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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

Videos

  • Hyperbolic Geometry is Projective Relativistic Geometry (Part2) Part 2 (of 6) of a Pure Mathematics Seminar given at UNSW in the School of Mathematics and Statistics. Assoc Prof NJ Wildberger explains a new approach to hyperbolic geometry which links it directly to Einstein and Minkowski's relativistic geometry viewed projectively. The idea is to extend Rational Trigonometry to the hyperbolic setting. The first part of the lecture motivates with a summary of classical hyperbolic geometry, then the purely algebraic set-up is introduced. Quite a few new results are introduced.
  • Hyperbolic Geometry is Projective Relativistic Geometry (Part3) Part 3 (of 6) of a Pure Mathematics Seminar given at UNSW in the School of Mathematics and Statistics. Assoc Prof NJ Wildberger explains a new approach to hyperbolic geometry which links it directly to Einstein and Minkowski's relativistic geometry viewed projectively. The idea is to extend Rational Trigonometry to the hyperbolic setting. The first part of the lecture motivates with a summary of classical hyperbolic geometry, then the purely algebraic set-up is introduced. Quite a few new results are introduced.
  • Hyperbolic Crochet - From Beginning to End. I made this Hyperbolic Crochet video, to give people an idea how the crenellated forms of Hyperbolic crochet emerge, when you increase at a constant rate. The inspiration came from The Institue for Figuring's website, / - well worth a look for more beautiful examples of others work, and the awareness they are bringing to the future of coral reefs from around the world. Thanks.
  • Hyperbolic paraboloid Rendering of a hyperbolic paraboloid
  • Hyperbolic Time Chamber Theme Hyperbolic Time Chamber
  • Hyperbolic Lady Thermal sailplane 3.0m span, 29 oz RTF. Speed 400 motor on 2S, very slow climb. Windy and weak thermal but still great fun.
  • Inverse Hyperbolic Functions - Derivatives Inverse Hyperbolic Functions - Derivatives. In this video, I give the formulas for the derivatives on the inverse hyperbolic functions and do 3 examples of finding derivatives. For more free math videos, visit
  • Hyperbolic Planes Take Off! I gave this talk at the 2011 Joint Mathematics Meetings in New Orleans. It was meant for an audience of mathematicians, but the big words aren't as important as the pretty pictures, so I hope everyone can enjoy! More information about everything I talked about can be found on also see
  • hyperbolic saddle A (Rhino) Grasshopper script that generates hyperbolic saddle shaped surfaces
  • Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007 Exponential and log Logarithmic differentiation; hyperbolic functions Note: More on "exponents continued" in lecture 7 View the complete course at: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
  • Hyperbolic Functions - Derivatives Hyperbolic Functions - Derivatives. In this video, I show the formulas for the derivatives of the hyperbolic functions and find a few derivatives. For more free math videos, visit
  • Not Knot (Part 1/2) Part 1 of 2 of Not Knot. Not Knot is a guided tour into computer-animated hyperbolic space. It proceeds from the world of knots to their complementary spaces -- what's not a knot. Profound theorems of recent mathematics show that most known complements carry the structure of hyperbolic geometry, a geometry in which the sum of three angles of a triangle always is less than 180 degrees. www.geom.uiuc.edu
  • Hyperbolic Crochet Coral Reef Video.wmv Marine biologist Nancy Knowlton demonstrates the Hyperbolic Crochet Coral Reef, on exhibit at the Smithsonian's National Museum of Natural History, in Washington, DC Learn more about this work of art and education produced by hundreds of crocheters of all ages, from 3 to 101, and what it teaches us about the real-life world of the coral reef.
  • Amber Case - An Introduction to Hyperbolic Geometry Traditional geometry is something we all learned in school. Some of us like it, and the rest of us don't. In traditional geometry, parallel lines stay parallel, and triangles are always 180 degrees. Theses are the rules, and they cannot be broken. Enter Hyperbolic Geometry. It's not new, but it is an AWESOME field of mathematics. Basically, it breaks all the rules. In this presentation, I'll demonstrate some of the history and implications of this field, a field that has inspired Escher and sent Euclid rolling in his grave. I'll also explain the mysterious 5th Postulate and how all of this applies to the web. Sound complicated? Don't panic! I'll use a lot of pictures and ***ogies. And with all of the beer you'll all be consuming, the ideas should enter your brain smoothly and enjoyable. This won't hurt a bit.
