The first published works expounding the existence of hyperbolic and other non-Euclidean geometries are those of a Russian mathematician, **Nikolay Ivanovich Lobachevsky**, who wrote on the subject in 1829, and, independently, the Hungarian mathematicians Farkas and János Bolyai, father and son, in 1831.

Contents

- 1 Who invented the hyperbolic geometry?
- 2 Who is the father of hyperbolic geometry?
- 3 When was hyperbolic geometry founded?
- 4 Why is it called hyperbolic geometry?
- 5 Who is the father of non-Euclidean geometry?
- 6 Do rectangles exist?
- 7 Who started geometry?
- 8 Who started non-Euclidean geometry?
- 9 Who discovered spherical geometry?
- 10 Is Euclidean geometry wrong?
- 11 What are the 3 types of geometry?
- 12 How was Euclids work influential?
- 13 Is hyperbolic geometry spherical?

## Who invented the hyperbolic geometry?

In 1869 –71 Beltrami and the German mathematician Felix Klein developed the first complete model of hyperbolic geometry (and first called the geometry “hyperbolic”).

## Who is the father of hyperbolic geometry?

Over 2,000 years after Euclid, three mathematicians finally answered the question of the parallel postulate. Carl F. Gauss, Janos Bolyai, and N.I. Lobachevsky are considered the fathers of hyperbolic geometry.

## When was hyperbolic geometry founded?

The complete system of hyperbolic geometry was published by Lobachevsky in 1829/1830, while Bolyai discovered it independently and published in 1832.

## Why is it called hyperbolic geometry?

Why Call it Hyperbolic Geometry? The non-Euclidean geometry of Gauss, Lobachevski˘ı, and Bolyai is usually called hyperbolic geometry because of one of its very natural analytic models.

## Who is the father of non-Euclidean geometry?

Carl Friedrich Gauss, probably the greatest mathematician in history, realized that alternative two-dimensional geometries are possible that do NOT satisfy Euclid’s parallel postulate – he described them as non-Euclidean.

## Do rectangles exist?

In neither geometry do rectangles exist, although in elliptic geometry there are triangles with three right angles, and in hyperbolic geometry there are pentagons with five right angles (and hexagons with six, and so on). At most one of them could be the true geometry of physical space.

## Who started geometry?

Euclid was a great mathematician and often called the father of geometry. Learn more about Euclid and how some of our math concepts came about and how influential they have become.

## Who started non-Euclidean geometry?

Riemann (1826-1866) – are traditionally associated with the discovery of non-Euclidean geometries.

## Who discovered spherical geometry?

geometry of the sphere (called spherics) were compiled into textbooks, such as the one by Theodosius (3rd or 2nd century bce) that consolidated the earlier work by Euclid and the work of Autolycus of Pitane (flourished c. 300 bce) on spherical astronomy.

## Is Euclidean geometry wrong?

There is nothing wrong with them. The problem is that until the 19th century they were thought to be the only ones possible, giving rise to a single possible geometry (the one called today “Euclidean”).

## What are the 3 types of geometry?

In two dimensions there are 3 geometries: Euclidean, spherical, and hyperbolic.

## How was Euclids work influential?

Who was Euclid? A Greek mathematician, often referred to as the “Father of Geometry”. His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics from the time of its publication until the late 19th or early 20th century.

## Is hyperbolic geometry spherical?

In spherical geometry there are no such lines. In hyperbolic geometry there are at least two distinct lines that pass through the point and are parallel to (in the same plane as and do not intersect) the given line.