Stars – part (ii)

The previous post was built on the observation that to draw a five-pointed star you use a single zig-zag line, and to draw a six-pointed star you must overlap two equilateral triangles. But there’s much more to find out.

 

The first time I explored these ideas I found some delightful surprises lying in wait, and the first one comes with seven-pointed stars. Actually there’s not one, but two seven-pointed stars you can draw, both by the single zig-zag line method. One version is – to my mind – elegant, and the other is fat and rather bloated

STAR 7 4STAR 7 3

 

And what about eight?   You may be beginning to expect that the superposition method will give an eight-pointed star, and if you use two squares that’s what you get.

STAR 8 3

But, wait a moment, there’s a second eight-pointed star – and this one is drawn by the single-line zig-zag method!

STAR 8 4

 

So we’ve already got a rich collection of results. With 5 points you get a zig-zag star; with 6 you get a star formed by overlap. 7 points gives you not one but two zig-zag stars, and 8 points produces both one zig-zag and one overlapping star. I’ll be very disappointed if you’re not already wondering about 9 pointed stars – zig-zags (and how many?), or overlap – or perhaps both?

 

Points Zig-zag Overlap Total
5 1 1
6 1 1
7 2 2
8 1 1 2
9 ? ? ?

It looks as if there are some rather seductive patterns to explore, doesn’t it?

.

More next time.

 

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