Geometry

1211 Submissions

[4] viXra:1211.0134 [pdf] replaced on 2012-11-26 06:15:14

Law of Sums of the Squares of Areas, Volumes and Hyper Volumes of Regular Polytopes from Clifford Polyvectors

Authors: Carlos Perelman, Fang Fang, Garret Sadler, Klee Irwin
Comments: 9 Pages.

Inspired by the recent sums of the squares law obtained by Kovacs-Fang-Sadler-Irwin we derive the law of the sums of the squares of the areas, volumes and hyper-volumes associated with the faces, cells and hyper-cells of regular polytopes in diverse dimensions after using Clifford algebraic methods.
Category: Geometry

[3] viXra:1211.0099 [pdf] replaced on 2013-07-14 16:04:32

Product of Distributions Applied to Discrete Differential Geometry

Authors: Vincenzo Nardozza
Comments: 16 Pages.

A method for dealing with the product of step discontinuous and delta functions is proposed. A standard method for applying the above defined product of distributions to polyhedron vertices is analysed and the method is applied to a special case where the well known defect angle formula, for the discrete curvature of polyhedra, is derived using the tools of tensor calculus.
Category: Geometry

[2] viXra:1211.0024 [pdf] submitted on 2012-11-05 13:29:38

Several Metrical Relations Regarding the Anti-Bisectrix, the Anti-Symmedian, the Anti-Height and their Isogonal

Authors: Ion Patrascu, Florentin Smarandache
Comments: 4 Pages.

We’ll prove now that there is a similar relation for the isometric cevians as Steiner's relation for the isogonal cevians.
Category: Geometry

[1] viXra:1211.0023 [pdf] submitted on 2012-11-05 13:31:16

The Duality and the Euler’s Line

Authors: Ion Patrascu, Florentin Smarandache
Comments: 3 Pages.

In this article we’ll discuss about a theorem which results from a duality transformation of a theorem and the configuration in relation to the Euler’s line.
Category: Geometry