I have five colors of post-it notes, and I want to make a post-it-coaster. The first time I did this, I did it by eye, and it didn't work so well. Last time, I realized that I actually know math.
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| The base post-it. |
Five post-its means I'm making a pentagon. The sum of interior angles of a polygon is 180 * (n-2) or 540. There are five such angles, so each one is 108. The excess from the 90 corner of a post it is 18. Converting this to radians tells us that q = pi/10, so tan(q) ~ 1/3 (due to small angle formula). The triangle formed from this has to meet the triangle from the opposite corner halfway across the base post-it (due to symmetry). This means that the intersection point is 1/6 the height of the post-it.
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| Make a mark there. |
Now all the remaining post-its can be placed, keeping that angle in common.
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| And you get a tiny corner that isn't totally correct, but it's close enough. |
