Hello! Please my lack of proper wording, but I'm not a native speaker, so I looked up some words, which may be incorrect. Anyway. I have three points on a sphere (globe) define …

There is a well known pattern that turns up in nature involving the golden ratio $\phi = \frac{\sqrt{5}-1}{2}$. To get this "sunflower spiral" pattern, put the $k$th node at an …

Suppose we have a (n-1 dimensional) Unit Sphere centered at the origin: $$ \sum_{i=1}^{n}{x_i}^2 = 1$$ What is the probability that a randomly selected point on the sphere, $ (x_1, …

using only a spherical ruler (to construct great lines) and a pair of compasses, how can you construct a regular dodecahedron on the surface of the sphere? thank you very much.

Suppose that $v_i$, for $i \in \{1, 2, \ldots 11, 12\}$, are twelve unit length vectors based at the origin in $R^3$. Suppose that $|v_i - v_j| \geq 1$ for all $i \neq j$. …

I have some code where the "hot part" relies on an inefficient solution to this problem. Problem: I have 3 inputs: a. A collection of N points on the surface of a sphere. b. A l …

Hi, my apologies if this is not the right place to ask this- I am not a mathematician (I'm a software engineer) and Im working on some 3D applications. My situation is this- give …

I am looking for a way to partially "grid" the surface of a sphere to have certain nice properties which will be defined precisely below. The areas should be "almost equal". It …

Short Version: How would one find the point of intersection of two rhumb line segments defined by two pairs of points on the globe? Assumptions such as a spherical Earth and foll …

How do you recenter a spherical coordinate system. For example, if the center were at $\left (0, 0, 0 \right )$ and I wanted to move the center of the spherical coordinate system t …

I'm looking for the algorithm that efficiently locates the "Loneliest Person on the Planet", where "loneliest" is defined as: Maximum minimum distance to another person -- that is …