# The Second Postulate of Euclid and the Hyperbolic Geometry

## TL;DR

This paper explores how violating Euclid's second postulate naturally leads to hyperbolic geometry, clarifying its relation to divergent series and relativistic calculations.

## Contribution

It establishes a direct link between Euclid's second postulate and hyperbolic geometry, highlighting implications for divergent series and relativity.

## Key findings

- Violation of Euclid's second postulate leads to hyperbolic geometry
- Hyperbolic geometry explains certain divergent series sums
- Connections to relativistic computations are identified

## Abstract

The article deals with the connection between the second postulate of Euclid and non-Euclidean geometry. It is shown that the violation of the second postulate of Euclid inevitably leads to hyperbolic geometry. This eliminates misunderstandings about the sums of some divergent series. The connection between hyperbolic geometry and relativistic computations is noted.

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Source: https://tomesphere.com/paper/1706.08378