Īn easy way of identifying non-Euclidean geometry is by studying two lines perpendicular to a third line.In Euclidean space, the lines remain at a constant distance from each other even when extended to infinity. Once such space had caught the attention of the human mind, art could not have evaded its clutches. Einstein’s Relativity shot the hyperbolic space to fame. Bernhard Riemann in 1858 formulated the geometry in terms of a tensor, allowing it to be used in higher dimensions as well. Around 1830, Janos Bolyai and Nikolai Lobachevsky separately published treaties on non-Euclidean geometry. It was only in the 19 th century that we begin to see steps in the creation of non-Euclidean geometry by Carl Gauss and Ferdinand Schweikart independently around 1818. From Ibn al-Haytham in the 11 th century to Giovanni Saccheri in the 18 th century, they all failed. Mathematicians were troubled by the fact that they could not prove Euclid’s fifth postulate. Examples of this are Hyperbolic space and Elliptical space. Its surface is not flat and it does not have null curvature. The space created in which this parallel postulate does not hold is termed non-Euclidean space. If two lines are drawn that intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, the two lines inevitably must intersect each other on that side if extended far enough. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as centre.ĥ. Any straight line segment can be extended indefinitely in a straight line.ģ. His postulates state that:ġ.A straight line can be drawn joining any two pointsĢ. based on Euclid’s postulate as stated in his first book of the Elements. It is found in nature, the Folded Coral Flynn Reef is an example.Įuclidean geometry was formulated around 300B.C. Kinematic properties and concepts such as the world line and proper time have been explained in Minkowski space using hyperbolic geometry, the space-time membrane in Relativity uses such non-Euclidean geometry as well. This new geometry- Euclidean space has gone on to find application in Mathematics and Physics. If we follow the same principle and draw a triangle on the surface, the sum of the angles would not necessarily be 180° as is the rule in Euclidean geometry that we are familiar with. To find the distances between two places, we would not draw a straight line between them, instead we would have to traverse the surface of the earth. The first question that comes to one’s mind is what does non-Euclidean space look like? To provide a familiar example, one can think of the surface of a sphere such as the earth. Non-Euclidean Geometry by i2ebis on depicting the fictional city ofR’lyeh from H.P. For the unfamiliar eye, what is non-Euclidean geometry? How would one define and identify such geometry? What are examples of it being used in art? How was art influenced by developments in theoretical physics? What is the artist trying to convey and how does non-Euclidean space help him? Do these ideas align themselves with a larger purpose? I shall delve into the use of such non-Euclidean geometry in art. It has also been used in art, to lend a more other-wordly, non-conformist feel to the work, especially during the Surrealist movement. It has found uses in Science such as in describing space-time. Non-Euclidean geometry is more like curved space, it seems non-intuitive and has different properties. Euclidean geometry is flat- it is the space we are familiar with- the kind one learns in school.
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