# Geometry

## 1305 Submissions

[2] **viXra:1305.0022 [pdf]**
*submitted on 2013-05-03 23:36:36*

### The Solution of the Problem of Relation Between Geometry and Natural Sciences

**Authors:** Temur Z. Kalanov

**Comments:** 11 Pages.

@@The work is devoted to solution of an actual problem – the problem of relation between geometry and natural sciences. Methodological basis of the method of attack is the unity of formal logic and of rational dialectics. It is shown within the framework of this basis that geometry represents field of natural sciences. Definitions of the basic concepts "point", "line", "straight line", "surface", "plane surface", and “triangle” of the elementary (Euclidean) geometry are formulated. The natural-scientific proof of the parallel axiom (Euclid’s fifth postulate), classification of triangles on the basis of a qualitative (essential) sign, and also material interpretation of Euclid’s, Lobachevski’s, and Riemann’s geometries are proposed.

**Category:** Geometry

[1] **viXra:1305.0013 [pdf]**
*submitted on 2013-05-03 01:15:25*

### The Critical Analysis of the Pythagorean Theorem and of the Problem of Irrational Numbers

**Authors:** Temur Z. Kalanov

**Comments:** 10 Pages.

@@The critical analysis of the Pythagorean theorem and of the problem of irrational numbers is proposed. Methodological basis for the analysis is the unity of formal logic and of rational dialectics. It is shown that: 1) the Pythagorean theorem represents a conventional (conditional) theoretical proposition because, in some cases, the theorem contradicts the formal-logical laws and leads to the appearance of irrational numbers; 2) the standard theoretical proposition on the existence of incommensurable segments is a mathematical fiction, a consequence of violation of the two formal-logical laws: the law of identity of geometrical forms and the law of lack of contradiction of geometrical forms; 3) the concept of irrational numbers is the result of violation of the dialectical unity of the qualitative aspect (i.e. form) and quantitative aspect (i.e. content: length, area) of geometric objects. Irrational numbers represent a calculation process and, therefore, do not exist on the number scale. There are only rational numbers.

**Category:** Geometry