Investigative Math Ideas
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Proofs Without Words

These visual examples of geometry ideas are sometimes called Proof Without Words.

  • Try this one.  It shows a conclusion about the sum of the three interior angles of any triangle by folding down the corners of the triangle.  Ingenious!
  • Next, try this one.  It shows the same conclusion about the sum of the three interior angles of any triangle in a different way.  Grab a vertex, move it around, and watch what happens.
  • How about the sum of the exterior angles of a polygon?  Go here.  This is an amazing way to show a powerful conclusion in geometry.  If you wish add a side to the polygon by using a Command click on a Mac.  Beautiful!
  • How about a proof for the Quadrilateral?  Or Pentagon? Or even a Hexagon? Go here.  (You may want to scroll down the page some).


Look at the visual proof of the Pythagorean Theorem using a dissection method.

One more proof of the Pythagorean theorem, this time using WATER!


Area of a Rectangle (animated)

Area of a Parallelogram (animated)

Area of a Triangle (animated)

Area of a Trapezoid (animated)

Area of a Circle (animated)
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Calvin and Hobbes by Bill Watterson
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YA Investigative Math