[7] **viXra:1710.0264 [pdf]**
*submitted on 2017-10-23 07:56:01*

**Authors:** Edgar Valdebenito

**Comments:** 7 Pages.

This note presents some fractals related with the function: f(z)=((1-z^5)^2/(1+z^10))-z

**Category:** Geometry

[6] **viXra:1710.0241 [pdf]**
*submitted on 2017-10-22 16:40:29*

**Authors:** Paris Samuel Miles-Brenden

**Comments:** 5 Pages. None.

None.

**Category:** Geometry

[5] **viXra:1710.0147 [pdf]**
*submitted on 2017-10-14 08:51:55*

**Authors:** James A. Smith

**Comments:** 13 Pages.

We show how to express the representation of a composite rotation in terms that allow the rotation of a vector to be calculated conveniently via a spreadsheet that uses formulas developed, previously, for a single rotation. The work presented here (which includes a sample calculation) also shows how to determine the bivector angle that produces, in a single operation, the same rotation that is effected by the composite of two rotations.

**Category:** Geometry

[4] **viXra:1710.0137 [pdf]**
*submitted on 2017-10-13 01:17:37*

**Authors:** Antoine Balan

**Comments:** 5 pages, written in french

The Dirac operator is twisted by a symmetric automorphism, the Dirac-Lichnerowicz formula is proved. An application for the Seiberg-Witten equations is proposed.

**Category:** Geometry

[3] **viXra:1710.0131 [pdf]**
*submitted on 2017-10-11 07:44:42*

**Authors:** Edgar Valdebenito

**Comments:** 8 Pages.

This note presents a fractal image for f(z)=ln(1+g(z)).

**Category:** Geometry

[2] **viXra:1710.0127 [pdf]**
*submitted on 2017-10-11 20:27:18*

**Authors:** Choe ryujin

**Comments:** 4 Pages.

Proof of happy ending problem

**Category:** Geometry

[1] **viXra:1710.0110 [pdf]**
*replaced on 2017-10-13 16:26:37*

**Authors:** Mauro Bernardini

**Comments:** 4 Pages. this version corrects some accidental writing errors of the previous loaded version.

This paper attempts to provide a new vision on the 4th spatial dimension starting on the known symmetries of the Euclidean geometry. It results that, the points of the 4th dimensional complex space are circumferences of variable ray. While the axis of the 4th spatial dimension, to be orthogonal to all the three 3d cartesinan axes, is a complex line made of two specular cones surfaces symmetrical on their vertexes corresponding to the common origin of both the real and complex cartesian systems.

**Category:** Geometry