Mircea Petrache

@MirceaSci

I do maths of point configurations, their quantitative properties & geometry.

Chile
Vrijeme pridruživanja: listopad 2019.

Medijski sadržaj

  1. 1. velj
  2. 8. sij

    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?

  3. 7. sij

    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?

  4. 3. sij

    Uhh.. seems that out of 3 voters, only 1 got it right.. here's a drawing of some of the cases:

  5. 3. sij
    Odgovor korisniku/ci
  6. 2. sij

    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:

  7. 27. pro 2019.

    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?

    Prikaži ovu nit
  8. 27. pro 2019.

    How to estimate qty. of carbon fixated by a forest? The answer hinges in modelling trees distribution, a question about . Trees don't grow too close (resource competition) or too far (free terrain will be exploited) & evolve in size in a predictable way.

  9. 21. pro 2019.

    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! of in action!

    Prikaži ovu nit
  10. 21. pro 2019.
    Odgovor korisniku/ci

    Just for fun: You could still divide easily by 3,6,9,12, etc.. Maybe multiples of 2 are more useful though!

  11. 17. pro 2019.

    Symmetric are the most appealing, some say. But WHY? What makes a "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?

    Prikaži ovu nit
  12. 14. pro 2019.
    Odgovor korisnicima i sljedećem broju korisnika:

    BTW here's the roof of in , Mexico.. looks similar no?

  13. 13. pro 2019.
    Odgovor korisniku/ci
  14. 12. pro 2019.
    Odgovor korisniku/ci

    Couldn't resist..

  15. 12. pro 2019.
    Odgovor korisnicima

    Is it the same Rob Phillips?

  16. 12. pro 2019.

    A very nice kind of 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.

  17. 10. pro 2019.

    nice talk by Lauro Morales from , about nonlinear elasticity, at the 12th Americas Conference on Differential Equations and Nonlinear Analysis

  18. 8. pro 2019.

    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]

    Prikaži ovu nit
  19. 8. pro 2019.

    ..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)

    Prikaži ovu nit
  20. 8. pro 2019.

    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 ?" you get ~A LOT~ of food for thought!

    Prikaži ovu nit

Čini se da učitavanje traje već neko vrijeme.

Twitter je možda preopterećen ili ima kratkotrajnih poteškoća u radu. Pokušajte ponovno ili potražite dodatne informacije u odjeljku Status Twittera.

    Možda bi vam se svidjelo i ovo:

    ·