 |
 |
[8] viXra:2005.0271 [pdf] submitted on 2020-05-28 19:07:20
Authors: Angelo Maimone, Giorgio Nordo
Comments: 11 Pages.
We provide a formula that expresses the number of (n − 2)-gaps of a generic digital n-object.
Such a formula has the advantage to involve only a few simple intrinsic parameters of the object and it is obtained by using a combinatorial technique based on incidence structure and on the notion of free cells.
This approach seems suitable as a model for an automatic computation, and also allow us to find some expressions for the maximum number of i-cells that bound or are bounded by a fixed j-cell.
Category: Geometry
[7] viXra:2005.0218 [pdf] submitted on 2020-05-21 13:24:40
Authors: James A. Smith
Comments: Pages.
After reviewing the sorts of calculations for which Geometric Algebra (GA) is especially convenient, we identify a common theme through which those types of calculations can be used to find the intersections of spheres with lines, planes, and other spheres.
Category: Geometry
[6] viXra:2005.0200 [pdf] submitted on 2020-05-19 15:42:36
Authors: J Gregory Moxness
Comments: 15 pages, 18 figures, 6 equations, and 9 citations
Using rows 2 through 4 of a unimodular 8X8 rotation matrix, the vertices of E8 4_21, 2_41, and 1_42 are projected to 3D and then gathered & tallied into groups by the norm of their projected locations. The resulting Platonic and Archimedean solid 3D structures are then used to study E8's relationship to other research areas, such as sphere packings in Grassmannian spaces, using E8 Eisenstein Theta Series in recent proofs for optimal 8D and 24D sphere packings, nested lattices, and quantum basis critical parity proofs of the Bell-Kochen-Specker (BKS) theorem.
Category: Geometry
[5] viXra:2005.0196 [pdf] submitted on 2020-05-18 20:22:46
Authors: Souren E. Karapetian
Comments: 17 Pages.
The author of this article asked himself: why is mathematics built on a mythical infinite straight line and plane, and what happens if it is built on a circle and a sphere - the most perfect objects of nature?
The author called the resulting theory Objective Mathematics (OM), bearing in mind that this theory operates on natural objects that exist in nature (a circle and a sphere) and does not use the axiomatic approach, in particular the infinite parallel straight lines and planes present in traditional mathematics (TM).
The constructs and proofs in this article are first made on a circle (one-dimensional OM), and then the resulting law is generalized to a sphere (two-dimensional OM) and 3-sphere (three-dimensional OM).
The results obtained 4 empirical laws and 21 laws.
The paper gives definitions of such concepts as:
• A harmonic four (quartet) on a circle,
• A logical three-dimensional count,
• Preliminary mathematics (Premathematics) in OM,
• Non-Euclidean geometry in OM,
• One-dimensional, two-dimensional, three-dimensional OM, etc.
As a result of the analysis, the author concludes that the universe is a three-dimensional sphere, where a ray of light is a large circle of this sphere.
Category: Geometry
[4] viXra:2005.0129 [pdf] submitted on 2020-05-11 15:25:17
Authors: Ebuka Precious Iwuagwu
Comments: 29 Pages.
The whole of the postulations made in this paper simply aim at describing the positioning and occurrence of the circumscribing center of a triangle so much so that given any specifications and orientation for a particular triangle, the position could be sketched to exact precision and accurate dimensions without a single construction. With these postulations we are able to to envision clearly and describe where the circumscribing center of a triangle will be located without a single construction detail, all stemming from the fact that by the postulations we are able to study the circumscribing center's behavior with respect to the angles in the triangle given a particular orientation. Contained also in this paper are the mathematical justifications for each postulation made. A rule analogous to the sine rule is also observed but here pertains to the three 'perpendicular heights' obtainable respectively from the three vertices in the triangle, wherein the other two maybe obtained when only one is given alongside all the angles in the triangle.
Category: Geometry
[3] viXra:2005.0070 [pdf] submitted on 2020-05-06 10:52:07
Authors: Denivaldo Silva
Comments: 26 Pages. More information and comments on Theory of Objectivity and Author Vidamor Cabannas (Denivaldo Silva) can be found at www.theoryofobjectivity.com
This commentary aims to demonstrate the number of sides that make up the spherical point that occurs before the appearance of the Universe and confirm that it is not possible to build a minimal, perfect, and logical sphere without it being composed in its maximum circumference for less than sixty and four straight sides, as presented in the Objectivity Theory.
Category: Geometry
[2] viXra:2005.0049 [pdf] replaced on 2021-03-04 08:22:14
Authors: Dante Servi
Comments: 13 Pages. Copyright by Servi Dante.
Questo è il testo in Italiano ed in Inglese allegato ad una mia attività pubblicata su GeoGebra.org riguardante il mio metodo per creare e gestire una spirale poligonale logaritmica.
This is the text in Italian and English attached to my activity published on GeoGebra.org regarding my method to create and manage a logarithmic polygonal spiral.
Category: Geometry
[1] viXra:2005.0026 [pdf] submitted on 2020-05-02 02:23:00
Authors: Radhakrishnamurty Padyala
Comments: 9 Pages.
A geometrical proof of Ptolemy's theorem is presented. It shows the equality of the sum of the areas of the rectangles formed from the lengths of opposite sides of a cyclic quadrilateral to be equal to the area of the rectangle formed from the lengths of the diagonals. Introducing symmetry by choosing one of the component triangles of the quadrilateral to be an equilateral triangle, we prove the theorem for different cases. We then show that the specific case of maximum area configuration corresponds to that of a kite. By changing the kite configuration to that of a rectangle, we derive Pythagoras theorem as a special case of Ptolemy's theorem.
Category: Geometry
| Third-Party Links: |
|