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The shape of the vesica pisces is derived from the intersection of two circles, the Pythagorean "measure of the fish" that was a mystical symbol of the intersection of the world of the divine with the world of matter and the beginning of creation. To the Pythagoreans, the whole of creation was based on number, and by studying the properties of number, they believed one could achieve spiritual liberation. The vesica pisces was the symbol of the first manifestation, the dyad (reflection) that gives birth to the entire manifest universe. Within the vesica can be found the triangle, the tetrad, the square, the pentacle, and many more polygons, making the vesica a true symbolic womb.
Curiously, the New Testament story of the loaves and fishes secretly reveals the geometric formula for the fish shaped device, as does the story of the miraculous catch: "Simon Peter went up, and drew the net to land full of great fishes, an hundred and fifty and three: and for all there were so many, yet was not the net broken. (John 21:11) " This is little remarked upon by Bible scholars and usually ignored by Christian bible interpreters.