12
votes
2answers
556 views

Right triangle with edge lengths equal to regular unit polygon edge lengths

This question came up naturally recently from a blog post of John Baez. There is an observation of Euclid that edges of a pentagon, hexagon, and decagon inscribed in a unit circle form the edges of a ...
11
votes
1answer
383 views

Heronian triangle with two sides that are prime

Can any prime number form a Heronian triangle with a second prime as another side? I cannot find a second prime to form a Heronian triangle with either 23 or 167. I have checked up to the 10^7th prime ...
10
votes
0answers
339 views

What is the field generated by an Archimedean Spiral?

Let $F \subset \mathbb R$ be the set of lengths of line segments that one can construct, starting from the points $(0,0)$ and $(1,0)$, using a straightedge, compass, and an Archimedean spiral - the ...
5
votes
1answer
339 views

What can be said about number-theoretic properties of the solid angle measures of polytopal cones in the weight lattice of sl(n)?

The following question might be elementary — it is too far from my area of expertise to tell. It has shown up in my research in an interesting way, which I will not go into here, but I'm happy to ...
11
votes
4answers
8k views

The Ramanujan Problems.

I originally thought of asking this question at the Mathematics Stackexchange, but then I decided that I'd have a better chance of a good discussion here. In the Wikipedia page on Ramanujan, there is ...