Geometry: using only compasses and straightedge
An octagon is an eight sided figure
Draw a perfect octagon.

Draw a circle. Draw a diameter AC through centre O. Draw another diameter DB at right angles. (How?)
Bisect (divide in two)  one of the right angles. (How?) Draw another diameter. It is at 45 degrees to the other diameter. In the same way draw a fourth diameter. The circle is now divided in 8 equal "pie slices".
Join where the points of the diameters meet the circle to make your perfect octagon (dark red.)