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http://plus.maths.org/content/taxonomy/term/436
enVisual curiosities and mathematical paradoxes
http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes
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Linda Becerra and Ron Barnes </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/21%20Oct%202010%20-%2016%3A38/icon.jpg?1287675519" /> </div>
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<p>When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions, which we call paradoxes. This article looks at examples of geometric optical illusions and paradoxes and gives explanations of what's really going on.</p>
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<p>When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions; appear to be true but in actual fact are self-contradictory; or appear contradictory, even absurd, but in fact may be true. Here again it is up to your brain to make sense of these situations. Again, your brain may get it wrong. These situations are referred to as paradoxes.<p><a href="http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes" target="_blank">read more</a></p>http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes#commentsarchitectureBanach-Tarski paradoxBarber's Paradoxeschergeometryimpossible objectoptical illusionparadoxPenrose staircasePenrose triangleperspectiveRussell's ParadoxWed, 17 Nov 2010 14:06:13 +0000mf3445337 at http://plus.maths.org/contentMaths and art: the whistlestop tour
http://plus.maths.org/content/maths-and-art-whistlestop-tour
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Lewis Dartnell </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/issue33/features/dartnell_art/icon.jpg?1104537600" /> </div>
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Many people find no beauty and pleasure in maths - but, as <b>Lewis Dartnell</b> explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense. </div>
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<div class="pub_date">January 2005</div>
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<p>The world around us is full of relationships, rhythms, correlations, patterns. And mathematics underlies all of these, and can be used to predict future outcomes. Our brains have evolved to survive in this world: to analyse the information it receives through our senses and spot patterns in the complexity around us. In fact, it's thought that the mathematical structure embedded in the rhythm
and melody of music is what our brains latch on to, and that this is why we enjoy listening to it.<p><a href="http://plus.maths.org/content/maths-and-art-whistlestop-tour" target="_blank">read more</a></p>http://plus.maths.org/content/maths-and-art-whistlestop-tour#comments33escherfractalgeometric abstractiongeometric patternsgolden ratiomathematics and artminimal surfaceorigamiregular polyhedrontessellationSat, 01 Jan 2005 00:00:00 +0000plusadmin2259 at http://plus.maths.org/contentFrom kaleidoscopes to soccer balls
http://plus.maths.org/content/kaleidoscopes-soccer-balls
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<img class="imagefield imagefield-field_abs_img" width="130" height="130" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/issue25/news/coxeter/icon.jpg?1051657200" /> </div>
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The work of Donald Coxeter, who died on 31 March 2003, will continue to inspire both mathematicians and artists. </div>
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<div class="pub_date">30/04/03</div>
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<p>The worlds of mathematics and art lost a great mind when <a href="http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Coxeter.html">Donald Coxeter</a>, said to be the greatest classical geometer of his generation, died on 31 March 2003 in Toronto, Canada, aged 96.</p><p><a href="http://plus.maths.org/content/kaleidoscopes-soccer-balls" target="_blank">read more</a></p>http://plus.maths.org/content/kaleidoscopes-soccer-balls#commentscurvatureeschergeodesic domegroup theoryhyperbolic geometrymathematics and artmathematics in the mediasymmetryTue, 29 Apr 2003 23:00:00 +0000plusadmin2725 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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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/30%20Jun%202010%20-%2016%3A30/mystery.gif?1277911831" /> </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/contentFrom quasicrystals to Kleenex
http://plus.maths.org/content/quasicrystals-kleenex
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Alison Boyle </div>
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This pattern with kite-shaped tiles can be extended to cover any area, but however big we make it, the pattern never repeats itself. <b>Alison Boyle</b> investigates aperiodic tilings, which have had unexpected applications in describing new crystal structures. </div>
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<p>The motto of the Nasrid kings who built the Alhambra of Granada was "God is the only victor". Allah is all-powerful: the Qur'an forbids the depiction of living beings in religious art lest it be seen as a blasphemous attempt to rival the creative powers of God. To avoid this, artists created intricate patterns to symbolise the wonders of creation. The repetitive nature of these complex
geometric designs suggests the infinite power of God.</p><p><a href="http://plus.maths.org/content/quasicrystals-kleenex" target="_blank">read more</a></p>http://plus.maths.org/content/quasicrystals-kleenex#comments16aperiodic tilingescherpenrose tilingperiodic tilingquasicrystalquasiperiodicitytessellationFri, 01 Dec 2000 00:00:00 +0000plusadmin2188 at http://plus.maths.org/content