EXAMPLE

For positive a and b, with a greater than or equal to b, construct the following figure where a and b are the legs of a right triangle. Eight copies of the right triangle are arranged with a square of sides a + b.


with equality if and only if a = b

 

Click HERE to see a GSP file where a + b is held constant but b approaches a in size.

 

 


Construct you own GSP animation of this approach.



Reference:

Ayoub, Ayoub B. (1997). Proof without words: Arithmetic Mean-Geometric Mean Inequality, Mathematics and Computer Education, 31, 191.

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