Geometry

2003 Submissions

[7] viXra:2003.0643 [pdf] submitted on 2020-03-29 15:59:30

Generalizing the Pythagorean and Euclidean Theorems. Die GDM Hat Ihren Namen Nicht Verdient

Authors: Martin Erik Horn
Comments: 104 Pages. German powerpoint slides of the GDM Online Conference 2020 with a short English summary

Transformations of equations with scalar quantities are a mathematical cornerstone concept of modern algebra. It will be demonstrated in this GDM presentation how transformations of geometrical quantities can form an equivalent mathematical cornerstone concept of modern geometry. Thus variables will not be only scalars, but also vectors, bivectors or other geometric entities. This Geometric Algebra will be discussed and analysed with respect to the Pythagorean and Euclidean theorems.
Category: Geometry

[6] viXra:2003.0637 [pdf] replaced on 2020-03-31 11:28:12

On a Triangle with Two Parallel Sides

Authors: Hiroshi Okumura
Comments: 2 Pages.

We consider the side lengths of a triangle with two parallel sides by division by zero.
Category: Geometry

[5] viXra:2003.0483 [pdf] replaced on 2020-03-26 23:51:32

On the Distance Between the Incenter and the Circumcenter of a Triangle

Authors: Kaoru Motose
Comments: An error ST on line 13 from the top of page 2 in the old preprint changed to correct letters SJ at 2020/03/26 by the author.

In this paper, using mainly the distance in the title, we present an alternative proof of Feuerbach's theorem and some remarks.
Category: Geometry

[4] viXra:2003.0380 [pdf] submitted on 2020-03-17 22:05:13

A Pair of Congruent Circles in Tenzan Tebikigusa Furoku

Authors: Hiroshi Okumura
Comments: 8 Pages.

We generalize non-Archimedean congruent circles appeared in Samp\=o Tenzan Tebikigusa Furoku to the collinear arbelos.
Category: Geometry

[3] viXra:2003.0276 [pdf] replaced on 2020-03-14 14:03:09

Excircles of a Triangle with Two Parallel Sides

Authors: Hiroshi Okumura
Comments: 2 Pages.

For a triangle $ABC$, the radius of the excircle touching $CA$ from the side opposite to $B$ equals $0$ if $BC$ and $CA$ are parallel.
Category: Geometry

[2] viXra:2003.0230 [pdf] replaced on 2020-03-15 08:51:36

On the Roots of Simplexes

Authors: Heritier Ifoma Nsombo
Comments: 2 Pages.

I present a general method for computation of rough estimates for “roots" of simplexes (polytopes). This method gives a hope of potentially refining the algorithm to compute the exact roots.
Category: Geometry

[1] viXra:2003.0143 [pdf] submitted on 2020-03-07 03:58:02

The Curvature of Functions for a Kaehler Manifold

Authors: Antoine Balan
Comments: 1 page, written in english

We define the notion of curvature of functions for a Kaehler manifold.
Category: Geometry