Euclid believed that his fifth postulate could be proven from the other ones, and he failed, and so did many mathematicians through the ages. This is unfortunate, as players are attracted to such games, thinking “hey, at last I will have a chance to understand that weird and important thing what all these mathematicians were crazy about!”, which is nowhere near the truth -while these games are usually very cool, they are usually based on relatively straightforward concepts that have nothing to do with the original thing.Įuclid has shown how everything in geometry (Pythagorean Theorem, etc.) could be derived from a small set of very simple postulates… but there was one thing he was not happy about: his fifth postulate, which was not actually that simple: If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles. Recently, the term “non-Euclidean geometry” has been appropriated by some game developers for any kind of game space which works in a different way than ours. So many popular expositions of mathematics discussing non-Euclidean geometry have been created that the term has rightfully entered the general public conscience, as something extremely alien, important, crazy, and difficult to understand. It is something that many great thinkers for more than 2000 years believed not to exist (not only in the real world, but also in fantasy worlds). The discovery of non-Euclidean geometry is one of the most celebrated, surprising, and crazy moments in the history of mathematics. ✍︎ A hexagon in the hyperbolic plane can have six right angles. This article provides a summary of what “non-Euclidean” means, and the various weird geometries used in games. While such games typically tend to be amazing and very fun, this is not what “non-Euclidean” traditionally means for mathematicians, for whom it has a more precise meaning, which is not “anything that is not a perfectly normal space”. The term “non-Euclidean” is often used by gamers (game developers, journalists, etc.) to mean any kind of game where the space does not work exactly as in our world. Non-Euclidean geometry and games Non-Euclidean geometry and games
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