Pentagon and the Golden Section

The regular pentagon and especially the regular stellar pentagon formed by its diagonals, the pentagram, have been attracting people's attention since the ancient times by their undeniable beauty. They are used today in the flags and emblems of the mightiest nations (not long ago Red Star was the symbol of our native country) and 2500 years ago pentagram was the emblem of the Pythagorean School.

Outstanding among the mathematical facts is the connection of the pentagon measurements with The Golden Section.

The figure shows a regular pentagon, and inscribed in it the pentagram formed by it's diagonals. The central area of the pentagram forms again a regular pentagon in the reverse position. In this pentagon another pentagram has been inscribed, and so on. In each pentagon the ratio of the diagonal to the side is equal to the number "tau", that is, they form Golden Section propotion. Besides, any two neighbouring segments in pentagrams form Golden Section also.

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