empilement des oursins

English translation: sea urchin stack

GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
 French term or phrase: empilement des oursins English translation: sea urchin stack Entered by:

 20:42 Feb 26, 2018
French to English translations [PRO]
Mathematics & Statistics / architecture and isoceles triangles polyhedrons
 French term or phrase: empilement des oursins Help please. These are various calculations. I can busk a lot of the terms and I will ask the customer to be sure. Buy I wonder if anyone can help me with : l’empilement des “oursins - stacking of urchins? Does not seem very likely but.... Thanks in a advance
 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...
Selected response from:

Francois Boye
United States
Local time: 02:04
 Thanks very much for your help4 KudoZ points were awarded for this answer

4sea urchin stack
 Francois Boye
Summary of reference entries provided
Of sea urchins, sphere packing, crystallography, and architectural design
 Nathalie Stewart

Discussion entries: 3

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...

 Francois BoyeUnited StatesLocal time: 02:04Specializes in fieldNative speaker of: FrenchPRO pts in category: 9
 Thanks very much for your help

 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.

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.

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Note added at 1 hr (2018-02-26 22:01:12 GMT)
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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")

 Nathalie StewartFranceNative speaker of: English, French

Peer comments on this reference comment (and responses from the reference poster)
agree  Charles Davis: I think it might be a way of referring to Kepler's conjecture. It must surely have something to do with Kepler, since "empilement" is packing and "urchin", as you say, was what K called a star polyhedron.
 47 mins
-> Thank you! It's possible... Hard to tell without more context. The subject line also mentions "architecture".

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