^^Impacchettamento di sfere.

impacchettamento "a piramide". Oranges in a Hexagonal Cubic Packing Arrangement. credits: HCP_Oranges.jpg

Snowballs stacked in preparation for a snowball fight.

Packing type

• HCP hexagonal close-packed  (front pyramid)
• FCC face-centered cubic, or
  CCP cubic close packed (rear pyramid) kings.edu

have the same density!

Il modo più efficiente di impacchettare insieme cerchi di diverse dimensioni non è ovvio. credits: Citrus_fruits.jpg   wp/Circle_packing

wp/Impacchettamento_di_sfere | Sphere_packing

• piu' in particolare

  Impacchettamento_compatto_di_sfere | Close-packing_of_equal_spheres

• piu' in generale

  wp/Packing_problems < Problema_di_ottimizzazione

es: Costipazione.

Impacchettamento e Tassellatura sono legati

poiche' posso impacchettare seguendo una tassellatura.

Congettura di Keplero  wp

• no packing of congruent balls in Euclidean three-space has density greater than that of the face-centered cubic packing.
  - 1611 Kepler, in the booklet Six-Cornered Snowflake.

This conjecture is the oldest problem in discrete geometry.

The Kepler conjecture forms part of Hilbert’s 18th problem, which raises questions about space groups, anisohedral tilings, and packings in Euclidean space.

1585 Thomas Harriot first pondered the mathematics of cannonball stacks and later asked Johannes Kepler if cannonball stack was truly the most dense.

ε-nets, ε-packings, ε-coverings, uniformly discrete sets, relatively dense sets, Delone sets wp

In the metric spaces

are closely related definitions of well-spaced sets of points,

packing radius and covering radius of these sets measure how well-spaced they are.

Links

1. Costipazione.
2. Piramide di sfere.
3. Reticolo cristallino.
4. wp/Maryna_V"jazovs'ka | https://www.youtube.com/watch?v=TlCJYxmnInQ Fields Medal: Maryna Viazovska.  Yulia Zdanovska