Non Euclidean and Euclidean geometry
applications
Answers
Answer:
Spherical geometry is applicable to all kinds of navigation and related calculations for movement on the earth (at least as a first approximation).
A more unusual application, which is still a subject of geometry research, is in computational origami. Consider a piece of paper folded with all folds through a single point. Can the paper be flattened without using any other folds except those final folds, without cutting the paper? Conversely, given a 'design' with the correct angle of paper around the vertex (that is 360 degrees) can the design be folded without additional folds? The proof that the answer is yes (being written up right now) using spherical geometry - since you might as well imagine the vertex is the center of the sphere, and you have cut off the paper with a circle centered at this vertex. The edges of the paper are now line segments on the sphere, and you are looking at motions of the polygon of such edges, on the sphere. If this seems esoteric, a young Canadian Geometer, Erik Demain (an assistant professor at MIT) just won a McArthur 'Genius Award' of half a million work, in part for his related work in computational origami, and related problems in the plane.
Explanation:
Euclidean geometry includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles and analytic geometry. ... Differential geometry uses techniques of calculus and linear algebra to study problems in geometry. It has applications in physics, including in general relativity.