In other words, in the hyperbolic disc the rectangles needed for the argument simply do not exist. |
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Recently, inspired by an article on artistic representations of the hyperbolic plane, McIntyre tried a slightly different approach. |
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I mean I liked it as much as I like finding the centres, vertices, foci, and asymptotes of various hyperbolic graphs. |
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Any object with a parabolic or hyperbolic trajectory moves so fast that it will never return. |
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Whereas hyperbolic activity and elliptic motion characterizes the cab, a big rig manifests an elliptic activity and hyperbolic motion. |
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Other examples will be given later in the paper when we discuss packings in hyperbolic spaces. |
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In this net, the input and output layers are linear, and the hidden layer has neurons with a hyperbolic tangent transfer function. |
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In fact, it corresponds to the graph of a function called the hyperbolic cosine. |
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Avoid hyperbolic language and narration that pump air into stories that have no real substance. |
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He studied time dependent hyperbolic partial differential equations and also began to work on the Cauchy problem. |
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See this issue's mystery mix for a comparison of Euclidean, hyperbolic, and spherical geometry. |
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The hyperbolic scheme seems to be of a piece with the bold strokes of the ancient epic. |
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Although this language sounds hyperbolic, it was by no means atypical of audience responses. |
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Part of what makes his doubts hyperbolic is that their extravagance renders them unlikely to dislodge our existing beliefs. |
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They should answer hyperbolic attacks with exaggerated speech of their own, if that's what it takes to stave off political annihilation. |
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This last result, known by his name, expressed a hyperbolic arc in terms of two elliptic ones. |
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It's much easier to be hyperbolic, or dismissive, or to give up trying to make judgments and just stick to writing lists. |
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We shall look at the asymptotics of the barycentres of independent copies of Brownian motions on the hyperbolic spaces. |
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Figure 33 shows a tessellation of the hyperbolic disc by regular pentagons. |
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In accordance with another embodiment of the present invention, the head assembly includes an hyperbolic reflector. |
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As is usually the case with Washington windbags, these claims are hyperbolic. |
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He found the standard addition formulas for hyperbolic functions, their derivatives and their relation to the exponential function. |
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This is, of course, how Beltrami first showed that hyperbolic geometry was no less consistent than Euclidean geometry. |
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A hyperbolic citation reiterates a normative notion in an exaggerated way in order to simultaneously work against it. |
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A frustrated thespian, he enjoyed delivering long-winded, hyperbolic, and melodramatic speeches that rolled off his tongue in a rich bass voice. |
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Here the play took off, and the exaggeration of the suits, which their hyperbolic language, seemed apt to text and production. |
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Amazingly enough, the tone of the article is a throwback to the hyperbolic language of the boom. |
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A large part of the difficulty is that the discourse of the populist Right is also often characterised by irrationalism and hyperbolic abuse. |
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Clearly the megalosaurus in the opening passage of Bleak House is a flight of hyperbolic fancy. |
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Real tragedies do not need hyperbole, for they are intrinsically hyperbolic. |
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Crayon, oil, colored pencil, and poster paint lend the work a saturated, hyperbolic sensibility. |
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And the world will not sit idly by while they flatten the region with daisy-cutters and hyperbolic bombs. |
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These two pairs of hyperbolic curves can be used for graphical analysis of these two different processes. |
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For example, Sir William's hyperbolic language lends itself to hyperbolic gestures that contribute to the comic business of his scenes. |
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Among closed surfaces, spherical, flat, and hyperbolic geometry are mutually exclusive. |
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The addition theorems for the hyperbolic secent, cosecent, versed sine, and haversed sine are not interesting. |
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A near hyperbolic relationship between respiration rates and meristem radii was observed. |
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It is the unboundedness of hyperbolic doubt that underwrites the No Atheistic Knowledge Thesis. |
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Kurosawa's, by contrast, exaggerate the theme, casting it in the hyperbolic terms of a dread-inducing and sometimes even apocalyptic horror. |
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Orlando communicates with Shel in a secret language of hyperbolic expressive power. |
