Tessellations in concrete

A tessellation is a set of polygons that fills a plane without gaps or overlaps. Pavement makers often draw grooves in patterns like this example from Piedmont; I think one reason is to help the concrete break unobtrusively, along the grooves, rather than spiderwebbing all over a nice clean driveway. Another reason would be to help out the next worker who has to patch or repair the job by enabling them to cut the old concrete neatly. But mainly I think it’s just to show artisanship and decorate something utilitarian.

As a geologist, I look at this and infer a sequence of events. First came the sidewalk, installed by the developer. Then came the main part of the driveway, where the concrete worker tried to tie the tessellation to the divisions in the sidewalk and also tried to match the sidewalk’s color. Then came the worker who widened the driveway. He exercised less care in matching the colors, and less creativity in drawing grooves.

I also like the pattern of stones in the wall behind the driveway. Wallmaking is a whole nother expert art.

Mathematicians don’t care about haphazard tessellations like these. They’re fascinated by more challenging tessellations with some degree of order, or tessellations that can extend to infinity or wrap around curved surfaces and so on. You can get a dizzying taste of the subject at Wikipedia.

Polygons, by definition, have straight sides. Many sidewalk makers cover their work with curved grooves, and some time I’ll post a few examples. Those might conceivably be called tessellations, but I think I’ll just call them space-filling exercises.

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