Straight lines are drawn from each corner of a square to the mid
points of the opposite sides. Express the area of the octagon that
is formed at the centre as a fraction of the area of the square.
Medieval stonemasons used this 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 which
are the vertices of an octagon. Is the octagon an exact regular
octagon ? Proof please.