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## hyperbolic

### Examples

• hyperbolic function n. Any of a set of six functions related, for a real or complex variable x, to the hyperbola in a manner ***ogous to the. — “hyperbolic function: Definition from ”,
• Hyperbolic geometry is one of the most important examples of a "non-Euclidean" geometry, Historically, hyperbolic geometry was discovered as a consequence of questions about the. — “The Hyperbolic Geometry Exhibit”, geom.uiuc.edu
• The ﬁnal class of functions we will consider are the hyperbolic functions. for all x. Since the hyperbolic sine function is deﬁned in terms of the exponential function,. — “Section 6.7 Hyperbolic Functions”, math.furman.edu
• of non-Euclidean geometry called hyperbolic geometry. Recall that one. of Euclid's unstated assumptions was that lines are inﬁnite. of hyperbolic geometry: Carl Frederick Gauss (1777–1855), Nicolai Loba. — “Hyperbolic Geometry”, faculty.etsu.edu
• Below, I will trace some of the history of hyperbolic art starting with Escher's hyperbolic inspiration from a figure by the mathematician H. S. M. Then I will discuss some of the hyperbolic art created by other artists, and I will finish by explaining the relationship between Escher's print. — “2003 MAM Poster Essay”, d.umn.edu
• Hyperbolic geometry and non-Euclidean geometry are considered in many In this chapter we will introduce the geometry of the hyperbolic plane as the intrinsic geometry of a particular surface in 3-space, in much the same way that we introduced spherical geometry by looking at the intrinsic geometry. — “Body”, math.cornell.edu
• hyperbolic algebra. hyperbolic angle. hyperbolic automorphism. hyperbolic coordinate hyperbolic cosine. hyperbolic cosine integral. hyperbolic cotangent. hyperbolic cube. — “hyperbolic - Wiktionary”,
• Definition of hyperbolic from Webster's New World College Dictionary. designating or of any of a set of six functions (hyperbolic sine, hyperbolic cosine, etc.) related to the hyperbola in a manner similar to that by which the trigonometric functions are related to the circle. — “hyperbolic - Definition of hyperbolic at ”,
• This is like trig substitution, but you use these newly-introduced hyperbolic functions instead. — “Karl's Calculus Tutor - 11.5 Hyperbolic Substitution”,
• Hyperbolic definition, having the nature of hyperbole; exaggerated. Hyperbolic Definition. Find Definitions For Any Word.Get Your Free Toolbar. — “Hyperbolic | Define Hyperbolic at ”,
• Definition of word from the Merriam-Webster Online Dictionary with audio pronunciations, thesaurus, Word of the Day, and word games. Next Word in the Dictionary: hyperbolic function. — “Hyperbolic - Definition and More from the Free Merriam”, merriam-
• Escher's Circle Limit Exploration This exploration is designed to help the student gain an intuitive understanding of what hyperbolic geometry may look like. Escher's prints are nice examples that illustrate what we would see when looking down on a hyperbolic universe. — “Hyperbolic Geometry - EscherMath”, math.slu.edu
• Definition of hyperbolic in the Online Dictionary. Meaning of hyperbolic. Pronunciation of hyperbolic. Translations of hyperbolic. hyperbolic synonyms, hyperbolic antonyms. Information about hyperbolic in the free online English dictionary and. — “hyperbolic - definition of hyperbolic by the Free Online”,
• In mathematics, hyperbolic functions are ***ogs of the ordinary trigonometric, or circular, functions. Hyperbolic functions occur in the solutions of some important linear differential equations, for example the equation defining a catenary, and Laplace's equation in Cartesian coordinates. — “Hyperbolic function - Wikipedia, the free encyclopedia”,
• The hyperbolic functions enjoy properties similar to the trigonometric functions; their definitions, though, are much more straightforward: While , , parametrizes the unit circle, the hyperbolic functions , , parametrize the standard hyperbola , x>1. — “Hyperbolic Functions”,
• The Math Forum's Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites relating to Hyperbolic Geometry. — “The Math Forum - Math Library - Hyperbolic Geom”,
• Among smooth dynamical systems, hyperbolic dynamics is characterized by the presence of expanding and contracting directions for the derivative. A particular class of hyperbolic sets that has engendered much interest is that of hyperbolic attractors. — “Hyperbolic dynamics - Scholarpedia”,
• The hyperbolic functions , , , , , (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and hyperbolic cotangent) are ***ogs of the circular functions, defined by removing s appearing The hyperbolic functions arise in many problems of mathematics and. — “Hyperbolic Functions -- from Wolfram MathWorld”,
• Hyperbolic geometry was created in the ﬁrst half of the nine***th century This postulate is to hyperbolic geometry as the parallel postulate 5 is to Eu. — “Hyperbolic Geometry”,
• Flash MX 2004 ActionScript2.0 Library: Hyperbolic - Wright Internet Solutions. — “WIS AS2 Library : com.wis.math.trig.Hyperbolic Documentation”, members.shaw.ca