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Or, to put it another way: Check it outyou can show that the Pythagorean theorem works. (Get Shockwave ).

This little factoid, and other Pythagorean triplets, can be the basis of a nice set of puzzles.

Heres the first. If you draw a 55 square on graph paper, how can you cut it up (following the lines on the graph paper) so that the pieces can be rearranged to form a 33 square and a 44 square.

Heres one possible solution: The 5x5 square, cut into four pieces Well, theres the 55 square.

These four pieces can be rearranged like so: The four pieces rearranged to make a 3x3 square and a 4x4 square As it turns out, you cant do it with fewer pieces than this each corner of the 55 square must be in a different piece.

But there are other pairs of square numbers that add up to a square number.

Salls spa game. I managed to find a way to cut a 1313 square into five pieces that could make a 55 square and a 1212 square.

I dont know. And what about 77 2424 2525 How few pieces can you cut a 2525 square into, so the pieces can be rearranged into a 77 square and a 2424 square This is already enough, by way of puzzles, to keep some schoolkids occupied for a loooooong time but there are an infinite number of pythagorean triplets, so theres an infinite number of puzzles of this type.

Then the puzzle is this: how can you chop up an RxR square, respecting the lines on the graph paper, so that the pieces can be rearranged into a PxP square and a QxQ square, using as few pieces as possible Note that if you allow the squares to be cut into pieces of any shape, or with straight cuts in any direction (not just parallel to the sides of the squares), then at most 7 pieces are enough to solve this puzzle.

This picture (public domain, from wikipedia) shows how: A Seven Piece Jigsaw that proves the pythagorean theorem Some other formulae that give interesting puzzles:.

If you have students whove exhausted the puzzles on this page, ask them to find one for you.

The left puzzle is trivial, simply rotate the 4 triangles so that the hypotenuse (since the hypotenuse of length c is equal the to length of the square) of every triangle is aligned with one side of the large square, the blue square should fit snugly in the middle.

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About this resource: This 25 question puzzle has students use the Pythagorean Theorem in order to find missing side measurements.

Once they find missing side measurements, they match up the letter associated with the answer to the problem number and put together a puzzle.

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NOVA Online The Proof Pythagorean Puzzle Pythagorean Puzzle Heres the deal; there was this Greek guy named who lived over 2,000 years ago during the sixth century B.C.E.

Pythagoras spent a lot of time thinking about math, astronomy, and music.

One idea he came up with was a mathematical equation thats used all the time, for example in architecture, construction, and measurement.

What it means is that in a right triangle (where one angle equals 90), the sum of the squares of two sides equals the square of the hypotenuse (the longest side).

Or, to put it another way: Check it outyou can show that the Pythagorean theorem works.

Pythagoras Puzzle Game Solutions