of the Sum of Squares by Christina Martin Math 310, Fall 2012 a2 + b2 a2 = c2 b2

  2. -Begin with two squares of arbitrary size, a2 and b2. Stick them together to form a hexagon. a2 b2

  3. -Next, draw a line segment at the bottom of each square. That is, create one line with length a, and one line of length b. a2 b2 a b

  4. -Next, draw a line segment at the bottom of each square. That is, create one line with length a, and one line of length b. -Then, switch the locations of the line segments: the b line is now at the base of the a2 square, and the a line is now at the base of the b2 square. b2 a2

  5. -Draw a line from the top left corner of the a2 square to the base where the b-line ends to form a triangle. -Create that triangle. -Rotate the triangle 90° counterclockwise. -Shift the triangle up to the top of the a2 square. a2 b2

  6. -Draw a line from the top right corner of the b2 square to the base where the a-lineends to form a triangle -Repeat the process starting from the top of the b2 square -Create that triangle. -Rotate the triangle 90° clockwise. -Shift the triangle up to the top of the b2 square. a2 b2

  7. c Thus the final result is c a2 +b2 = c2 C2 a2 b2 b2 b2

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