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Monthly
Puzzle Problema del Mese Puzzle du Mois: April-May
2008
by
Gianni A. Sarcone & Marie-Jo Waeber |
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Puzzles
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Puzzle
# 117 Italiano Français
Difficulty
level:    ,
some math knowledge required.
The
Geometry of the Bees
The wax
cells of any honeycomb are approximately assembled together as illustrated
in fig. 1, so that the opening of every cell faces outward. Each cell is actually
a rhombic decahedron, that is an hexagonal prism having three rhombi at its closed
end (as shown in fig. 2 below). Continue...
In
short, each cell is a ten-sided structure with one side open.
Mathematicians made extensive studies of the isoperimetric
properties of the honeycomb cells and believed them to
be the most efficient design possible. If the faces of every
cell contain the LARGEST possible volume with the LEAST possible
surface, what is the value of the angle alpha?
The faces of the hexagonal prism are each 1-unit wide
Related
puzzles:
- Square
vs rectangle problem.
- The best cardboard
box.
Suggest a
solution Close
- La
geometria delle api
Le celle
di cera di un favo sono disposte come illustrato in fig.
1, con le aperture verso l’esterno. Ogni cella è,
di fatto, un decaedro rombico, cioè un prisma cavo a sei
facce con fondo cuspidato terminato da tre rombi uguali. Prova
a determinare l'inclinazione dell’angolo minore dei rombi
(angolo alfa nella fig. 2) in modo che la cella contenga il volume
maggiore possibile con la minore superficie possibile. Le facce
del prisma esagonale sono larghe 1 unità.
Parole
chiave: isoperimetrico, decaedro rombico.
Suggerisci una
soluzione Chiudi
- Abeilles
géomètres
Les alvéoles d’un
rayon de miel sont disposées comme illustré en
fig. 1, avec les ouvertures vers l’extérieur. Chaque
alvéole est en fait un décahèdre rhombique,
c’est-à-dire un prisme à section hexagonale
avec un fond formé de 3 rhombes égaux. Essaie de
déterminer la valeur de l’angle alpha (fig. 2),
de sorte que l’alvéole contienne le plus grand volume
possible avec la plus petite surface possible.
Les
faces du prisme hexagonal ont chacune une largeur de 1 unité.
Mots
clés: isopérimétrique, décahèdre
rhombique.
Propose une
solution Fermer
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fig.
1
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fig.
2 |
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Mail
monthly puzzle solution to:
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Envoie la solution à:
Marie-Jo
Waeber
Archimedes' Lab
Casella Postale 1700
16100 Genova Centro
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