Apsamikkum

An apsamikkum is an Old Babylonian concave-sided region bounded by four congruent circular arcs. It can be constructed as the central region between four congruent mutually tangent circles arranged with fourfold rotational symmetry, and is sometimes called a concave square (Melville 2005, Robson 2008).

Several apsamikkum problems occur on the Old Babylonian clay tablet BM 15285 (Melville 2005, Robson 2008). The tablet is now held by the British Museum in London, and the image below combines its obverse and reverse.

Because it resembles the noses of bovids on Babylonian lyres, some Assyriologists also call it a "cow's nose" (Robson 2008); the comparison is shown below.

Another Old Babylonian figure bounded by circular arcs is the ox-eye.

If is the length of one of the four circular arcs, each of which is a quarter circle, then the exact area is

Old Babylonian computations instead used the approximation , giving the sexagesimal area coefficient and hence (Melville 2005, Robson 2008).