The Pentagram

Regular 5-pointed star pentagram

The Pentagram (or Pentangle) looks like a 5-pointed star.

You may think it has something to do with witchcraft, but in fact it is more famous as a magical symbol and is also a holy symbol in many religions.

In fact, this simple figure is quite amazing.

Inside a Pentagram is a Pentagon pentagram pentagon

Pentagon sides extending to form a pentagram

You can make a pentagram by first drawing a pentagon, then extending the edges.

Diagonals of a pentagon forming an internal pentagram

Or by drawing lines from corner to corner inside a pentagon.

Star Polygon

In fact a Pentagram is a special type of polygon called a "star polygon".

Pentagram with segments labeled a, b, c, and d for ratio comparison

Ratios

The regular pentagram (a perfectly even 5-point star) has a special number hidden inside called the Golden Ratio, which equals approximately 1.618:

When I drew this, I measured the 4 lengths and I got a=216, b=133, c=82, d=51. So let us check to see what the ratios are:

If I had drawn and measured more accurately, I would have been even closer!

Why not have a go yourself:

  • Draw a regular pentagram
  • Measure the lengths
  • Calculate the ratios

Try using a ruler or a drawing app to check the ratios yourself. Do your measurements match the Golden Ratio?

The pentagram is also great fun to draw ... or make!

sketching a pentagram
christmas star is a pentagram

Irregular Pentagram

So far we have explored the regular pentagram (all sides equal and all angles equal), but irregular pentagrams also exist!

 Comparison between a perfectly symmetrical pentagram and a distorted one
Pentagon Golden Ratio Geometry Index