Circle packing in an equilateral triangle
Circle packing in an equilateral triangle is a packing problem in discrete mathematics where the objective is to pack n unit circles into the smallest possible equilateral triangle. Optimal solutions are known for n < 13 and for any triangular number of circles, and conjectures are available for n < 28.
A conjecture of Paul Erdős and Norman Oler states that, if n is a triangular number, then the optimal packings of n − 1 and of n circles have the same side length: that is, according to the conjecture, an optimal packing for n − 1 circles can be found by removing any single circle from the optimal hexagonal packing of n circles. This conjecture is now known to be true for n ≤ 15.
Minimum solutions for the side length of the triangle:
A closely related problem is to cover the equilateral triangle with a fixed number of equal circles, having as small a radius as possible.
- Circle packing in an isosceles right triangle
- Malfatti circles, a construction giving the optimal solution for three circles in an equilateral triangle
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