The meaning of the secret symbol that Pythagoreans kill for is the 5-pointed star inscribed in a regular pentagon. The diagonals forming the star intersect in such a way that a smaller pentagon is formed pointing in the opposite direction. If the diagonals of the smaller figure are intersected they form yet another oppositely directed smaller pentagon. This process can be carried on ad infinitum.
Its secret is that an infinite numbers of golden ratios are hidden within the intersected proportional line segments. Naturally, phenomena exhibiting this golden ratio are a symbol of beauty or truth. Moreover, it appears as the limit of the ratio of Fibonacci numbers.