The salinon (meaning 'salt-cellar' in Greek) is a geometrical figure that consists of four . It was first introduced in the Book of Lemmas, a work attributed to Archimedes.
Construction
Let
A,
D,
E, and
B be four points on a line in the plane, in that order, with
AD =
EB. Let
O be the bisector of segment
AB (and of
DE). Draw semicircles above line
AB with
AB,
AD, and
EB, and another semicircle below with diameter
DE. A salinon is the figure bounded by these four semicircles.
Properties
Area
Archimedes introduced the salinon in his
Book of Lemmas by applying Book II, Proposition 10 of Euclid's
Elements. Archimedes noted that "the area of the figure bounded by the circumferences of all the semicircles is equal to the area of the circle on CF as diameter."
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]
Namely, if is the radius of large enclosing semicircle, and is the radius of the small central semicircle, then the area of the salinon is:
Arbelos
Should points
D and
E converge with
O, it would form an
arbelos, another one of Archimedes' creations, with
symmetry along the
y-axis.
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]
See also
External links
