The other day I saw a design out of an old Arabian dictionary. It was two interlocking squares, joined together by arcs into one continuous line. It looked like something I could copy with a straight edge and compass, and in fairly quick order, I was able to work out the underlying geometry.
I worked on a color version in InkScape.
The next day, I wondered if one could do something similar with two interlocking pentagons. Since it's slightly easier to make a pentagon in InkScape than with analog tools, I sat down at the computer and worked out how to place the arcs on the lines. Since I was working with pentagons, I decided to use red as the main color.
The next day after that, I wondered what other polygons would work with the interweaving straight lines and arcs arrangement. I thought hexagons would be too tight for the arcs to fit aesthetically, and two interlocking triangles would result in "Happy Hanukah" jokes from Mark. So I set out to work with a septagon.
This is where I discovered that the figures with angles more acute than right angles don't allow arcs to nestle into their corners so easily. I had to experiment with septagrams with rays of various thicknesses before finding one that would work.
The arcs, it turns out, will have an angle of 180 minus (360/number of corners in the figure) and be centered on the intersection where two lines meet. I think the double-square pattern came out the best; the other two are fine... and I have a feeling I could nudge the radius of the arcs and the thickness of the lines some to make the "spokes" of the pattern more even.
I like them, and maybe I'll put them into a story. . .
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