Circle packing in an isosceles right triangle
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 are shown in the table below. 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 and were extended up to n = 10.
In 2011 a heuristic algorithm found 18 improvements on previously known optima, the smallest of which was for n=13.
| 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... |
