Pythagorean Theorem

Author

Eric W. Weisstein
December 15, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/PythagoreanTheorem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PythagoreanTheorem.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Figure

Show[Graphics[{
Line[{{0,0},{4,0},{0,3},{0,0}}],
Line[{{0,0},{1,0},{1,1},{0,1}}.2],
Text[TraditionalForm[a],{2,-.2}],
Text[TraditionalForm[b],{-.2,1.5}],
Text[TraditionalForm[c==(Sqrt[(a^2)+(b^2)])],{2.2,2.}]
}],AspectRatio->Automatic]

Bhaskara's Proof

Bhaskara[a_,b_,opts___]:=GraphicsArray[{
Graphics[{
Line[{{0,0},{a,0},{a,a},{0,a},{0,0}}],
Line[{{a,0},{a+b,0},{a+b,b},{a,b},{a,0}}],
Line[{{0,a},{b,0},{b+a,b}}],
Line[{{a,a},{b,a}}],
Line[{{b,0},{b,b}}]
},AspectRatio->Automatic,PlotRange->{{0,a+b},{-a,b}}],
Graphics[{
Line[{{0,0},{b,-a},{b+a,b-a},{a,b},{0,0}}],
Line[{{0,0},{b,0}}],
Line[{{a,0},{a,b}}],
Line[{{b+a,b-a},{a,b-a}}],
Line[{{b,-a},{b,b-a}}],
Line[{{2a,b-a},{2a,(b-a)(1+a/b)}}],
Line[{{a,0},{a,-(a-(b-a)a/b)}}]
},AspectRatio->Automatic,PlotRange->{{0,a+b},{-a,b}}]
}]

Show[Bhaskara[.5,1.3],ImageSize->500]