Insect Architecture

Name: Insect Architecture
Author: Rennie, James

Rennie, James

Insects -- Behavior

M. Réaumur further remarks, that the base of each cell, instead of
forming a plane, is usually composed of three pieces in the shape of
the diamonds on playing cards, and placed in such a manner as to form a
hollow pyramid. This structure, it may be observed, imparts a greater
degree of strength, and, still keeping the solution of the problem
in view, gives a great capacity with the smallest expenditure of
material. This has actually, indeed, been ascertained by mathematical
measurement and calculation. Maraldi, the inventor of glass hives,
determined, by minutely measuring these angles, that the greater were
109° 28', and the smaller 70° 32'; and M. Réaumur, being desirous to
know why these particular angles are selected, requested M. Koenig, a
skilful mathematician (without informing him of his design, or telling
him of Maraldi's researches), to determine by calculation what ought
to be the angle of a six-sided cell, with a concave pyramidal base,
formed of three similar and equal rhomboid plates, so that the least
possible matter should enter into its construction. By employing what
geometricians denominate the _infinitesimal calculus_, M. Koenig found
that the angles should be 109° 26' for the greater, and 70° 34' for
the smaller, or about two-sixtieths of a degree, more or less, than
the actual angles made choice of by bees. The equality of inclination
in the angles has also been said to facilitate the construction of the
cells.

M. Huber adds to these remarks, that the cells of the first row, by
which the whole comb is attached to the roof of a hive, are not like
the rest; for, instead of six sides, they have only five, of which
the roof forms one. The base, also, is in these different, consisting
of three pieces on the face of the comb, and on the other side of
two: one of these only is diamond-shaped, while the other two are of
an irregular four-sided figure. This arrangement, by bringing the
greatest number of points in contact with the interior surface, insures
the stability of the comb.

[Illustration: Arrangement of Cells.]

Public-domain text, read in full here on John Shaqi.

Opening the text

Insect ArchitectureRennie, James

Science

Insect Architecture

Rennie, James

Insects -- Behavior

M. Réaumur further remarks, that the base of each cell, instead of
forming a plane, is usually composed of three pieces in the shape of
the diamonds on playing cards, and placed in such a manner as to form a
hollow pyramid. This structure, it may be observed, imparts a greater
degree of strength, and, still keeping the solution of the problem
in view, gives a great capacity with the smallest expenditure of
material. This has actually, indeed, been ascertained by mathematical
measurement and calculation. Maraldi, the inventor of glass hives,
determined, by minutely measuring these angles, that the greater were
109° 28', and the smaller 70° 32'; and M. Réaumur, being desirous to
know why these particular angles are selected, requested M. Koenig, a
skilful mathematician (without informing him of his design, or telling
him of Maraldi's researches), to determine by calculation what ought
to be the angle of a six-sided cell, with a concave pyramidal base,
formed of three similar and equal rhomboid plates, so that the least
possible matter should enter into its construction. By employing what
geometricians denominate the _infinitesimal calculus_, M. Koenig found
that the angles should be 109° 26' for the greater, and 70° 34' for
the smaller, or about two-sixtieths of a degree, more or less, than
the actual angles made choice of by bees. The equality of inclination
in the angles has also been said to facilitate the construction of the
cells.

M. Huber adds to these remarks, that the cells of the first row, by
which the whole comb is attached to the roof of a hive, are not like
the rest; for, instead of six sides, they have only five, of which
the roof forms one. The base, also, is in these different, consisting
of three pieces on the face of the comb, and on the other side of
two: one of these only is diamond-shaped, while the other two are of
an irregular four-sided figure. This arrangement, by bringing the
greatest number of points in contact with the interior surface, insures
the stability of the comb.

[Illustration: Arrangement of Cells.]

Public-domain text, read in full here on John Shaqi.

Insect Architecture

Insect Architecture

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