The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two closed
disks of common radius 
whose centers are separated by 
(Pedoe 1995, p. xii). The height of the lens
is given by letting 
in the equation for a circle-circle intersection
 |
(1)
|
giving
 |
(2)
|
The vesica piscis therefore has two equilateral triangles inscribed in it as illustrated above.
The area of the vesica piscis is given by plugging 
into the circle-circle
intersection area equation with 
,
 |
(3)
|
giving
 |  |  |
(4)
|
 |  |  |
(5)
|
(OEIS A093731). Since each arc of the lens is precisely 1/3 of a circle, its perimeter is given by
 |
(6)
|
The same geometric figure occurs in Old Babylonian mathematics as the ox-eye (Friberg 2007, pp. 319 and 323-326). The related Old Babylonian grain
figure is also a symmetric equal-circle lens, but is
not a vesica piscis. Its circle centers are separated
by 
rather than 
, making its bounding arcs quarter
circles rather than one-third circles
and producing a narrower lens.
Renaissance artists frequently surrounded images of Jesus with the vesica piscis (Pedoe 1995, p. xii; Rawles 1997).
