spherical geometry
http://plus.maths.org/content/taxonomy/term/821
enMaths in a minute: Not always 180
http://plus.maths.org/content/maths-minute-strange-geometries
<p>Over 2000 years ago the Greek mathematician <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Euclid.html">Euclid</a> came up with a list of five postulates on which he thought geometry should be built. One of them, the fifth, was equivalent to a statement we are all familiar with: that the angles in a triangle add up to 180 degrees. However, this postulate did not seem as obvious as the other four on Euclid's list, so mathematicians attempted to deduce it from them: to show that a geometry obeying the first four postulates would necessarily obey the fifth.<p><a href="http://plus.maths.org/content/maths-minute-strange-geometries" target="_blank">read more</a></p>http://plus.maths.org/content/maths-minute-strange-geometries#commentsEuclidean geometrygeometryhyperbolic geometryspherical geometryWed, 03 Jul 2013 12:47:01 +0000mf3445921 at http://plus.maths.org/contentThe trouble with five
http://plus.maths.org/content/trouble-five
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Craig Kaplan </div>
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Squares do it, triangles do it, even hexagons do it — but pentagons don't. They just won't fit together to tile a flat surface. So are there <i>any</i> tilings based on fiveness? <b>Craig Kaplan</b> takes us through the five-fold tiling problem and uncovers some interesting designs in the process. </div>
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<div class="pub_date">December 2007</div>
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<p>We are all familiar with the simple ways of tiling the plane by equilateral triangles, squares, or hexagons. These are the three <i>regular</i> tilings: each is made up of identical copies of a <i>regular polygon</i> — a shape whose sides all have the same length and angles between them — and adjacent tiles share whole edges, that is, we never have part of a tile's edge overlapping part of
another tile's edge.</p>
<p><!-- FILE: include/centrefig.html --></p><p><a href="http://plus.maths.org/content/trouble-five" target="_blank">read more</a></p>http://plus.maths.org/content/trouble-five#comments45Euclidean geometryfive-fold tiling problemgeometryhyperbolic geometrypenrose tilingspherical geometrysymmetrytilingSat, 01 Dec 2007 00:00:00 +0000plusadmin2319 at http://plus.maths.org/contentMathematical mysteries: Strange Geometries
http://plus.maths.org/content/mathematical-mysteries-strange-geometries
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Helen Joyce </div>
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<p>The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics.</p>
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<div class="pub_date">Jan 2002</div>
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<h2>Euclidean Geometry</h2>
<p>The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics. Euclid's work is discussed in detail in <a href="/issue7/features/proof1/index.html">The Origins
of Proof</a>, from Issue 7 of <i>Plus</i>.</p><p><a href="http://plus.maths.org/content/mathematical-mysteries-strange-geometries" target="_blank">read more</a></p>http://plus.maths.org/content/mathematical-mysteries-strange-geometries#comments18curvaturecurvature of spaceescherEuclid's ElementsEuclidean geometryflatnesshyperbolic geometryMathematical mysteriesMercator projectionspherical geometrytrigonometrySat, 01 Dec 2001 00:00:00 +0000plusadmin4754 at http://plus.maths.org/content