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Is A 2-Sided Polygon Possible?

less than 1m read
·Nov 10, 2024

65, 4, 3, 2, 1. Why don't we ever learn about dgon and monogon? Well, it's because they're impossible, right? No real eyes realize that you and I walk around on Dion and monagons every day. But big flat tells us that two straight lines can only meet at no points, one point, or every point.

A Dion, a polygon where two straight lines meet at two points, that could only happen if the lines curve. Then, it wouldn't be a polygon. But what if the lines don't curve? What if instead the space they inhabit curves? This line is straight. A two-dimensional observer would agree that it never turns, but unbeknownst to them, the line does curve into a higher spatial dimension beyond their comprehension.

Add another straight line sharing those vertices, and you've got a spherical loon, and it's a true two-sided polygon. But it's only possible in spherical geometry. On top of that, the hemisphere you live on is a monogon, a one-sided polygon. Its one and only side is any spherically straight line you can draw on the globe: a great circle.

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