Unit Spheres in a Pile
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Unit Spheres in a Pile
There are an unknown number of unit spheres in a pile shaped like a right circular cone. All of the dimensions of the cone are known and the angle of the cone's base is equal to the sphere's angle of repose. How many spheres are in the pile?
- doogly
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Re: Unit Spheres in a Pile
The angle of repose is a property of the material, it's not enough to just say that they are spheres.
The packing density is variable. See
https://en.wikipedia.org/wiki/Sphere_packing
The packing density is variable. See
https://en.wikipedia.org/wiki/Sphere_packing
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
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Re: Unit Spheres in a Pile
I did not know the term 'sphere packing'. When I googled it, I found this Wolfram page. It gives the densities for several different arrangements. Thank you for the help.
- doogly
- Dr. The Juggernaut of Touching Himself
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Re: Unit Spheres in a Pile
Worth noting that proving the "obvious" densest packing was actually so is a Gauss achievement. He is the best.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
- LucasBrown
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Re: Unit Spheres in a Pile
Gauss only proved that for lattices. The full theorem was only resolved in 1998.
- doogly
- Dr. The Juggernaut of Touching Himself
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- Joined: Mon Oct 23, 2006 2:31 am UTC
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Re: Unit Spheres in a Pile
Oh right, I should have qualified that better.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
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