# Geometry

## 1404 Submissions

[3] **viXra:1404.0409 [pdf]**
*replaced on 2014-06-04 23:42:12*

### On the System Analysis of the Foundations of Trigonometry

**Authors:** Temur Z. Kalanov

**Comments:** 22 Pages.

Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.

**Category:** Geometry

[2] **viXra:1404.0205 [pdf]**
*submitted on 2014-04-16 06:20:33*

### Mixt-Linear Circles Adjointly Ex-Inscribed Associated to a Triangle

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 6 Pages.

In [1] we introduced the mixt-linear circles adjointly inscribed associated to a triangle,
with emphasizes on some of their properties. Also, we’ve mentioned about mixt-linear circles
adjointly ex-inscribed associated to a triangle.
In this article we’ll show several basic properties of the mixt-linear circles adjointly exinscribed
associate to a triangle.

**Category:** Geometry

[1] **viXra:1404.0080 [pdf]**
*submitted on 2014-04-11 00:15:03*

### The Generalized Helices of Consecutively Order is Mannheim Pairs

**Authors:** Abel Cavaşi

**Comments:** 2 Pages.

A relationship between generalized helices and Mannheim pairs.

**Category:** Geometry