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He summed series, and discovered addition theorems for trigonometric and hyperbolic functions using the differential equations they satisfy. |
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The sinh, cosh, and tanh subroutines compute the hyperbolic trigonometric functions of their parameters. |
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Debates help them break through the blaze of hyperbolic attacks and confusing countercharges. |
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I mean, in the media, all the time, the thing that we're most interested in is the most sensational, the most hyperbolic. |
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We can go ahead and bend the octagon into three dimensions to get an idea of the topology generated by this tiling of the hyperbolic plane. |
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This is a representation of a pentagonal tiling of the hyperbolic plane in which four pentagons meet at each vertex. |
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He praises her perfection in hyperbolic, mythological terms in the long speech which precedes the choric conclusion to the play. |
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How can one thing hold so much potential, even taking into account the hyperbolic enthusiasm of public relations experts and journalists? |
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So when notoriously purist and discerning jazz critics single out a rising star to heap hyperbolic praise upon, gig after gig, it really is time to sit up and take notice. |
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Descriptions were heaps of hyperbolic adjectives and set phrases, a murky torrent. |
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Lauren Child has taken this hyperbolic, green fairy tale and invested it with new verve, spin and intelligence. |
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The shape and structure of the Philips Pavilion are comprised solely of hyperbolic parabaloids and self-supporting conoids. |
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Even so, fears of a meltdown by jet-setting executives have been hyperbolic to a fault. |
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How is the hyperbolic character of methodic doubt supposed to contribute to the method's success? |
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On one side, some people vaunt in hyperbolic terms the benefits for humanity of the current scientific and technical revolution. |
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Her feigned obliviousness and hyperbolic assertions indicated an underlying liberal sensibility. |
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The catenary and the related hyperbolic functions play roles in other applications. |
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Indeed, after nearly four years, there is a treasure trove of hyperbolic, over-the-top soundbites about it. |
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I will be singing her praises with hyperbolic terms of exaltation, extolling her to the highest degree, her aura will be raised to mythical proportions. |
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This new contact system based on hyperbolic grid configuration has already proved of value in the automotive industry. |
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It may sound hyperbolic to speak of drug trafficking as a threat to national security. |
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Without the availability of any empirical evidence for the Netherlands, a hyperbolic profile is considered the most plausible one. |
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It is not hyperbolic to say that the outlook today in the region is more worrying than it has been for some time. |
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It swims in circular, elliptical or hyperbolic trajectories using currents, rock walls and sometimes even ship¹s hulls to trap prey. |
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Therefore would the member please consider the facts rather than engage in hyperbolic rhetoric which I do not think serves the debate very well? |
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A large number of comets which appear in the inner solar system follow hyperbolic paths. |
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Today we call these three geometries Euclidean, hyperbolic, and absolute. |
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I know that I have exaggerated or made hyperbolic the abuse in my family when talking about it tangentially, either out of black humor or bitterness. |
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Around this time Menger's interests in mathematics broadened and he began to work on hyperbolic geometry, probabilistic geometry and the algebra of functions. |
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Moreover, the geometries axiomatized in the book have consistent and decidable extensions, namely, Euclidean or hyperbolic geometry over real-closed fields. |
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First, like many upstarts, SodaStream has taken an in-your-face, hyperbolic approach to marketing. |
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But these hyperbolic hosannas are, unfortunately, no substitute for a rebirth of modern political leadership, which, in fact, continues to wither on the vine. |
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Here again, this rhetoric is inflated, hyperbolic and unjustified. |
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In this note we investigate local properties for microlocally symmetrizable hyperbolic systems with just time dependent coefficients. |
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At times the fervency of the male seems hyperbolic in its poetic conceits, as in Der Mond and Dass doch gemalt, but Wolf wisely treats these poems with complete earnestness. |
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It can be shown that the set of hyperbolic codirections consists of distinct pairs of oppositely-directed convex cones. |
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We've all bewailed the return to obsequiously hyperbolic commentary and a fervour redolent of Girl Scouts promising to honour their Queen and country. |
