Polar Coordinate

Analysis

Distance on a Sphere

This article considers distances on a sphere and compare their properties with those in Euclidean space. We present the hypothesis that distances in gravity may not be exactly distances in Euclidean space, but may be approximations of distances on a sphere.
Probability

Probability Distribution on the Sphere

This article consider a probability distribution that is uniformly distributed on a sphere. In the case of a two-dimensional sphere, the probability distribution of each coordinate has a uniform distribution, and has some interesting properties.
Physics

Schrödinger Equation in the Free State (3 Dimensions)

In this article, we derive the solution to the three-dimensional Schrödinger equation when we consider a Gaussian wave packet model (white noise model) in the same way as in the one-dimensional case.