pentagram
Pentagram
2007-05-24 07:32:45
2008-01-14 06:14:15
Definition
pentagon
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A {\em pentagram} is the figure formed by the five diagonals of a \PMlinkname{regular}{RegularPolygon} pentagon.\, The name comes from the Greek $\pi\varepsilon\nu\tau\alpha\gamma\varrho\alpha\mu\mu o\nu$. Its \PMlinkescapetext{roots} are $\pi\varepsilon\nu\tau\varepsilon$ `five' and $\gamma\varrho\alpha\mu\mu o\varsigma$ `stoke, \PMlinkescapetext{line}'.\, These Greek \PMlinkescapetext{words} are transliterated as {\em pentagrammon}, {\em pente}, and {\em 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.
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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\, $(\sqrt{5}-2)d$.