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## 'Medieval Octagon Interactivity' printed from http://nrich.maths.org/

The blue square is fixed and the centres of the blue and
yellow squares coincide. The yellow square rotates about its
centre.

In the middle ages stone masons used a ruler and compasses
method to construct exact octagons in a given square window.
Open your compasses to a radius of half the diagonal of the
square and construct an arc with centre one vertex of the
square - mark the 2 points where the arc crosses the sides.
Do that for all 4 vertices of the square giving 8 points.
Join these points to draw an octagon. Can you prove that the
octagon is regular?

You might find the proof by relating the construction to the
rotating square. Where does the regular octagon appear when
you rotate the yellow square in this diagram?