The ox-eye, also called the Babylonian bull's-eye, is the symmetric lens formed by two congruent circular arcs.
The Old Babylonian table of constants published as TMS 3 records three constants for the ox-eye. The tablet was excavated at Susa and is now in the Louvre Museum collection in Paris. Ox-eyes also occur in Neugebauer's reconstruction of problem 33 on the Old Babylonian clay tablet BM 15285, now held by the British Museum in London (Friberg 2007, pp. 323-326).
The modern reconstruction above has bounding arcs that are each one third of a circle. Geometrically, the ox-eye
is exactly a vesica piscis: the two bounding circles have equal radii 
and their centers are separated by 
. The related grain
figure is not a vesica piscis; its center separation
is 
, its arcs
are quarter circles, and its lens
is narrower. Another related Babylonian arc figure is the
four-sided apsamikkum, or "cow's nose."
If 
is the length
of either bounding arc and 
is its radius, then the
exact area is
 |
The exact long and short transversals have lengths 
and 
, respectively. Using 
for the area of a circle
with circumference 
and the Old Babylonian value 
for 
instead gives the sexagesimal area coefficient 
, long transversal 
, and short transversal 
(Katz 2009, pp. 16 and 29).
