A pentagram or pentacle is a fivepointed star. Pentagrams were used symbolically in ancient Greece and Babylonia. The Pentagram has magickal associations, and many people who practice pagan faiths wear them. Some Christians associate the symbol with Satanism, though most who use it are not Satanists.
Some sources refer to the pentagram as the "star of Solomon".
A perfect pentagram is easiest drawn by drawing a perfect pentagon, joining the corners with lines and erasing the original pentagon. You may also extend the sides of the pentagon until they meet, obtaining a bigger pentagram.
The word "pentagram" comes from the Greek word πεντάγραμμον (pentagrammon), a noun form of πεντάγραμμος (pentagrammos), πεντέγραμμος (pentegrammos) a word meaning roughly "fivelined" or "five lines".

The first uses of the pentagram we know of is in Mesopotamian writings dating to about 3000 B.C. In the Babylonian context, the edges of the pentagram were probably orientations: forward, backward, left, right, and "above". These directions also had an astrological meaning, representing the five planets Jupiter, Mercury, Mars and Saturn, and Venus as the "Queen of Heaven" (Schekina or Ishtar) above.
The Pythagorean Use of the Pentagram
Pentagram illustrating the golden mean hidden in it. 
The Pythagoreans called the pentagram ύγιεια Hugieia ("health" also the Greek god of health, Hygieia), and saw in it the pentagram a mathematical perfection: among other things, the pentagram hides the golden mean: when drawn with perfect angles each line is divided into several smaller segments, and if you divide the length of the longer segment with the shorter segment of any pair of segments you will get 1.618... In the illustration:
The five vertices were also used by the pythagoreans to represent the five Classical elements:
Pentagram image from Heinrich Cornelius Agrippa's "Libri Tres de Occulta Philosophia" illustrating the golden symmetry of the human body. The signs on the perimeter are astrological. 
Another pentagram from Agrippas book, this one has the Pythagorean letters inscribed around the circle. 
The vertices were labeled in the letters of υγιεια though the ordering (clockwise or counterclockwise) used, and starting vertex, could vary.
Satanists use pentagrams much the way they use the Christian cross: they turn it upside down either as a sign of disrespect, or just as a variant. They use the Pythagorean pentagram inscribed in a double circle, with the head of Baphomet inside the pentagram. The pythagorean Greek letters are replaced by the Hebrew letters forming the name Leviathan.
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