# Geometry

## 1111 Submissions

[3] **viXra:1111.0113 [pdf]**
*replaced on 2012-07-24 23:23:58*

### Equidistant Curve Coordinate System(differential Forms)

**Authors:** Morio Kikuchi

**Comments:** 7 Pages.

The differential forms of two kinds in equidistant curve coordinate system can be changed into the differential forms in spherical orthogonal coordinate system by making a radius of the infinity sphere smaller limitlessly and making a constant of length larger limitlessly.

**Category:** Geometry

[2] **viXra:1111.0092 [pdf]**
*submitted on 24 Nov 2011*

### Smooth Infinitesimal Analysis Based Model of Multidimensional Geometry

**Authors:** Alexander Egoyan

**Comments:** 6 pages.

In this work a new approach to multidimensional geometry based on smooth infinitesimal analysis (SIA) is
proposed. An embedded surface in this multidimensional geometry will look different for the external and internal
observers: from the outside it will look like a composition of infinitesimal segments, while from the inside like a set of
points equipped by a metric. The geometry is elastic. Embedded surfaces possess dual metric: internal and external.
They can change their form in the bulk without changing the internal metric.

**Category:** Geometry

[1] **viXra:1111.0005 [pdf]**
*replaced on 2012-05-23 01:12:23*

### Equidistant Curve Coordinate System (3 Dimensions)

**Authors:** Morio Kikuchi

**Comments:** 15 Pages.

In three-dimensional equidistant curve coordinate system, a constant of length on a sphere depends upon its radius. Equidistant curve and round line have the relation of the inversion between a plane and a coordinate sphere, generally between a coordinate sphere and another coordinate sphere.

**Category:** Geometry