Geometry

2204 Submissions

[3] viXra:2204.0134 [pdf] submitted on 2022-04-22 08:31:50

On the Number of Integral Points on the Boundary of a K-Dimensional Sphere

Authors: Theophilus Agama
Comments: 7 Pages. This results uses the method of compression to lower bound the number of integral points on the boundary of a sphere with a fixed radius.

Using the method of compression, we show that the number of integral points on the boundary of a $k$-dimensional sphere of radius $r$ satisfies the lower bound \begin{align} \mathcal{N}_{r,k} \gg r^{k-1}\sqrt{k}.\nonumber \end{align}
Category: Geometry

[2] viXra:2204.0072 [pdf] submitted on 2022-04-13 20:30:43

On the General Distance Problem in $\mathbb{r}^k$

Authors: Theophilus Agama
Comments: 7 Pages. This is a result of a general version of distance problem in a Euclidean space of arbitrary dimension.

Using the method of compression we obtain a generalized lower bound for the number of $d$-unit distances that can be formed from a set of $n$ points in the euclidean space $\mathbb{R}^k$. By letting $\mathcal{D}_{n,d}$ denotes the number of $d$-unit distances that can be formed from a set of $n$ points in $\mathbb{R}^k$, then we obtain the lower bound \begin{align} \mathcal{D}_{n,d}\gg \frac{n\sqrt{k}}{d}.\nonumber \end{align}.
Category: Geometry

[1] viXra:2204.0048 [pdf] submitted on 2022-04-09 23:11:15

An Analysis of the Barber Pole System of my Definition

Authors: Yuji Masuda
Comments: 2 Pages.

The purpose of this chapter is to publish some analysis of the Barber Pole.
Category: Geometry