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.
Submit your idea for an investigation to InterMath.