2
votes
1answer
340 views

Minimizing the Perimeter of a polyomino

Imagine I generate some polyomino (http://en.wikipedia.org/wiki/Polyomino) with $N$ unit squares, under the constraint that I want to maximize the number of shared edges between unit squares, or ...
1
vote
1answer
264 views

Frustrating the number of possible common edges between two connected components composed of square Penrose tiles

Imagine I have two bags of square and planar unit square tiles, with Penrose-like "nodules" on their edges s.t. two tiles can only be placed together if their edges are flush (i.e. if the two vertices ...
12
votes
1answer
294 views

The sparsest planar net that captures every unit segment

Let $\cal C = \lbrace C_i \rbrace$ be a collection of rectifiable curves in the plane with the property that every unit-length segment meets at least one curve in at least one point. Call such a ...
3
votes
1answer
247 views

Radial tilings with variable area ratios

I was looking at this neat page on logarithmic spiral tilings when a question popped up: http://www.uwgb.edu/dutchs/symmetry/log-spir.htm It seems that in all of the tilings shown, the area of each ...