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The Pythagorean Theorem is both very useful and widely known. However, it is simply a special case of a much broader theorem, that very few people know.

In the special case where the line segment is a perpendicular bisector, b=d, and we have the Pythagorean case.

Hoehn’s theorem does not mean Pythagoras was wrong (there are more than 400 known proofs of the Pythagorean Theorem), but math teachers should consider teaching Hoehn’s Theorem in conjunction with its Pythagorean sibling.

For more information, see www.cut-the-knot.org/pythagoras/Hoehn.shtml.