# Illustrations of non-Euclidean geometry in virtual reality

@article{Skrodzki2020IllustrationsON, title={Illustrations of non-Euclidean geometry in virtual reality}, author={Martin Skrodzki}, journal={ArXiv}, year={2020}, volume={abs/2008.01363} }

Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself particularly well to geometrical objects. An example for this category of mathematical objects are hyperbolic geometric spaces. When Euclid lay down the foundations of mathematics, his formulation of geometry reflected the surrounding space, as humans perceive… Expand

#### One Citation

How to see the eight Thurston geometries

- Mathematics, Computer Science
- ArXiv
- 2020

This paper proposes a technique for immersive visualization of relevant three-dimensional manifolds in the context of the Geometrization conjecture that generalizes traditional computer graphics ray tracing. Expand

#### References

SHOWING 1-10 OF 51 REFERENCES

Non-euclidean Virtual Reality II: Explorations of H² ✕ E

- Computer Science
- 2017

The goal is to make three-dimensional non-euclidean spaces feel more natural by giving people experiences inside those spaces, including the ability to move through those spaces with their bodies, particularly for users who are not familiar with moving through space using “computer game” controls. Expand

The Fourth Dimension and Non-Euclidean Geometry in Modern Art

- Art, Mathematics
- 1983

In this groundbreaking study, first published in 1983 and unavailable for over a decade, Linda Dalrymple Henderson demonstrates that two concepts of space beyond immediate perception -- the curved… Expand

Understanding Curved Spacetime

- 2018

According to general relativity (GR), we live in a four-dimensional curved universe. Since the human mind cannot visualize those four dimensions, a popular analogy compares the universe to a… Expand

How to see the eight Thurston geometries

- Mathematics, Computer Science
- ArXiv
- 2020

This paper proposes a technique for immersive visualization of relevant three-dimensional manifolds in the context of the Geometrization conjecture that generalizes traditional computer graphics ray tracing. Expand

Real-time rendering in curved spaces

- Computer Science
- IEEE Computer Graphics and Applications
- 2002

A hypersphere surface provides a finite 3D world in which the user can fly freely without encountering boundaries, while hyperbolic space provides a spacious environment. The algorithm for rendering… Expand

Non-euclidean geometry in the modeling of contemporary architectural forms

- Mathematics
- 2013

When seeking inspiration for development of spatial architectural structures, it is important to analyze the interplay of individual structural elements in space. A dynamic development of digital… Expand

A survey of the use of non-euclidean geometry in electrical engineering

- Computer Science
- 1958

Abstract An attempt is made to give a brief resume of some of the non-Euclidean geometry models and some of their applications in electrical engineering. The survey starts with a discussion of diff… Expand

Non-Euclidean Virtual Reality III: Nil

- Computer Science, Mathematics
- 2020

A method of rendering real-time scenes in Nil geometry is described, and this is used to give an expository account of some interesting geometric phenomena. Expand

The Misnamings of Playfair’s Axiom

- 2016

The term “Playfair’s Axiom” is a mainstay of school geometry textbooks as well as one of the few things many mathematicians know about John Playfair (1748–1819), Professor of Mathematics and then of… Expand

Elementary Mathematics from an Advanced Standpoint: Geometry

- Mathematics
- 1941

elementary mathematics from an advanced standpoint geometry felix klein. Book lovers, when you need a new book to read, find the book here. Never worry not to find what you need. Is the elementary… Expand