Salinon

The Salinon (Greek for " salt cellar ") is a formed of four semicircles, mirror-symmetrical geometric figure. It was first described by Archimedes probably in his Book of Lemmas.

Construction

Is the origin of a Cartesian coordinate system. On the axis outside the two points, and are (in each case at the same distance to ), and inside the points (also with the same distance to ); so is. You build a semi-circle over, and two smaller, equal-sized semi-circles over and. Finally, draw a fourth half circle under. The Salinon is the area bounded by these four semicircles figure ( salmon color in the drawing). It cuts the axis at the points and.

Properties

Archimedes described the properties of the Salinon as a set of 14 in his Book of Lemmas with reference to Euclid's Elements, Book 2, Proposition 10

Denoting by and the small, medium semicircle ( ) the radius of the large semicircle ( ) with, shall apply to the surface of Salinon:

In addition:

• The points on the four semi-circles with the largest distance from the axis ( and including ) form a square.
• The perimeter of this square has the same area (purple in the figure ) as the Salinon.
• If the diameter of the semicircle below to zero ( the points and thus in coincide ), the Salinon passes into a to - axis mirror-symmetric Arbelos, another figure of semicircles whose investigation is attributed to Archimedes.