Before the usage of computers or calculators, early Greek mathemeticians used constructions to do math. Constructions are mathematical drawings using only a compass and straight edge. These drawings were capable of producing sums, differences, products and quotients. It was also possible to find square roots.
Notice that the star has only straight line segments, as well as circular curves. This is because the star was "constructed!" This star is special because it contains a regular octagon. Looking at the inner edges reveals an octagon with eight equal sides.
When starting with a square, following this strict procedure of drawing lines and circles will yield a regular octagon, and after extending specific lines, the 8-point star.
This simple process yields an interesting and beautiful result. Mathematics can often use a simple set of rules to describe complicated situations. This is apparent throughout geometry, physics, algebra, and even in fractals. Because Abstract Mathematics and Friends is dedicated to expanding mathematical knowlege, it is only right for its logo to be a reminder of the exploratory constructions done by mathematicians of the past.