Current File : /var/www/html/diaspora/api_internal/public/topics/cache/d5d1b23ccf65aff7a31c45f6ad30ba40
a:5:{s:8:"template";s:9093:"<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<meta content="width=device-width, initial-scale=1" name="viewport"/>
<title>{{ keyword }}</title>
<link href="//fonts.googleapis.com/css?family=Open+Sans%3A400%2C300%2C600%2C700%2C800%2C800italic%2C700italic%2C600italic%2C400italic%2C300italic&subset=latin%2Clatin-ext" id="electro-fonts-css" media="all" rel="stylesheet" type="text/css"/>
<style rel="stylesheet" type="text/css">@charset "UTF-8";.has-drop-cap:not(:focus):first-letter{float:left;font-size:8.4em;line-height:.68;font-weight:100;margin:.05em .1em 0 0;text-transform:uppercase;font-style:normal}.wc-block-product-categories__button:not(:disabled):not([aria-disabled=true]):hover{background-color:#fff;color:#191e23;box-shadow:inset 0 0 0 1px #e2e4e7,inset 0 0 0 2px #fff,0 1px 1px rgba(25,30,35,.2)}.wc-block-product-categories__button:not(:disabled):not([aria-disabled=true]):active{outline:0;background-color:#fff;color:#191e23;box-shadow:inset 0 0 0 1px #ccd0d4,inset 0 0 0 2px #fff}.wc-block-product-search .wc-block-product-search__button:not(:disabled):not([aria-disabled=true]):hover{background-color:#fff;color:#191e23;box-shadow:inset 0 0 0 1px #e2e4e7,inset 0 0 0 2px #fff,0 1px 1px rgba(25,30,35,.2)}.wc-block-product-search .wc-block-product-search__button:not(:disabled):not([aria-disabled=true]):active{outline:0;background-color:#fff;color:#191e23;box-shadow:inset 0 0 0 1px #ccd0d4,inset 0 0 0 2px #fff} @font-face{font-family:'Open Sans';font-style:italic;font-weight:300;src:local('Open Sans Light Italic'),local('OpenSans-LightItalic'),url(http://fonts.gstatic.com/s/opensans/v17/memnYaGs126MiZpBA-UFUKWyV9hlIqY.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:italic;font-weight:400;src:local('Open Sans Italic'),local('OpenSans-Italic'),url(http://fonts.gstatic.com/s/opensans/v17/mem6YaGs126MiZpBA-UFUK0Xdcg.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:italic;font-weight:600;src:local('Open Sans SemiBold Italic'),local('OpenSans-SemiBoldItalic'),url(http://fonts.gstatic.com/s/opensans/v17/memnYaGs126MiZpBA-UFUKXGUdhlIqY.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:italic;font-weight:700;src:local('Open Sans Bold Italic'),local('OpenSans-BoldItalic'),url(http://fonts.gstatic.com/s/opensans/v17/memnYaGs126MiZpBA-UFUKWiUNhlIqY.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:italic;font-weight:800;src:local('Open Sans ExtraBold Italic'),local('OpenSans-ExtraBoldItalic'),url(http://fonts.gstatic.com/s/opensans/v17/memnYaGs126MiZpBA-UFUKW-U9hlIqY.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:normal;font-weight:300;src:local('Open Sans Light'),local('OpenSans-Light'),url(http://fonts.gstatic.com/s/opensans/v17/mem5YaGs126MiZpBA-UN_r8OXOhs.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:normal;font-weight:400;src:local('Open Sans Regular'),local('OpenSans-Regular'),url(http://fonts.gstatic.com/s/opensans/v17/mem8YaGs126MiZpBA-UFW50e.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:normal;font-weight:600;src:local('Open Sans SemiBold'),local('OpenSans-SemiBold'),url(http://fonts.gstatic.com/s/opensans/v17/mem5YaGs126MiZpBA-UNirkOXOhs.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:normal;font-weight:700;src:local('Open Sans Bold'),local('OpenSans-Bold'),url(http://fonts.gstatic.com/s/opensans/v17/mem5YaGs126MiZpBA-UN7rgOXOhs.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:normal;font-weight:800;src:local('Open Sans ExtraBold'),local('OpenSans-ExtraBold'),url(http://fonts.gstatic.com/s/opensans/v17/mem5YaGs126MiZpBA-UN8rsOXOhs.ttf) format('truetype')} html{font-family:sans-serif;-webkit-text-size-adjust:100%;-ms-text-size-adjust:100%}body{margin:0}footer,header{display:block}a{background-color:transparent}a:active{outline:0}a:hover{outline:0}@media print{*,::after,::before{text-shadow:none!important;-webkit-box-shadow:none!important;box-shadow:none!important}a,a:visited{text-decoration:underline}}html{-webkit-box-sizing:border-box;box-sizing:border-box}*,::after,::before{-webkit-box-sizing:inherit;box-sizing:inherit}@-ms-viewport{width:device-width}@viewport{width:device-width}html{font-size:16px;-webkit-tap-highlight-color:transparent}body{font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:1rem;line-height:1.5;color:#373a3c;background-color:#fff}[tabindex="-1"]:focus{outline:0!important}ul{margin-top:0;margin-bottom:1rem}a{color:#0275d8;text-decoration:none}a:focus,a:hover{color:#014c8c;text-decoration:underline}a:focus{outline:thin