The Vesica piscis is a shape which is the intersection of two circles with the same radius, intersecting in such a way that the center of each circle lies on the circumference of the other. The name literally means the “bladder of a fish” in Latin. The shape is also called mandorla (“almond” in Italian).
The mathematical ratio of the width of the vesica piscis to its height is the square root of 3, or 1.7320508… (since if straight lines are drawn connecting the centers of the two circles with each other, with the two points where the circles intersect, two equilateral triangles join along an edge). The ratios 265:153 = 1.7320261… and 1351:780 = 1.7320513… are two of a series of approximations to this value, each with the property that no better approximation can be obtained with smaller whole numbers. Archimedes of Syracuse, in his On the Measurement of the Circle, uses these ratios as upper and lower bounds:
One of the numbers in these ratios (153) also appears in the Gospel of John (21:11) as the number of fish Jesus caused to be caught in a miraculous Draught of Fish, and significance has sometimes been attached to this.
The vesica piscis has been the subject of mystical speculation at several periods of history, and is viewed as important in Freemasonry and some forms of Kabbalah. More recently, numerous New Age authors have interpreted it as a yonic symbol and claimed that this, a reference to the female genitals, is a traditional interpretation.
In Christian art, some aureolas are in the shape of a vertically oriented vesica piscis, and the seals of ecclesiastical organizations can be enclosed within a vertically oriented vesica piscis (instead of the more usual circular enclosure).
The vesica piscis has been used as a symbol within Freemasonry, most notably in the shapes of the collars worn by officiants of the Masonic rituals.  It was also considered the proper shape for the enclosure of the seals of Masonic lodges.
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