Circle packing in an isosceles right triangle
Encyclopedia
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. Solutions to the equivalent problem of maximizing the minimum distance between n points in an isosceles right triangle, are known to be optimal for n< 8. In 2011 a heuristic algorithm found 18 improvements on previously known optima, the smallest of which was for n=13.
Packing problem
Packing problems are a class of optimization problems in mathematics which involve attempting to pack objects together , as densely as possible. Many of these problems can be related to real life packaging, storage and transportation issues...
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. Solutions to the equivalent problem of maximizing the minimum distance between n points in an isosceles right triangle, are known to be optimal for n< 8. 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... |