Circle packing in a right isosceles triangle is a packing problem where the objective is to pack n unit circles into the smallest possible isosceles right triangle.
Minimum solutions (lengths shown are length of leg) are shown in the table below.[1] Solutions to the equivalent problem of maximizing the minimum distance between n points in an isosceles right triangle, were known to be optimal for n < 8[2] and were extended up to n = 10.[3]
In 2011 a heuristic algorithm found 18 improvements on previously known optima, the smallest of which was for n = 13.[4]
Number of circles | Length |
---|---|
1 | = 3.414... |
2 | = 4.828... |
3 | = 5.414... |
4 | = 6.242... |
5 | = 7.146... |
6 | = 7.414... |
7 | = 8.181... |
8 | = 8.692... |
9 | = 9.071... |
10 | = 9.414... |
11 | = 10.059... |
12 | 10.422... |
13 | 10.798... |
14 | = 11.141... |
15 | = 11.414... |