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The vesica piscis is an ancient symbol which has been adopted by many religions, most notably by the Christians. You may be familiar with one form of the vesica piscis, a fish which is often used as a symbol by Christians, but this ancient symbol has also been used by pagan religions and mathematicians once attached great importance to it as well. The vesica piscis has been so well integrated into human culture that you can probably find an example of it in art or architecture in your region.
This shape is formed by overlapping two circles of the same size such that the perimeter of each circle comes into contact with the middle of the other circle. The result looks like a venn diagram, with an almond shape in the middle formed by the overlapping circles. In Latin, this shape is known as the mandorla or almond, while the entire figure is called the vesica piscis, or “bladder of the fish.” The mathematical ratio formed was of great interest to the Greeks, and again during the medieval era, when the vesica piscis showed up abundantly in art and architecture, reflecting a fascination with the Angient Greeks and Romans.
There are all sorts of symbolic meanings for the vesica piscis and the mandorla. Many works of early Christian art depict religious figures inside a vesica piscis or mandorla, for example, and early Christians identified themselves with a small fish shaped piece of jewelry or embroidered motif when Christianity was frowned upon in Europe. The pagans believed that the shape was related to fertility, as the mandorla does look sort of like the female reproductive parts, and this pointed oval shape shows up in a surprising number of places as a result.
In Celtic symbolism, some artists create triquetras, which are made by overlapping three mandorlas to create a triangular shape. This sacred shape often appears as a motif in Celtic jewelry and as a decorative element in Celtic architecture, and it appears in a number of forms. Some artists even make crosses by linking four of these symbols; these crosses are known as Carolingian crosses.
Like many shapes with ancient symbolic meanings, the vesica piscis pops up in a lot of places, and it occurs again and again, even in cultures which had no contact with each other. The common occurrence of this shape illustrates the universal human fascination with math and ratios. You can find the vesica piscis in works of art and architecture around the world. It also shows up in seals and logos, especially among Christian organizations, in which case it is common to see only the mandorla.