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[parent] pentagram (Definition)

A pentagram is the figure formed by the five diagonals of a regular pentagon. The name comes from the Greek $\pi\varepsilon\nu\tau\alpha\gamma\varrho\alpha\mu\mu o\nu$ . Its roots are $\pi\varepsilon\nu\tau\varepsilon$ `five' and $\gamma\varrho\alpha\mu\mu o\varsigma$ `stoke, line'. These Greek words 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.


\begin{pspicture}(-3,-3)(3,3) \pspolygon[linestyle=dashed](0,3)(-2.853,0.927)(-1... ...ots(0,3)(-2.853,0.927)(-1.763,-2.427)(1.763,-2.427)(2.853,0.927) \end{pspicture}

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 $(\sqrt{5}-2)d$ .




"pentagram" is owned by pahio. [ full author list (2) ]
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Cross-references: side, length, similar, pentagon, diagonals
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This is version 8 of pentagram, born on 2007-05-24, modified 2008-01-14.
Object id is 9456, canonical name is Pentagram.
Accessed 1144 times total.

Classification:
AMS MSC51F99 (Geometry :: Metric geometry :: Miscellaneous)

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