Time for MATH MINUTE! (provide your favorite theme music here).

Get out your paper & pencil because I have a new puzzle for you!!

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PUZZLE #28 Pythagorean triangles Apr. 23 – Apr. 27

Speaking of triangles, a right triangle is a triangle which has an angle of 90 degrees.

According to the Pythagoras Theorem, every right triangle must satisfy the equation

a² + b² = c²,

where a, b, and c are the lengths of the sides with c the hypotenuse (of course).

For example, the right triangle with a side of length 4 and a hypotenuse of length 5, must have the other side of length 3, since in order to satisfy the Pythagorean equation we must have 5² - 4² = 25 – 16 = 9 = 3².

Now, is it possible for a right triangle to have a side of length 12 and a hypotenuse of length 13 such that the other side has a natural number for length?

What about 24 and 25? 40 and 41?

How many possible solutions of this type can there be?

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Send your comments, ideas and solutions before Monday to this email address, and be sure to put < MM > in the subject line parksjm@potsdam.edu

Visit us here online at      http://www2.potsdam.edu/parksjm/MM.htm

to see the results every Monday.

See you next time on MATH MINUTE!  (theme music fades out here).