pentagram

A pentagram is the figure formed by the five diagonals of a regular (http://planetmath.org/RegularPolygon) pentagon.  The name comes from the Greek $\pi \epsilon \nu \tau \alpha \gamma \varrho \alpha \mu \mu o\nu$. Its are $\pi \epsilon \nu \tau \epsilon$ ‘five’ and $\gamma \varrho \alpha \mu \mu o\varsigma$ ‘stoke, ’.  These Greek are transliterated as pentagrammon, pente, and grammos, respectively.

In the picture below, a regular pentagon is drawn dashed in black, the pentagram is drawn in blue, and the regular pentagon in the middle of the pentagram is shaded in cyan.

All pentagrams are similar.  If the length of the pentagon diagonal is $d$, then each side of the small pentagon in the middle of the pentagram is of length  $(\sqrt{5}-2)d$.

Title	pentagram
Canonical name	Pentagram
Date of creation	2013-03-22 17:08:52
Last modified on	2013-03-22 17:08:52
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	11
Author	pahio (2872)
Entry type	Definition
Classification	msc 51F99