Some topological fun

A friend sent me this tweet, start of a thread of some mathematically neat parks.

This jungle gym has the shape of one of the classic three-dimensional representations of the Klein bottle. It’s one of pop mathematics’s favorite shapes, up there with the Möbius strip, another all-time favorite.

Both the Klein bottle and the Möbius strip have many possible appearances, for about the same reason there are many kinds of trapezoids or octagons or whatnot. Möbius strips are easy enough to make in real life. Klein bottles, not so; the shape needs four dimensions of space and we just don’t have them. We’ll represent it with a shape that loops back through itself, but a real Klein bottle wouldn’t do that, for the same reason a wireframe cube’s edges don’t intersect the way the lines of its photograph do.

It makes a good wireframe shape, though. I’m surprised not to see more playground equipment using it.

Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

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