penrose tiling
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enShattering crystal symmetries
https://plus.maths.org/content/shattering-crystal-symmetries
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<p>In 1982 Dan Shechtman discovered a crystal that would revolutionise chemistry. He has just been awarded the 2011 Nobel Prize in Chemistry for his discovery — but has the Nobel committee missed out a chance to honour a mathematician for his role in this revolution as well?</p>
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Imagine you are looking at a crystal. Zoom down to the structure of atoms. Most of us would picture an ordered lattice filled with repeating blocks of atoms. So did chemists – that is until 1982 when Dan Shechtman looked through his electron microscope and saw that his crystal had an impossible structure with forbidden symmetries. His discovery shattered scientific consensus in crystallography and has now earned him the 2011 Nobel Prize in Chemistry.
</p><p><a href="https://plus.maths.org/content/shattering-crystal-symmetries" target="_blank">read more</a></p>https://plus.maths.org/content/shattering-crystal-symmetries#commentsmathematical realitychemistrygroup theoryNobel prizepenrose tilingquasicrystalThu, 13 Oct 2011 14:07:21 +0000Rachel5571 at https://plus.maths.org/contentThe trouble with five
https://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="https://plus.maths.org/content/trouble-five" target="_blank">read more</a></p>https://plus.maths.org/content/trouble-five#comments45Euclidean geometryfive-fold tiling problemgeometryhyperbolic geometrypenrose tilingspherical geometrysymmetrytilingSat, 01 Dec 2007 00:00:00 +0000plusadmin2319 at https://plus.maths.org/contentDisorderly quasicrystals
https://plus.maths.org/content/disorderly-quasicrystals
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Mathematicians offer new proof of quasicrystals' strange electronic properties. </div>
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<div class="pub_date">29/05/2007</div>
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<p>Mathematically speaking, things in David Damanik's world don't line up — and he can prove it.</p>
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<p>David Damanik, associate professor of mathematics at Rice University, has published a key proof in the study of quasicrystals. Photo credit: Jeff Fitlow.</p><p><a href="https://plus.maths.org/content/disorderly-quasicrystals" target="_blank">read more</a></p>https://plus.maths.org/content/disorderly-quasicrystals#commentsaperiodic tilingcrystallographygeometrypenrose tilingphysicsSchrödinger equationMon, 28 May 2007 23:00:00 +0000plusadmin2555 at https://plus.maths.org/contentRoger Penrose: A Knight on the tiles
https://plus.maths.org/content/roger-penrose-knight-tiles
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The Plus Team </div>
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Will we ever be able to make computers that think and feel? If not, why not? And what has all this got to do with tiles? <i>Plus</i> talks to <b>Sir Roger Penrose</b> about all this and more. </div>
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<div class="pub_date">Jan 2002</div>
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<p><a href="https://plus.maths.org/content/roger-penrose-knight-tiles" target="_blank">read more</a></p>https://plus.maths.org/content/roger-penrose-knight-tiles#comments18aperiodic tilingartificial intelligencecomplex numberGrand Unified Theoryhuman consciousnessnon-algorithmic thoughtnon-recursive mathematicspenrose tilingquantum mechanicstessellationTuring testSat, 01 Dec 2001 00:00:00 +0000plusadmin2196 at https://plus.maths.org/contentFrom quasicrystals to Kleenex
https://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="https://plus.maths.org/content/quasicrystals-kleenex" target="_blank">read more</a></p>https://plus.maths.org/content/quasicrystals-kleenex#comments16aperiodic tilingescherpenrose tilingperiodic tilingquasicrystalquasiperiodicitytessellationFri, 01 Dec 2000 00:00:00 +0000plusadmin2188 at https://plus.maths.org/content