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Saturday, November 9, 2013

Regular polygons, exercise.

With a drawing program yesterday's pictures are easy to fake, of course. But these drawing programs don't give you the numbers.

Exercise.

Place a decagon edge-to-edge on a square with sides of length 1 ( see figure ). What is the distance between the two marked points?



( Answer: $ \frac{1}{4} \left(3 \sqrt{10-2 \sqrt{5}}+\sqrt{50-10 \sqrt{5}}+4\right) $ )

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