Though early non-Eucledian geometry was studied by Bolyai in the Transylvanian mountains of eastern Europe, Lobachevski of Russia simultaneously, and independently of Bolyai, explored geometry omitting Euclid’s fifth postulate and arriving at similar conclusions about hyperbolic geometry. Both artists certainly create works that change one’s view of the world.Īre there examples of non-Euclidean geometry in non-European cultures? It’s a world that appears distorted as if some elements are reflected in water while other elements appear flattened. Though Dali’s work was less straightforward in it’s use of non-Euclidean geometry than Escher’s, the viewer still has a sense of something being other-worldly when viewing their work. Dali, a well known surrealist used non-Euclidean geometry to reject the usual rules of artwork in such works as The Persistence of Memory is his display of melting clocks in a scalding desert (Henderson, 2013). 250-252).” Escher essentially captured the essence of infinity in his tessellations.Īt the culmination of cubist, surrealist and expressionist art at the turn of the 20th Century, there were many artists who used non-Euclidean geometry in their artwork in a less obvious fashion. 4-5).” In these tessellations, symmetrical objects increase endlessly from a center point while decreasing in size “to approach an infinite number of points on the boundary of an enclosed region (Schattschneider, 1990, p. Escher explores hyperbolic symmetries in his work “Circle Limit (The Institute for Figuring, 2014, pp. Introduced to the concept by Donal Coxeter in a booklet entitled ‘A Symposium on Symmetry (Schattschneider, 1990, p. Where can elliptic or hyperbolic geometry be found in art? Compare at least two different examples of art that employs non-Euclidean geometry. Hyperbolic geometry is very useful for describing and measuring such a surface because it explains a case where flat surfaces change thus changing some of the original rules set forth by Euclid. This relativity of space to time is Einstein’s Theory of General Relativity (Greene, 2011). This causes the measurements taken on it’s ‘surface’ to bend, ripple and twist. Instead of space being measured as a flat surface or a box, it’s a box that bends, ripples and twists. These adjustments are what make up the shape of space-time. In order for this measurement to be true, the surface of space must not be absolute and the existence of time must not be absolute the speed of light is constant so other things must adjust to accommodate it. Light always has a fixed speed, no matter how we observe it (671 million mph). If we knew the given speed of light then it’s speed would change the same amount as the moving car, right? Actually, this is not true. Now, imagine that your speed is being measured by the radar sign but instead of measuring the speed of the car, the radar detects the light from the headlights. You know you are moving faster because you can feel the change in speed and see the measurement on the speedometer or on a radar sign. You realize you’re running late so you ask the driver to speed up. What are some applications of hyperbolic geometry (negative curvature)? Elliptic geometry or spherical geometry is just like applying lines of latitude and longitude to the earth making it useful for navigation. This type of geometry is used by pilots and ship captains to navigate the globe (Castellanos, 2007, pp. What are some applications of elliptic geometry (positive curvature)? Hyperbolic geometry is like dealing with the surface of a donut and elliptic geometry is like dealing with the surface of a donut hole. One way that helped me picture it is to think of negative space from a cut-out three dimensional object. 4).” Some real physical examples of this type of geometry are the curvatures or ruffles observed in lettuce or kelp (The Institute for Figuring, 2014). “In what physical context(s) does it make sense to think of curved space?Ī curved space may make sense when pictured as a “saddle or a Pringle (Mastin, 2010, pp. Remember that your claims must be supported by properly cited sources.” A substantive response will move our understanding forward through comments, questions or new resources. This is a discussion post, please follow principles answered in MyPost doc file to fulfill the following student work: “you are expected to initiate topics and provide substantive response to the student. History of Mathematics: Non-Euclidean Geometries and Curved Space (M5AR)
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