Kissing Numbers in 3D: Exploring Different Sphere Sizes

In summary, "kissing numbers" in 3D refer to the maximum number of non-overlapping spheres that can be arranged around a central sphere. These numbers are determined using mathematical algorithms and have practical applications in fields such as physics, chemistry, and materials science. Kissing numbers can change with different sphere sizes and have been studied by mathematicians for centuries. Real-world examples of kissing numbers in 3D include the arrangement of oranges in a crate, the structure of crystals, and the arrangement of atoms in molecules.
  • #1
jal
549
0
I am looking for info on kissing numbers.
If all the spheres are of one unit then there are 12 spheres in 3d that can kiss the center sphere.
Question:
If the outer spheres are smaller by say 1/4, 1/2 etc. what would be the kissing numbers?
I assume that this has already been done but my search has not found anything.
jal
 
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  • #2
The reason it works out nice for spheres of equal size is because the dodecahedron has 12 faces. I think the answer is going to be ugly for sphere kissings that don't correspond to platonic solids.
 

FAQ: Kissing Numbers in 3D: Exploring Different Sphere Sizes

What are "kissing numbers" in 3D?

"Kissing numbers" refer to the maximum number of non-overlapping spheres that can be arranged around a central sphere in three-dimensional space.

How are kissing numbers determined in 3D?

The kissing numbers in 3D can be determined using mathematical algorithms and techniques, such as the densest packing of spheres and the Leech lattice. These methods involve finding the most efficient way to arrange spheres in three-dimensional space without overlap.

Why are kissing numbers important in 3D?

Kissing numbers in 3D have practical applications in fields such as physics, chemistry, and materials science. They can help us understand the arrangement of atoms in crystals and the packing of molecules in liquids, which can have significant impacts on the properties and behaviors of these substances.

Can kissing numbers change with different sphere sizes in 3D?

Yes, the kissing numbers in 3D can change with different sphere sizes. As the size of the central sphere increases, the maximum number of spheres that can be arranged around it also increases. This relationship is known as the "kissing number problem" and has been studied by mathematicians for centuries.

Are there any real-world examples of kissing numbers in 3D?

Yes, there are many real-world examples of kissing numbers in 3D. One famous example is the arrangement of oranges in a crate, where the maximum number of oranges that can be packed around a central orange is 12. Kissing numbers in 3D also play a role in the structure of certain crystals and the arrangement of atoms in molecules.

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