  • The Complete Hyperbolic Crochet Video - Pseudosphere My Hyperbolic Crochet Animation - beginning to end, has been quite popular. So, I thought I'd video a Hyperbolic Pseudosphere being crocheted from first stitch to last, then speeding it up so the viewer could see one being created from beginning to end. The original footage totaled 152 minutes and 32 seconds (filmed over a couple of days!), so you can enjoy the process in a fraction of the time! (time-lapse) I hope you enjoy this video. ***Best viewed in High Quality***
  • Hyperbolic trig functions | MIT 18.01SC Single Variable Calculus, Fall 2010 Hyperbolic trig functions Instructor: Joel Lewis View the complete course: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
  • Hyperbolic Functions - Definitions and graph of cosh x A short introduction to hyperbolic functions. Don't get mislead by their 'unpopularity' compared to trigonometric functions. Hyperbolic functions do have their uses. Check out for an indepth study and for more calculus related topics.
  • Hyperbolic Functions - The Basics Hyperbolic Functions - The Basics. In this video, I give the definitions of the hyperbolic functions, do a rough graph of three of the hyperbolic functions, evaluate a few of the functions at different values, and lastly I justify a couple of identities. For more free math videos, visit
  • Frank Farris Introduces "Hyperbolic Wallpaper" Frank Farris introduces his talk "Hyperbolic Wallpaper." For more go to
  • The Hyperbolic Geometry Song This is a math project I did back in 9th Grade about Hyperbolic Geometry. It's a parody of one of my old favorite songs, Superman by Five for Fighting. I wrote the lyrics, animated the movie, and *shudder* sang the song. Feel free to laugh at my singing, I don't pretend I'm any good. I got an A on the project, though. **EDIT: Due to consistent requests for lyrics, here they are: ---- The Hyperbolic Geometry Song Lyrics by Jason Merrin Song parody of "Superman" by Five for Fighting Geometric lines In negatively curved space Can curve in all different directions In this strange but common case Not a regular line on a regular plane As it goes farther out it increases in length It's hyperbolic geometry Hyperbolic geometry's not strange In fact it is just fine Especially for a person Who wants three or more parallel lines I think it's right, I think it's a hit That outside of the Poincare disc is infinite And riding a horse is a tough battle Without a pseudosphere disc shaped saddle It's hyperbolic geometry The closer to the edge a segment gets The longer it is This will be on the quiz The closer it gets To infinity Hyperbolic triangles Which sort of look like trees Are always curved strangely So that they're less than 180 degrees Not a regular line on a regular plane Shaped like a potato chip on a subway train Not a regular line on a regular plane A complicated challenge for the human brain The human brain The human brain The human brain It's hard for the brain Not a regular ...
  • Hyperbolic Tree Browser -- 1995 One of the earliest focus+context visualizaitons for trees (hierarchies). This technique has embedded in many software products and deployments through Inxight (est. $30+M in 11 years)
  • Hyperbolic circle In non-euclidean geometry, a circle is a conic that is doubly tangent to the absolute conic. For more information, films, and interactive material, see
  • LEGO hyperbolic paraboloid This is a LEGO Technic Hyperbolic Paraboloid. It is an example of a ruled surface. See for more info.
  • Origami - Hyperbolic Parabola A tutorial on how to make a hyperbolic parabola. Intermediate-Advanced. You need 1 square piece of lightweight paper. (origami paper is obviously the best, but other light paper will work). The first time I made one it took me 2-3 hours to figure it out on my own, I hope this helps you get through it faster. Enjoy. (next time I may narrate since the text is hard to see on youtube). to download. For a diagram: www.math.lsu.edu
  • Dilemma - Hyperbolic Belgian track written 1990 By Ken Dutrieue. Producer - Fasseau JP. Information about Ken Dutrieue is highly appreciated!
  • Buliding a hyperbolic tessellation Building {3,7}
  • Hyperbolic Functions - Derivatives Derivatives of hyperbolic functions leading up to the problem of the catenary. Check out for an indepth study and for more calculus related topics.
  • Hyperbolic Functions The hyperbolic functions. A comparison with the circular functions. The derivatives & integrals of the hyperbolic functions.
