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
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.
But, wait a moment, there’s a second eight-pointed star – and this one is drawn by the single-line zig-zag method!
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?
It looks as if there are some rather seductive patterns to explore, doesn’t it?
More next time.