# Determining how many Circles fit in a Triangle

• Nov 16th 2005, 12:59 PM
t_witt
Determining how many Circles fit in a Triangle
I would like some help on the following. Is there a way to calculate how many 3" diameter circles will fit in a given right triangle? Is so, can you please tell me how to do this? I need to yeild the most circles as possible.

• Nov 18th 2005, 12:10 PM
hpe
Quote:

Originally Posted by t_witt
I would like some help on the following. Is there a way to calculate how many 3" diameter circles will fit in a given right triangle? Is so, can you please tell me how to do this? I need to yeild the most circles as possible.

That depends on the size of the triangle.
• Nov 18th 2005, 12:20 PM
t_witt
The triangle can be any size. I'm trying to write a program to calculate how many circles will fit in a right triangle. The user will input the width and height.
• Nov 18th 2005, 01:25 PM
MathGuru
Interesting question, What is it for by the way?
• Nov 19th 2005, 05:45 AM
hpe
Quote:

Originally Posted by t_witt
The triangle can be any size. I'm trying to write a program to calculate how many circles will fit in a right triangle. The user will input the width and height.

Google for "circle packing". A simple solution (most likely suboptimal) consists in placing the right triangle in the first quadrant of the plane (with the right angle at the origin), imagining a square grid with squares of side length =6, and counting how many complete squares are inside the triangle, plus any partial squares that can still contain a circle of radius 3. For large triangles, a hexagonal packing probably is better.
• Nov 20th 2005, 01:23 PM
ThePerfectHacker
I would plot the vertices of this right triangle on the x-y coordinate plane, than investigate the problem from there. But it definitely depends on the radius and size of the triangle. I believ with complete faith that infinitely many triangles can be draw inside this triangle.
• Nov 21st 2005, 04:33 AM
t_witt
Thanks hpe I will give that a try.

The reason for this routine is that I work for a company that builds and installs wine cellars. We need the ability to calucate how many bottles will fit in a diamond cube. A quater of a diamond cube is a right triangle. Currently we reference a chart to determin how many bottles will fit in a cube. I'm trying to streamline the process.
• Nov 21st 2005, 11:55 AM
hpe
Quote:

Originally Posted by t_witt
Thanks hpe I will give that a try.

The reason for this routine is that I work for a company that builds and installs wine cellars. We need the ability to calucate how many bottles will fit in a diamond cube. A quater of a diamond cube is a right triangle. Currently we reference a chart to determin how many bottles will fit in a cube. I'm trying to streamline the process.

Then you'll have restrictions on the size of the triangle (due to weight considerations). What prevents you from using equilateral trianglea as basic packing shapes? These are known to be optimal (see picture).