  • Liatris - Hyperbolic Live in ACROCK, the audio isn't so good... if you want to know the band better, please go to /liatrismusic
  • Hyperbolic Guitar by Donal Donohoe An attempt to capture the exponential expanse of hyperbolic space in the rhythm of music. Exploring the relationship between hyperbolic geometry and music, this tune was composed after attending a lecture about hyperbolic geometry by Dr. Daina Taimina at the Science Gallery, Trinity College Dublin. For more information visit:
  • Mike Song Hyperbolic Time Chamber (Glitch Hop Freestyle) late night session... the winter upload spree continues... Please keep comments about the camera angles to yourself. Thanks for the positive feedback! Or any feedback for that matter, thanks! December 29, 2009 #69 - Most Discussed (Today) - Entertainment #89 - Most Viewed (Today) - Entertainment - Canada #35 - Top Favorited (Today) #6 - Top Favorited (Today) - Entertainment #73 - Top Favorited (This Week) - Entertainment #22 - Top Rated (Today) - Entertainment #24 - Top Favorited (This Week) - Entertainment
  • Lecture - 8 Deviation from Hyperbolic Enzyme Kinectics Lecture Series on Enzyme Science and Engineering by Prof.Subhash Chand, Department of Biochemical Engineering,IIT Delhi. For more details on NPTEL visit nptel.iitm.ac.in
  • Rand Paul Victory Speech & MSNBC panelists' view of what this means - 11/2/10 - MSNBC http WatchRichard Gage's 2 hr presentation "9 Blueprint for Truth" using the scientific method to show that the 3 WTC towers could NOT have collapsed straight down at near free fall speed because of fires or structural damage. IF YOU ARE A SKEPTIC, THEN THIS VIDEO IS A MUST WATCH. Click the link below to watch for free: AE911 's Mission Statement " To research and to disseminate the truth of the 9/11 collapses of all 3 WTC high-rise buildings to every architect and engineer. " READ and DOWNLOAD REPUBLIC MAGAZINES now for FREE
  • Lec 7 | MIT 18.01 Single Variable Calculus, Fall 2007 Hyperbolic functions (cont.) and exam 1 review Note: the review for the exam in lecture 7 is not comprehensive because the students already have practice exams available to them. Lecture 8 is Exam 1, so no video was recorded. View the complete course at: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
  • DBZ- Goku and Gohan in the Hyperbolic time chamber goku and gohan first enter the time chamber and gohan sees for the first time the conditions in which he will train to become a super sayian. I have no ownership over any form of dragonball z content. It is the sole ownership of funimation.
  • HYPERBOLIC CROCHET CORAL REEF: A WOOLLY WONDER @ THE SCIENCE GALLERY Highlights of the opening of HYPERBOLIC CROCHET CORAL REEF: A WOOLLY WONDER in March 2010 at the SCIENCE GALLERY, Trinity College, Dublin. Created and Curated by Margaret and Christine Wertheim of the Institute For Figuring in Los Angeles One of the acknowledged wonders of the natural world, the Great Barrier Reef stretches along the coast of Queensland, Australia, in riotous profusion of colour and form unparalleled on our planet. But global warming and pollutants so threaten this fragile marvel it now faces devastation, along with reefs around the world. In homage to these disappearing treasures, Australian sisters Christine and Margaret Wertheim instigated a project to crochet a handmade reef, a woolly testimony that celebrates also a strange geometry realised throughout the oceanic realm.
  • Hyperbolic Buckyballs (7,3) tiling of the hyperbolic plane.
  • Dr. Doug Dunham - Repeating hyperbolic pattern algorithms About 50 years ago MC Escher created his four "Circle Limit" patterns, which were repeating patterns in the Poincare circle model of hyperbolic geometry. They were based on the regular tessellations (6,4) and (8,3) of the hyperbolic plane. In general, (p,q) represents a tessellation by regular p-sided polygons with q of them meeting at each vertex. About 30 years ago two students and I came up with an algorithm to draw hyperbolic Escher patterns. Also we will discuss special cases of a more general algorithm not based on regular tessellations. Dr. Doug Dunham is from University of Minnesota-Duluth. Note: Original video was 320x240. Note also some images removed for copyright issues.
  • Lorentz Transformations with Hyperbolic Geometry *I'm sorry about the video quality. I tried to do this one with giant nursing home letters to help clear it up. Unfortunately, I ran out of paper before I could plug anything into the equations....hopefully someone gets something worthwhile from it anyway.
  • Hyperbolic Functions - Graph of sinh x A short introduction to hyperbolic functions. Don't get mislead by their 'unpopularity' compared to trigonometric functions. Hyperbolic functions do have their uses. Check out for an indepth study and for more calculus related topics.
  • Hyperbolic Geometry is Projective Relativistic Geometry (Part1) Part 1 (of 6) of a Pure Mathematics Seminar given at UNSW in the School of Mathematics and Statistics. Assoc Prof NJ Wildberger explains a new approach to hyperbolic geometry which links it directly to Einstein and Minkowski's relativistic geometry viewed projectively. The idea is to extend Rational Trigonometry to the hyperbolic setting. The first part of the lecture motivates with a summary of classical hyperbolic geometry, then the purely algebraic set-up is introduced. Quite a few new results are illustrated with diagrams.
  • Bruce Faulconer - DBZ Volume 1 - Hyperbolic Time Chamber High Quality Link: Bruce Faulconer - DBZ Volume 1 - Hyperbolic Time Chamber