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A "pyramid" in the shape of a regular tetrahedron of side 1 casts a shadow which happens to be an equilateral triangle as in figure. What's the distance between the tip of the pyramid and the tip of its shadow?pic.twitter.com/YnbmPFvELu
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X be the cuboctahedron (see picture) A subset Y of X's vertices "traps the center" if any small perturbation of the center of X would decrease its distance to at least one point of Y. In order to trap the center, Y must have at least 6 vertices. Can you find all 6-vertex Y's?pic.twitter.com/YPl15uRR3k
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Uhh.. seems that out of 3 voters, only 1 got it right.. here's a drawing of some of the cases: https://twitter.com/MirceaSci/status/1212795078210658304 …pic.twitter.com/tJl0cIAg4z
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A moire' pattern is what you see when you misalign two periodic patterns and a new periodicity at a larger scale arises. Playing with misorientations can have consequences in graphene: https://physicstoday.scitation.org/doi/10.1063/PT.3.4384 …pic.twitter.com/Qxlx8NuQ4c
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Take a regular tetrahedron of sidelength 1 and on each of its 4 faces, build (externally) a regular tetrahedron sharing that face. The centers of symmetry of these 4 new tetrahedra form another regular tetrahedron. What is its sidelength?pic.twitter.com/FF6XUO22c3
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How to estimate qty. of carbon fixated by a forest? The answer hinges in modelling trees distribution, a question about
#pointconfigurations. Trees don't grow too close (resource competition) or too far (free terrain will be exploited) & evolve in size in a predictable way.pic.twitter.com/tfOlRumDc7
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Honeycomb lattice has combinatorics so that it avoids some double bond configurations. This gives a simple "NOT" gate if the info is encoded in spins And i seems stable at room temperature!
#combinatorics of#pointconfigurations in action! https://phys.org/news/2019-12-magnetism-graphene.html …pic.twitter.com/KN8OZwWcBj
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Just for fun: You could still divide easily by 3,6,9,12, etc.. Maybe multiples of 2 are more useful though!pic.twitter.com/YPkTahG5UR
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Symmetric
#pointconfigurations are the most appealing, some say. But WHY? What makes a#pointconfiguration "nice"? Let's turn that question on its head: "Trypophobia" is the disgust of some point/hole patterns, and the people affected seem to be up to 20%. Do you have it?pic.twitter.com/h28KPsDUhd
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BTW here's the roof of
@AeropuertoLEON in@Guanajuato, Mexico.. looks similar no?pic.twitter.com/CUAunIJ3vr
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A very nice kind of
#pointconfiguration consisting of corner-sharing SiO4 tetrahedra that build rings of various shapes and sizes. The mechanical properties of silica glass are mainly governed by this network geometry, but the precise principle is not completely understood. https://twitter.com/Acta_Materialia/status/1205034691096727552 …pic.twitter.com/vYvsKByeqt
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nice talk by Lauro Morales from
@UNAM_MX, about nonlinear elasticity, at the@cimatoficial 12th Americas Conference on Differential Equations and Nonlinear Analysispic.twitter.com/aCqj9Sd9ZK
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And if you wonder why it changes so much between elements, here's "what force the next atom feels depending on the distance" in a crystal with only one given element (negative sign= attractive force, positive sign= repulsive force) [more background about figure in next part]pic.twitter.com/PrS6WW4D5l
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..And in case you're wondering, here you go with some of the crystal shapes, schematically. (The ones with letters in parentheses, they are small modifications, and the ones going completely bezerk in one picture, from I to XII, are for sulphur, which I didn't get to study yet)pic.twitter.com/gVX8aIBhdd
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I'm reading "Phase diagrams of the elements" by Young, 1991. Not sure how severely outdated it is. But, if you often ask yourself: "what about the interaction between points has what effect on the shape of a
#pointconfiguration ?" you get ~A LOT~ of food for thought!pic.twitter.com/bI0HQcwhK0
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