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hypatia's triumph

Hypatia was an Egyptian female mathematician born in A.D. 370. One problem she posed was the following:

Find a number that is the sum of two squares and whose square is also the sum of two squares.

Can you solve Hypatia's problem? Are there more solutions? Is there a pattern between any pair of solutions? Justify your answers.

(Source: Mathematics Teaching in the Middle School, Apr 1994)

 Related External Resources

Squaring the Triangle [ java applet ]
Adjust the side lengths of a right triangle, and view the changes in the hypotenuse and areas of adjacent squares.

Pythagorean Theorem [ java applet ]
This series of explorations illustrates why the sum of squares of the legs of a right triangle is equal to the square of the hypotenuse.

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