Maximizing Spheres: How Many Can Fit Around One?

  • Thread starter Thread starter Nabeshin
  • Start date Start date
  • Tags Tags
    Spheres
AI Thread Summary
In three-dimensional space (R3), the maximum number of identical spheres that can touch a central sphere is 12, known as the kissing number. While the upper bound of 27 spheres is mentioned, this figure refers to a theoretical volume filling rather than actual contact points. The discussion emphasizes the challenge of calculating the exact number of spheres that can surround a central sphere while maintaining contact. The concept of the kissing number is crucial for understanding this arrangement. Further exploration of geometric packing and sphere arrangements could provide additional insights.
Nabeshin
Science Advisor
Messages
2,207
Reaction score
16
Suppose I have a bunch of spheres, all with the same radius r. Now, take one sphere and set it aside in R3. The question then, is, how many spheres can I place around this sphere such that at least one part of them is touching the central sphere?

I've arrived at a very strict upper bound of 27 spheres, because 27 spheres would fill the entire volume of space between the surface of the central sphere and the outer sufaces of the surrounding spheres. Other than that, I don't really know how to get to an actual number. Thoughts?
 
Mathematics news on Phys.org
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...

Similar threads

Replies
9
Views
893
Replies
3
Views
22K
2
Replies
52
Views
7K
Replies
9
Views
5K
Replies
6
Views
4K
Replies
23
Views
3K
Back
Top