21.7k views
4 votes
What is non- euclidean geometry

1 Answer

2 votes

Final answer:

Non-Euclidean geometry is a type of geometry that deals with figures on a curved surface, unlike Euclidean geometry which is based on a flat space. It challenges Euclidean assuB) y = x^3 - 3x^2 + Cmptions, such as straight lines being the shortest distance between two points. This type of geometry is fundamental in the study and understanding of the universe's structure.

Step-by-step explanation:

Non-Euclidean geometry differs fundamentally from traditional Euclidean geometry. While Euclidean geometry assumes a 'flat' space, the non-Euclidean geometry is more about the geometry of curved space. It is primarily involved with the properties and relations of lines, angles, and figures on a curved surface, as seen on a sphere or hyperboloid.

For example, Euclidean postulates such as the shortest distance between two points would be a straight line, or that the total of angles in a triangle is 180 degrees, or that parallel lines never intersect, do not hold in non-Euclidean spaces. In non-Euclidean geometry, straight lines on a spherical surface, for instance, follow great circles and two such 'straight lines' can meet. It's a critical concept that allows us form a geometric representation of the universe and plays a key role in A Geometric Theory of Gravity.

Learn more about Non-Euclidean Geometry

User Josh Griggs
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories