London Tsai 

This shape is the quintessential reverse curve. Mathematically, we call it hyperbolic as it has negative curvature. What is miraculous about it is that it is found all around us in nature. For example, take a look at leaves of plants and trees. A key property of hyperbolic shapes is that they do not hold water, which, if you think about it, is pretty important. In high school, we learn about Euclidean geometry. The key notion is that of Euclid's parallel postulate: Given a line L and a point P not on the line, there is exactly one line through P that is parallel to L. For centuries, people tried to prove that this postulate followed from Euclid's basic axioms. It wasn't until the 19th century when mathematicians Bolyai and Lobachevsky independently discovered hyperbolic geometry, which does not satisfy Euclid's postulate. You can think of hyperbolic geometry as geometry on a pringle. A striking feature of hyperbolic geometry is that the angles of a triangle add up to less than 180 degrees! LT www.londontsai.com 