An Extra Illustration of J. E. Böttcher's Proof of the Pythagorean Theorem

The applet below is intended to provide a motivating illustration for a proof of the Pythagorean Theorem by J. E. Böttcher that is listed as #36 in the collection. The proof proceeds in three steps to observe which you are required to press the "Step" button. The vertices of the triangle and the triangle itself are draggaible so that you can see who the proof works in various configurations.

In the first step, one half of the configuration is rotated around the axis shown as a dashed line. This is not a planar operation.

The second step is a preparation to the third one where two right triangles are rotated 90° to fill holes in a big square. On the second step, the pieces are recolored to make the transition to the third step.


The only browser that currently runs Java applets is Firefox where, too, you have to make the site cut-the-knot.org trusted in the Java setup

An Extra Illustration of J. E. Bottcher's Proof of the Pythagorean Theorem


What if applet does not run?

References

  1. Andrew Percy & Alistair Carr, Leaning on Socrates to derive the Pythagorean Theorem, Australean Mathematics Teacher, 66 (2) 2010, 8-12

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