Intereting Posts

A Brownian motion $B$ that is discontinuous at an independent, uniformly distributed random variable $U(0,1)$
A continuous mapping is determined by its values on a dense set
intuition on the fundamental group of $S^1$
line equidistant from two sets in the plane
Why do the rationals, integers and naturals all have the same cardinality?
Characterizing bell-shaped curves
Finding a quartic polynomial in $\mathbb{Q}$ with four real roots such that Galois group is ${S_4}$.
A function that is both open and closed but not continuous
Darboux's Integral vs. the “High School” Integral
Do the sequences from the ratio and root tests converge to the same limit?
Hopf fibration and $\pi_3(\mathbb{S}^2)$
Show that a differential equation satisfies Lipschitz condition
geodesics on a surface of revolution
Is $\mathbf{R}^\omega$ in the uniform topology connected?
Result and proof on the conditional expectation of the product of two random variables

My goal is to put $n$ points on a sphere in $\mathbb{R}^3$ to divide it in $n$ parts, so that their disposition would be as “equivalent” as possible. I don’t exactly know what “equivalent” mathematically means, perhaps that the min distance between two points is maximal.

Anyway in $2$ dimensions it is simple to divide a circle in $n$ parts. In $3$ dimensions I can figure out some good re-partitions for particular values of $n$ but I lack a more general approach.

- Find if three points in 3-dimensional space are collinear
- Determine if projection of 3D point onto plane is within a triangle
- How to calculate volume of 3d convex hull?
- How to find shortest distance between two skew lines in 3D?
- how to calculate area of 3D triangle?
- What is the equation for a 3D line?

- Division of regular tetrahedron
- A geometric inequality, proving $8r+2R\le AM_1+BM_2+CM_3\le 6R$
- Decidability of tiling of $\mathbb{R}^n$
- Maximum area of a square in a triangle
- Normal Intersection of Parabola
- Deriving an implicit Cartesian equation from a polar equation with fractional multiples of the angle
- Isotopy and homeomorphism
- How to draw an ellipse if a center and 3 arbitrary points on it are given?
- How do you determine if a point sits inside a polygon?
- How to find the vertices angle after rotation

A nontrivial problem, I think. You might find some links into the research literature on Ed Saff’s homepage.

You can try the physical method: treat each point as an electron constrained in a sphere, and randomly distribute these point particles in the sphere, then you can solve the equations of motion to reach a stable (minimum energy) state, where each particle maximally separated from its closest neighbours (electric repulsive forces). Here is how to apply this method on a sphere surface.

- Effect the zero vector has on the dimension of affine hulls and linear hulls
- Difficulty level of Courant's book
- Vandermonde determinant by induction
- How do I count the subsets of a set whose number of elements is divisible by 3? 4?
- For positive invertible operators $C\leq T$ on a Hilbert space, does it follow that $T^{-1}\leq C^{-1}$?
- How to enumerate subgroups of each order of $S_4$ by hand
- Borel Measures: Atomic Decomposition
- How important is it to remember computational tricks as a pure mathematician?
- Best Sets of Lecture Notes and Articles
- Symmetric and exterior power of representation
- Combination of quadratic and arithmetic series
- What specific algebraic properties are broken at each Cayley-Dickson stage beyond octonions?
- In more detail, why does L'Hospital's not apply here?
- Bivariate polynomials over finite fields
- Literature on group theory of Rubik's Cube