All Questions
4 questions
11
votes
2
answers
455
views
Dodecahedral rolling distance
Let a dodecahedron sit on the plane,
with one face's vertices on an origin-centered unit circle.
Fix the orientation so that the edge whose indices are $(1,2)$ is horizontal.
For any $p \in \mathbb{R}...
- 151k
9
votes
1
answer
282
views
Thinnest covering of the plane by regular pentagons
Q. Is it known what is the thinnest covering of the infinite plane by regular pentagons?
By covering I mean every point of the plane is covered.
By thinnest I mean the proportion of the plane covered ...
- 151k
14
votes
1
answer
295
views
The space of triangles that fit inside a given triangle, parametrized by edge lengths
Given a triangle T with sides a, b, and c, describe its "fitting set," the set of all points (x,y,z) in 3-dimensions for which a triangle with sides x, y, z exists that fits in T.
Such a set lies in ...
- 141
34
votes
4
answers
2k
views
About the ratio of the areas of a convex pentagon and the inner pentagon made by the five diagonals
Question : Letting $S{^\prime}$ be the area of the inner pentagon made by the five diagonals of a convex pentagon whose area is $S$, then find the max of $\frac{S^\prime}{S}$.
...
- 4,757