empilement des oursins
English translation: sea urchin stack
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| 20:42 Feb 26, 2018 |
| French to English translations [PRO] Mathematics & Statistics / architecture and isoceles triangles polyhedrons | |||||
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|  Selected response from: Francois Boye United States Local time: 10:49 | ||||
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| Summary of answers provided | ||||
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| 4 | sea urchin stack |
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| Of sea urchins, sphere packing, crystallography, and architectural design |
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| Discussion entries: 3 | |
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Answers
2 hrs confidence: 
| l’empilement des “oursins sea urchin stack Explanation: https://en.wikipedia.org/wiki/Stack_(mathematics) How to maximize (baking) surface area? I like eating crust, so I am trying different baking molds to try to get the most crust per dough. More generally, I'm interested in the reverse of this more specific question — how to maximize the surface area of a body given a constant volume. Let's ignore all the practicalities and make it a pure mathematical problem. I'm not a mathematician, so I don't even know how to try to solve it. Intuitively I came up with the following body, but I have no way of verifying its optimality: imagine a sea urchin with infinitely many infinitesimal spikes that are not touching, all anchored to an infinitesimal blob in the center. It is less and less dense as you progress from the center, so some branching could improve it. So, what is the optimal body, given no other constraints? Please exclude Gabriel's Horn if possible; no infinite dimensions unless they fit into an oven, I mean, a finite space. -------------------------------------------------- Note added at 2 hrs (2018-02-26 23:40:45 GMT) -------------------------------------------------- https://math.stackexchange.com/questions/610393/how-to-maxim... |
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Reference comments
1 hr peer agreement (net): +1 |
| Reference: Of sea urchins, sphere packing, crystallography, and architectural design Reference information: Just some ideas... by no means a solution, but possibly some directions you might want to follow. https://fr.wikipedia.org/wiki/Empilement_compact https://en.wikipedia.org/wiki/Sphere_packing https://www.afc.asso.fr/32-aicr2014/cristallo-explications La cristallographie est irremplaçable pour l’étude de toutes sortes de matériaux, qu’ils soient idéalement organisés (cristaux parfaits), partiellement organisés (polymères), cristallisés artificiellement (cristaux de protéines) ou peu organisés (liquides, verres). Elle est aussi à la base de l’élaboration de la plupart des nouveaux matériaux, des cellules photovoltaïques aux composites de l’automobile ou de l’aéronautique. ...Analyser des matériaux biologiques aux propriétés remarquables (fil de toile d’araignée, piquants d’oursin, bois...) pour les reproduire artificiellement... https://pubs.acs.org/doi/abs/10.1021/cm0603809 Urchin-like nanostructures consisting of high-density spherical nanotube radial arrays... https://www.witpress.com/Secure/elibrary/papers/DN04/DN04001... Structure optimization in the shell structure of a sea urchin. www.itke.uni-stuttgart.de/download.php?id=738 The shell of the sea urchin (Fig. 5) consists of a modular system of polygonal plates, which are linked together at the edges by finger-like calcite protrusions [5]. Shell action is very similar to plate action, as a finely faceted plate polyhedron is nothing but a slightly discontinuous shell which is stabilized by shear forces acting along the lines of connection [4]. High load bearing capacity is thus achieved by the particular geometric arrangement of the plates and their joining system. Therefore, the sea urchin serves as a perfect model for shells made of prefabricated elements. -------------------------------------------------- Note added at 1 hr (2018-02-26 22:01:12 GMT) -------------------------------------------------- See also "Kepler's Urchin" (small stellated dodecahedron) and "Kepler conjecture" ("no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements") |
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