2
votes
1answer
135 views

Bounding the number of integer solutions of the following inequality

Let $r\geq 1$ be a real number, $-1\leq x\leq 1$ a real number and $y>2$ a real number. We consider this data to be fixed. How can I obtain an upper bound on the number of $(a,b,c,d)\in ...
11
votes
2answers
191 views

Embedding the Infinite Binary Tree in Regular Tilings

Consider the regular tiling $(m,n)$ in which $m$ $n$-agons meet at each vertex. Most of the time this tilings have to "live" in the hyperbolic plane. The edges of its polygons define a graph where two ...