The Pentagram

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

 

pentagram pentagon

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

 

pentagram pentagon

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

Polygon

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

 

pentagram lengths

Ratios

The regular pentagram 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's 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:

Irregular Pentagram

This has all been about the regular pentagram (all sides and angles equal), but there are also irregular pentagrams.

 pentagram regular and irregular

 

Pentagon Golden Ratio Geometry Index