dotted;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}a{-ms-touch-action:manipulation;touch-action:manipulation}.container{padding-right:.9375rem;padding-left:.9375rem;margin-right:auto;margin-left:auto}.container::after{display:table;clear:both;content:""}@media (min-width:544px){.container{max-width:576px}}@media (min-width:768px){.container{max-width:720px}}@media (min-width:992px){.container{max-width:940px}}@media (min-width:1200px){.container{max-width:1140px}}.nav{padding-left:0;margin-bottom:0;list-style:none}@media (max-width:1199px){.hidden-lg-down{display:none!important}} @media (max-width:568px){.site-header{border-bottom:1px solid #ddd;padding-bottom:0}}.footer-bottom-widgets{background-color:#f8f8f8;padding:4.143em 0 5.714em 0}.copyright-bar{background-color:#eaeaea;padding:.78em 0}.copyright-bar .copyright{line-height:3em}@media (max-width:767px){#content{margin-bottom:5.714em}}@media (max-width:991px){.site-footer{padding-bottom:60px}}.electro-compact .footer-bottom-widgets{padding:4.28em 0 4.44em 0}.electro-compact .copyright-bar{padding:.1em 0}.off-canvas-wrapper{width:100%;overflow-x:hidden;position:relative;backface-visibility:hidden;-webkit-overflow-scrolling:auto}.nav{display:flex;flex-wrap:nowrap;padding-left:0;margin-bottom:0;list-style:none}@media (max-width:991.98px){.footer-v2{padding-bottom:0}}body:not(.electro-v1) .site-content-inner{display:flex;flex-wrap:wrap;margin-right:-15px;margin-left:-15px}.site-content{margin-bottom:2.857em}.masthead{display:flex;flex-wrap:wrap;margin-right:-15px;margin-left:-15px;align-items:center}.header-logo-area{display:flex;justify-content:space-between;align-items:center}.masthead .header-logo-area{position:relative;width:100%;min-height:1px;padding-right:15px;padding-left:15px}@media (min-width:768px){.masthead .header-logo-area{flex:0 0 25%;max-width:25%}}.masthead .header-logo-area{min-width:300px;max-width:300px}.desktop-footer .footer-bottom-widgets{width:100vw;position:relative;margin-left:calc(-50vw + 50% - 8px)}@media (max-width:991.98px){.desktop-footer .footer-bottom-widgets{margin-left:calc(-50vw + 50%)}}.desktop-footer .footer-bottom-widgets .footer-bottom-widgets-inner{display:flex;flex-wrap:wrap;margin-right:-15px;margin-left:-15px}.desktop-footer .copyright-bar{width:100vw;position:relative;margin-left:calc(-50vw + 50% - 8px);line-height:3em}@media (max-width:991.98px){.desktop-footer .copyright-bar{margin-left:calc(-50vw + 50%)}}.desktop-footer .copyright-bar::after{display:block;clear:both;content:""}.desktop-footer .copyright-bar .copyright{float:left}.desktop-footer .copyright-bar .payment{float:right}@media (max-width:991.98px){.footer-v2{padding-bottom:0}}@media (max-width:991.98px){.footer-v2 .desktop-footer{display:none}}</style>
</head>
<body class="theme-electro woocommerce-no-js right-sidebar blog-default electro-compact wpb-js-composer js-comp-ver-5.4.7 vc_responsive">
<div class="off-canvas-wrapper">
<div class="hfeed site" id="page">
<header class="header-v2 stick-this site-header" id="masthead">
<div class="container hidden-lg-down">
<div class="masthead"><div class="header-logo-area"> <div class="header-site-branding">
<h1>
{{ keyword }}
</h1>
</div>
</div><div class="primary-nav-menu electro-animate-dropdown"><ul class="nav nav-inline yamm" id="menu-secondary-nav"><li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-home menu-item-4315" id="menu-item-4315"><a href="#" title="Home">Home</a></li>
<li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-4911" id="menu-item-4911"><a href="#" title="About">About</a></li>
<li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-4912" id="menu-item-4912"><a href="#" title="Contact">Contact</a></li>
</ul></div> </div><div class="electro-navbar">
<div class="container">
</div>
</div>
</div>
</header>
<div class="site-content" id="content" tabindex="-1">
<div class="container">
<div class="site-content-inner">
{{ text }}
</div> </div>
</div>
<footer class="site-footer footer-v2" id="colophon">
<div class="desktop-footer container">
<div class="footer-bottom-widgets">
<div class="container">
<div class="footer-bottom-widgets-inner">
{{ links }}
</div>
</div>
</div>
<div class="copyright-bar">
<div class="container">
<div class="copyright">{{ keyword }} 2020</div>
<div class="payment"></div>
</div>
</div></div>
</footer>
</div>
</div>
</body>
