Geometry

2405 Submissions

[6] viXra:2405.0167 [pdf] replaced on 2024-07-30 06:51:11

Gaps and Overlappings

Authors: Volker W. Thürey
Comments: 5 Pages.

In the first part, we investigate the tiling of the plane by convex polygons, andwe introduce many constants. At the end, we calculate one. We provide an example,where we cover the plane with convex 8-gons.In a second part, we take other curves and convex polygons.
Category: Geometry

[5] viXra:2405.0133 [pdf] submitted on 2024-05-26 15:03:01

Rectangle is Also a Parallelogram, and Square Too Has Parallel Sides

Authors: Arjun Dahal, Bipeen Singh Kunwar
Comments: 2 Pages.

We present a short theoretical proof to show that rectangle is also a parallelogram, and square too has parallel sides.
Category: Geometry

[4] viXra:2405.0120 [pdf] submitted on 2024-05-22 07:35:37

A Simple Approximation of pi

Authors: Wolfgang Sturm
Comments: 1 Page.

To approximate pi, the area of a circle segment is extrapolated to the full circle area and divided by the square radius.
Category: Geometry

[3] viXra:2405.0105 [pdf] replaced on 2024-06-28 21:00:51

The Method of Layered Separation of N-Cubes Along the Main Diagonal and Its Application in Geometry

Authors: Vladislav Koshchakov
Comments: 9 Pages. In Russian

The non-obvious possibility of decomposing any n-cube consisting of n-cubes (includingvisually perceptible 2D and 3D) into layers of these cubes sequentially placed along the maindiagonal of this n-cube is presented. At the same time, the number of n-cubes in each layerturned out to be closely related to the numbers of Pascal's triangle. The coefficients of cutting each n-cube from the last (n-1) layers of them with a section of dimension (n-1)D are calculated. Examples are given that allow us to outline some ways to further explore this possibility. In Addition, the possibility of using this method to prove the tetrahedron volume formula without using infinitesimal methods is shown.
Category: Geometry

[2] viXra:2405.0068 [pdf] submitted on 2024-05-13 20:51:14

Quadrature of the Circle with Compass and Straightedge and a Surprising Result for the Value of π in π R^2

Authors: Sigrid Obenland
Comments: 3 Pages.

It is general believe and deemd to be proven that the value of π in the formula for calculating the area of a circle; i.e. π r^2, is identical to the value of π in theformula for calculating the circumference of a circle; i.e. 2π r, which is irrational.Therefore, quadrature (or squaring) of the circle with compass and straightedge (or ruler) has been deemed to be impossible. We show that this was a prejudice and proof that quadrature is possible and clearly delivers π = 3 in the formula π r2 for calculating the area of the circle. We also show a physical experiment thatunambiguously proofs this result.
Category: Geometry

[1] viXra:2405.0028 [pdf] submitted on 2024-05-06 08:07:01

Deriving Curves from Points in the Cartesian Plane

Authors: Kohji Suzuki
Comments: 20 Pages.

We derive curves from predetermined points in the Cartesian plane and obtain the elliptic.
Category: Geometry