pentagram

A pentagram is a five-pointed star shape formed by connecting five points evenly spaced on a circle. It can be drawn as a single continuous line or by drawing a regular pentagon and extending its sides to intersect. The most common form features a star outline with a smaller pentagon-shaped region in the center.

In geometry, the pentagram is a regular star polygon, denoted {5/2} in Schläfli notation. It has five vertices and five equal edges, and its lines intersect to create a smaller, similar pentagon inside. A key property is that the pentagram can be derived from a regular pentagon by drawing all its diagonals; the ratio of a pentagon’s diagonal to its side is the golden ratio.

Etymology and history: the word pentagram combines the Greek pente for five and gramma for line or figure. The symbol has appeared in various ancient cultures and traditions, and it has been associated with mathematical and philosophical ideas in early Greek thought, notably by the Pythagoreans, who valued its geometric symmetry and proportion.

Symbolism and usage: in modern times the pentagram is used in a range of contexts. When drawn with a single point upward, it is often interpreted as a symbol of protection, balance, or harmony; in some traditions the five points are linked to elements or qualities. An inverted (upside-down) orientation has also appeared in occult and esoteric contexts. The term pentacle can refer to the pentagram when it is inscribed in a circle.

Beyond symbolism, the pentagram appears in heraldry, architecture, art, and mathematics education as a classic example of a regular star polygon and its connections to the pentagon and the golden ratio.