The Pentagram

The Pentagram (or Pentangle) is 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

 

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

 

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

Ratios

But the pentagram has a special number hidden inside called the Golden Ratio, which equals approximately 1.618

  • a/b = 1.618...
  • b/c = 1.618...
  • c/d = 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:

  • 216/133 = 1.624...
  • 133/82 = 1.622...
  • 82/51 = 1.608...

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

Irregular Pentagram

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