Geometry

2012 Submissions

[8] viXra:2012.0204 [pdf] submitted on 2020-12-28 11:05:40

The Infinite Manifolds

Authors: Antoine Balan
Comments: 3 Pages. In English

We define the infinite manifolds and the infinite bundles which are spaces of dimension the cardinality of the continuum.
Category: Geometry

[7] viXra:2012.0194 [pdf] replaced on 2021-01-01 06:57:14

Gauss-Bonnet Theorem for Surfaces Embedded in a Four Dimensional Space

Authors: Vincenzo Nardozza
Comments: 3 Pages.

We study the Gauss-Bonnet theorem applied to a specific example.
Category: Geometry

[6] viXra:2012.0130 [pdf] submitted on 2020-12-16 11:12:58

Proving Basic Theorems about Chords and Segments via High-School-Level Geometric Algebra

Authors: James Smith
Comments: Pages.

We prove the Intersecting-Chords Theorem as a corollary to a relation-ship, derived via Geometric Algebra, about the product of the lengths of two segments of a single chord. We derive a similar theorem about the product of the lengths of a secant a chord.
Category: Geometry

[5] viXra:2012.0129 [pdf] submitted on 2020-12-16 11:15:46

Using Geometric Algebra: A High-School-Level Demonstration of the Constant-Angle Theorem

Authors: James A. Smith
Comments: 8 Pages.

Euclid proved (Elements, Book III, Propositions 20 and 21) proved that an angle inscribed in a circle is half as big as the central angle that subtends the same arc. We present a high-school level version of Hestenes' GA-based proof ([1]) of that same theorem. We conclude with comments on the need for learners of GA to learn classical geometry as well.
Category: Geometry

[4] viXra:2012.0128 [pdf] submitted on 2020-12-16 13:46:19

Simple Close Curve Gagnetization and Application to Bellman's Lost in the Forest Problem

Authors: Theophilus Agama
Comments: 7 Pages.

In this paper we introduce and develop the notion of simple close curve magnetization. We provide an application to Bellman's lost in the forest problem assuming special geometric conditions between the hiker and the boundary of the forest.
Category: Geometry

[3] viXra:2012.0116 [pdf] submitted on 2020-12-14 19:29:26

One Property of The Geodesic Lines of The Ellipsoid of Revolution

Authors: Abdelmajid Ben Hadj Salem
Comments: Pages.

In this note, we give one propriety of the geodesic lines of the ellipsoid of revolution.
Category: Geometry

[2] viXra:2012.0110 [pdf] replaced on 2020-12-17 03:39:19

The Continuous Tensor Calculus

Authors: Antoine Balan
Comments: 2 pages, written in french

We define the continuous tensor calculus which is the tensor calculus when the dimension of the spaces is the cardinality of the continuum. The spaces are called infinite manifolds
Category: Geometry

[1] viXra:2012.0067 [pdf] replaced on 2020-12-11 08:34:18

Remarks on the Circle Arising from Laurent Expansion

Authors: Hiroshi Okumura
Comments: 2 Pages.

We consider the notable circle for the arbelos arising from Laurent expansion appeared in [1], [2, 3] in detail.
Category: Geometry