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MatematikaRia.com


The Pentagram

The Pentagram (or Pentangle) is a 5pointed 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
So far we have only been looking at the regular pentagram (all sides and angles equal), but there are also irregular pentagrams.




