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The word "hyperbola" derives from the Greek ὑπερβολή, meaning "over-thrown" or "excessive", from which the English term hyperbole also derives. Hyperbolae were discovered by Menaechmus in his investigations of the problem of doubling the cube, but were then called sections of obtuse cones. [2]
Canton Tower, Guangzhou, China Kobe Port Tower, Kobe, Japan Cooling tower, Puertollano, Spain. This page is a list of hyperboloid structures.These were first applied in architecture by Russian engineer Vladimir Shukhov (1853–1939).
The hyperbola is the isogonal conjugate of , the line joining the circumcenter and the incenter. [3] This fact leads to a few interesting properties. Specifically all the points lying on the line have their isogonal conjugates lying on the hyperbola.
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A triangle immersed in a saddle-shape plane (a hyperbolic paraboloid), along with two diverging ultra-parallel lines. In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry.
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A ray through the unit hyperbola x 2 − y 2 = 1 at the point (cosh a, sinh a), where a is twice the area between the ray, the hyperbola, and the x-axis. For points on the hyperbola below the x-axis, the area is considered negative (see animated version with comparison with the trigonometric (circular) functions).