Non-Euclidean Geometry
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Torrent - Dimensions - A walk through mathematics
Nine chapters, two hours of math that take you gradually up to the fourth dimension.
Exotic spheres, or why 4-dimensional space is a crazy place
The world we live in is strictly 3-dimensional: up/down, left/right, and forwards/backwards, these are the only ways to move. For years, scientists and science fiction writers have contemplated the possibilities of higher dimensional spaces. What would a 4- or 5-dimensional universe look like?
F or the past year or so I've been spending most of my waking hours in a place where light, matter, energy and time obey different laws of physics than those that rule our own universe. Studying the way things move and interact under these alternative laws reveals some familiar behaviour, some strange and eerily beautiful phenomena, and some terrifying risks. To reach what I will call the Riemannian universe involves nothing more than changing a minus sign to a plus sign in a simple equation that governs the geometry of space-time.
Plus, Minus: A Gentle Introduction to the Physics of Orthogonal
The Ontology And Cosmology Of Non-Euclidean Geometry
Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence.