The salinon (meaning 'salt-cellar' in Greek) is a geometrical figure that consists of four semicircles. It was first introduced in the '' Book of Lemmas'', a work attributed to

Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists ...

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 diameters ''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 sequal to the area of the circle on CF as diameter." Namely, if

r_1

is the radius of large enclosing semicircle, and

r_2

is the radius of the small central semicircle, then the area of the salinon is:

A=\frac\pi\left(r_1+r_2\right)^2.

Arbelos

Should points ''D'' and ''E'' converge with ''O'', it would form an arbelos, another one of Archimedes' creations, with

symmetry Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...

along the ''y''-axis.

References

{{Reflist

External links

L’arbelos. Partie II
by Hamza Khelif a
www.images.math.cnrs.fr
of

CNRS The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 ...