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I won't comment on that hyperbolic introduction. |
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The three most common forms of decline curves are exponential, hyperbolic, and harmonic. |
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Greeting one another with the sort of hyperbolic flattery associated with female bonding, they bat away compliments with the requisite self-lacerating retorts. |
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Every since Romanticism, the jester, the entertainer and the clown have been the hyperbolic and intentionally distorted images that artists happily give to both themselves and the condition of their art. |
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It would be hyperbolic to crown Steve Beshear as a profile in courage. |
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Indeed, 18 flat topologies along with an infinite number of spherical and hyperbolic ones are theoretical candidates to describe the shape of physical space. |
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In this configuration the on-axis image is produced at the real hyperbolic focus but off-axis performance suffers. |
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Written in a brisk but highly colored prose that swells into hyperbolic lushness whenever the opportunity arises. |
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Wilson's evaluation may sound slightly hyperbolic, but if we consider Google's previous prioritization of engineering over design, then this precise and considered attention to interfaces is something exceptional. |
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However, by throwing out Euclid's fifth postulate we get theories that have meaning in wider contexts, hyperbolic geometry for example. |
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Aggregated RMSE coefficients for hyperbolic discounting were significantly lower than those for the exponential equation. |
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From a tanking candidate, it sounds desperate and hyperbolic. |
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At the risk of being slightly hyperbolic, the fourth season of The Simpsons is the greatest thing in the history of the universe. |
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I am not normally given to hyperbolic comments, but if we continue to lose staff at the rate of 27 per month I fear that one day the judges may come to work and find themselves alone. |
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The result is simply the best signal-to-noise specification in the market, and the perfect complement to the inert source and patented hyperbolic analyzer. |
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Specifically, NeuralTools uses the hyperbolic tangent function. |
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The so acquired average age-efficiency profile is usually more or less geometric, even though the individual assets have a hyperbolic age-efficiency profile. |
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This function is frequently included with the hyperbolic function as a point of comparison. |
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This generates the characteristic hyperbolic function that is typically associated with reinforcement bars. |
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Perhaps the most popular analysis method is to fit the indifference points at each delay or probability with a hyperbolic function. |
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The solid and dashed curves show the best-fitting hyperbolic functions for the American and Japanese students, respectively. |
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There's also an advanced math library, including trigonometry and hyperbolic functions. |
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Inxight StarTree nodes are laid out in a uniform way on a hyperbolic plane, which is mapped onto a circular display region. |
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Escher skillfully convey the illusion of infinitely repeating forms and the strange properties of hyperbolic planes. |
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In the studies for his first major composition for orchestra, the forceful Metastaseis, multiple glissandi are rendered as hyperbolic paraboloids. |
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The calculus preview in each chapter focuses on a single calculus concept, such as algebra and limits, the are problem and the hyperbolic functions. |
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And the researchers have developed an in-depth theory that uses hyperbolic geometry to describe a negatively curved shape of complex networks such as the Internet. |
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The inspiration for making crochet reef forms begins with the technique of hyperbolic crochet discovered in 1997 by Cornell University mathematician Dr Daina Taimina. |
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Six survey and expository papers and 11 research papers explore hyperbolic geometry, symplectic geometry, geometric topology, and other areas of geometry and topology. |
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One disadvantage of the hyperbolic function is that age-price functions estimated from a hyperbolic function require an assumption to be made about a real discount rate. |
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The development of hyperbolic geometry taught mathematicians that postulates should be regarded as purely formal statements, and not as facts based on experience. |
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Right and skew-right circulant matrices remains invariant on their type when evaluated on trigonometric and hyperbolic functions that are used in this paper. |
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The hyperbolic character of biodiversity growth can be similarly accounted for by a feedback between diversity and community structure complexity. |
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Through the adjacent Market Arcade is a covered market hall, which has listed building status, due in part to its distinctive roof formed by hyperbolic paraboloids. |
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