Non-Euclidean geometry

[Lois]

Non-Euclidean geometry is a branch of geometry that explores geometrical systems which differ from classical Euclidean geometry, developed by the ancient Greek mathematician Euclid. While Euclidean geometry is based on the concept of flat surfaces and straight lines, non-Euclidean geometry studies spaces where this assumption does not hold true.

There are two main types of non-Euclidean geometry: hyperbolic geometry and elliptic geometry.

1. Hyperbolic Geometry: In hyperbolic geometry, the parallel postulate of Euclidean geometry is modified. In Euclidean geometry, the parallel postulate states that through a given point, there is exactly one line parallel to a given line. In hyperbolic geometry, however, there can be more than one line parallel to a given line through the same point. This results in the curvature of space, where the angles of a triangle add up to less than 180 degrees. Hyperbolic geometry has many applications in modern mathematics, including in the study of complex analysis, differential geometry, and topology.

2. Elliptic Geometry: Elliptic geometry, also known as Riemannian geometry, differs from Euclidean geometry in that it does not satisfy the parallel postulate at all. Instead, in elliptic geometry, no parallel lines exist, and the shortest distance between two points is along a great circle (a circle on the surface of a sphere whose center is at the center of the sphere). In elliptic geometry, the angles of a triangle add up to more than 180 degrees. Elliptic geometry has applications in fields such as cosmology, where it is used to model the curvature of spacetime in Einstein's theory of general relativity.

Non-Euclidean geometry has revolutionized our understanding of space and has profound implications in various areas of mathematics, physics, and other sciences. It has led to the development of new mathematical concepts and theories, providing insights into the nature of our universe that were previously unknown in the framework of classical Euclidean geometry.

 

 

[Nungali]

3 & 4

 

https://en.wikipedia.org/wiki/Synthetic_geometry

 

https://en.wikipedia.org/wiki/Projective_geometry

 

and of course

Synthetic projective geometry - Archive.org

 

[Lois]

45 minutes ago, Nungali said:

3 & 4

 

https://en.wikipedia.org/wiki/Synthetic_geometry

 

https://en.wikipedia.org/wiki/Projective_geometry

 

and of course

Synthetic projective geometry - Archive.org

 

 

 

From studying various things I derived 2 philosophical postulates 1. Everything happens in your mind. 2. The world corresponds to itself. At first glance, nothing special, but these are very far-reaching postulates.

 

 

[Nungali]

A synthetic projective geometric artist  ;

 

 

Lady Frieda Harris.

 

Examples of  her work ;

 

         

  Tarot cards , Priestess.                   Magus .

 

Initiation 'Tracing Boards' ;

 

First Degree.

 

Second  Degree .

 

Third Degree

 

 

 

 

http://www.phoenixmasonry.org/masonicmuseum/tracing_boards_frieda_harris.htm