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Results tagged with polygons
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user 4354
13
votes
Accepted
What is the shape of the $n$-gon which gives the maximum of a function?
Thus the maximum ratio equals $\frac{n}{2(1-\cos\frac{2\pi}n)}$ and the optimal polygons are those whose $x$- and $y$-coordinates are sequences of the above form. …
- 6,210
8
votes
Accepted
Nonconvex manhole covers
Here is a construction of a polygon that cannot fall through the hole.
Begin with a regular $MN$-gon circumscribed around a unit circle, where $M\gg N\gg 1$ and $N$ is even. For every $M$th side, dra …
- 32.4k