</html>";s:4:"text";s:3631:"ELEMENTARY CONSTRUCTIONS IN THE HYPERBOLIC PLANE Sybille MICK Graz University of Technology, Austria ABSTRACT: Constructions of regular n-gons in the Poincaré disk model and in the Beltrami-Klein model of the hyperbolic geometry are presented. Lobachevsky (1829) and J. Bolyai (1832) independently recognized that Euclid's fifth postulate—saying that for a given line and a point not on the line, there is exactly one line parallel to the first—might be changed and still be a consistent geometry. Mathematics Teacheris a publication of … (2018) Elementary Hyperbolic Geometry. Hyperbolic Geometry by Charles Walkden. Thus O is outside L. Hyp erb olic space has man y interesting featur es; some are simila r to tho se of Euclidean geometr y but some are quite di!eren t. In pa rtic-ular it ha s a very rich group of isometries, allo wing a huge variet y of crysta llogr aphic symmetry patterns. This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. “An Introduction to Hyperbolic Functions in Elementary Calculus” Jerome Rosenthal, Broward Community College, Pompano Beach, FL 33063 Mathematics Teacher,April 1986, Volume 79, Number 4, pp. ometr y is the geometry of the third case. As C is orthogonal to L, M is perpendicular to N. Then N is perpendicular to M, the tangent to C at A, so N passes through O. Purpose of this note is to provide an introduction to some aspects of hyperbolic geometry. Lobachevsky (1829) and J. Bolyai (1832) independently recognized that Euclid's fifth postulate—saying that for a given line and a point not on the line, there is exactly one line parallel to the first—might be changed and still be a consistent geometry. Learn the basics of geometry for free—the core skills you'll need for high school and college math. Elementary hyperbolic geometry was born in 1903 when Hilbert [32] provided, using the end-calculus to introduce coordinates, a first-order axiomatization for it by adding to the axioms for plane absolute geometry (the plane axioms contained in groups I (Incidence), II (Betweenness), III (Congruence)) a hyperbolic parallel axiom stating that HPA Chapter 1 Geometry of real and complex hyperbolic space 1.1 The hyperboloid model Let n>1 and consider a symmetric bilinear form of signature (n;1) on the … Full curriculum of exercises and videos. Let M be the tangent to C at A, and N the tangent to L at A. Fact 1 If circle C with centre O is orthogonal to circle L with centre P, then O lies outside L, and P lies outside C.. Many of the elementary concepts in hyperbolic geometry can be described in linear algebraic terms: geodesic paths are described by intersections with planes through the origin, dihedral angles between hyperplanes can be described by inner products of normal vectors, and hyperbolic reflection groups can be given explicit matrix realizations. 298–300. This is a complete and relatively elementary course explaining a new, simpler and more elegant theory of non-Euclidean geometry; in particular hyperbolic geometry. Cite this chapter as: Garcia S.R., Mashreghi J., Ross W.T. This ma kes the geometr y … It is a purely algebraic approach which avoids transcendental functions like log, sin, tanh etc, relying instead on … Hyperbolic functions occur in the theory of triangles in hyperbolic spaces. Proof Suppose that C and L meet at the point A. Hyperbolic functions occur in the theory of triangles in hyperbolic spaces. In: Finite Blaschke Products and Their Connections. ";s:7:"keyword";s:50:"moroccanoil hydrating styling cream for curly hair";s:5:"links";s:1383:"<a href="http://testapi.diaspora.coding.al/topics/aglio-olio-topping-efd603">Aglio Olio Topping</a>,
<a href="http://testapi.diaspora.coding.al/topics/calcium-bromide-cation-efd603">Calcium Bromide Cation</a>,
<a href="http://testapi.diaspora.coding.al/topics/research-methodology-in-philosophy-efd603">Research Methodology In Philosophy</a>,
<a href="http://testapi.diaspora.coding.al/topics/oils-for-hair-growth-for-black-hair-efd603">Oils For Hair Growth For Black Hair</a>,
<a href="http://testapi.diaspora.coding.al/topics/space-channel-5%3A-part-2-pc-efd603">Space Channel 5: Part 2 Pc</a>,
<a href="http://testapi.diaspora.coding.al/topics/questions-to-ask-during-courtship-efd603">Questions To Ask During Courtship</a>,
<a href="http://testapi.diaspora.coding.al/topics/chocolate-turkish-delight-cheesecake-efd603">Chocolate Turkish Delight Cheesecake</a>,
<a href="http://testapi.diaspora.coding.al/topics/piano-sonata-no-11-in-a-major%2C-k-331-300i-efd603">Piano Sonata No 11 In A Major, K 331 300i</a>,
<a href="http://testapi.diaspora.coding.al/topics/italian-marinated-vegetables-efd603">Italian Marinated Vegetables</a>,
<a href="http://testapi.diaspora.coding.al/topics/merguez-sandwich-near-me-efd603">Merguez Sandwich Near Me</a>,
<a href="http://testapi.diaspora.coding.al/topics/phoenix-wright%3A-ace-attorney-steam-efd603">Phoenix Wright: Ace Attorney Steam</a>,
";s:7:"expired";i:-1;}
Mini Shell