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Results tagged with polygons
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user 13093
1
vote
What polygons can be shrunk into themselves?
Here is my variant, a bit more geometrical.
Denote by $P$ the original polygon, and $P_\lambda$ the contracted polygon with a factor $\lambda \in (0,1)$ which lies inside $P$. Note that $P_\lambda$ i …
- 2,222
0
votes
First Dirichlet eigenvalue on regular polygons
The quantity $\lambda(P)|P|$ is scale invariant since $\lambda(tP)=\frac{1}{t^2}\lambda(P)$. Therefore, its derivative with perturbations preserving the regularity of the polygon equals zero.
The deri …
- 2,222