{{Short description|Geometric shape}} thumb|right|300px|The salinon (red) and the circle (blue) have the same area.
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.<ref>{{cite journal|title=On the Salinon of Archimedes|first=T. L.|last=Heath|author-link=Thomas Heath (classicist)|journal=The Journal of Philology|volume=25|issue=50|year=1897|pages=161–163|url=https://archive.org/details/journalofphilolo25claruoft/page/160}}</ref>
==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.<ref>{{cite journal | last = Nelsen | first = Roger B. | date = April 2002 | doi = 10.2307/3219147 | issue = 2 | journal = Mathematics Magazine | jstor = 3219147 | page = 130 | title = Proof without words: The area of a salinon | volume = 75}}</ref>
==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."<ref name=CUT> {{cite web |url=http://www.cut-the-knot.org/proofs/Lemma.shtml |title=Salinon: From Archimedes' ''Book of Lemmas'' |work=Cut-the-knot |accessdate=2008-04-15 |last=Bogomolny | first = Alexander |author-link=Alexander Bogomolny }}</ref>
Namely, if <math>r_1</math> is the radius of large enclosing semicircle, and <math>r_2</math> is the radius of the small central semicircle, then the area of the salinon is:<ref name=WOLF>{{mathworld|title=Salinon|urlname=Salinon}}</ref> <math display=block>A=\frac{1}{4}\pi\left(r_1+r_2\right)^2.</math>
===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.<ref name=CUT/>
==See also==
==References== {{Reflist}}
==External links== *[http://images.math.cnrs.fr/L-arbelos-Partie-II.html L’arbelos. Partie II] by Hamza Khelif at [http://images.math.cnrs.fr/ www.images.math.cnrs.fr] of CNRS
Category:Piecewise-circular curves Category:Archimedes