# 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