Geometry

2202 Submissions

[5] viXra:2202.0060 [pdf] submitted on 2022-02-11 17:06:43

On the Number of Integral Points Between a K Dimensional Sphere and a Grid

Authors: Theophilus Agama
Comments: 7 Pages.

Using the method of compression we show that the number of integral points in the region bounded by the $2r\times 2r \times \cdots \times 2r~(k~times)$ grid containing the sphere of radius $r$ and a sphere of radius $r$ satisfies the lower bound \begin{align} \mathcal{N}_{r,k} \gg r^{k-\delta}\times \frac{1}{\sqrt{k}}\nonumber \end{align}for some small $\delta>0$.
Category: Geometry

[4] viXra:2202.0046 [pdf] submitted on 2022-02-09 19:25:21

Square Equations Represented with Gnomon

Authors: Juan Elias Millas Vera
Comments: 5 Pages.

In this paper I am going to present a soft extension of gnomon theory in geometry. The well known case for n^2 can be adjusted to (2n+1)^2 and (2n)^2. I show it with simple graphs and an algebraic explanation.
Category: Geometry

[3] viXra:2202.0036 [pdf] submitted on 2022-02-06 02:04:29

Research on Mathematical Butterfly Patterns Conducted up to 2013

Authors: Yuji Masuda
Comments: 3 Pages.

In the study of the deformation mechanism of metallic materials, this structure consisting of two metallic crystals with different crystal orientations, called the corresponding grain boundary, has been evaluated by a parameter called the ∑ value. In addition, it has been pointed out that the DSC (=Displacement of Complete pattern Shift)dislocation model may be affected by up to ∑ value 29 at the corresponding grain boundary. In this paper, we will focus only on the ∑ value, and use only the mathematical point of view.
Category: Geometry

[2] viXra:2202.0009 [pdf] submitted on 2022-02-03 20:06:09

On the General Gauss Circle Problem

Authors: Theophilus Agama
Comments: 7 Pages.

Using the method of compression we show that the number of integral points in a $k$ dimensional sphere of radius $r>0$ is \begin{align} N_k(r)\gg \sqrt{k} \times r^{k-1+o(1)}.\nonumber \end{align}
Category: Geometry

[1] viXra:2202.0006 [pdf] submitted on 2022-02-02 12:02:48

On a Variant of the Gauss Circle Problem

Authors: Theophilus Agama
Comments: 7 Pages.

Using the method of compression we show that the number of integral points in the region bounded by the $2r\times 2r$ grid containing the circle of radius $r$ and a circle of radius $r$ satisfies the lower bound \begin{align} \mathcal{N}_r \gg r^{2-\delta}\nonumber \end{align}for some small $\delta>0$.
Category: Geometry