A discussion of a geometric shape that became a symbol known as mandorla or vesica piscis, starting from a Pythagorean point of view

A discussion of a geometric shape that became a symbol known as mandorla or vesica piscis, starting from a Pythagorean point of view: Here we propose a discussion about the 'mandorla' or 'vesica piscis'. It is a type of 2-dimensional lens, that is, a geometric shape formed by the intersection of two circles with the same radius, intersecting in such a way that the centre of each circle lies on the perimeter of the other. The aim of the discussion is that of understanding when such a geometric shape became a symbol and when this symbol received a specific name. We will find that the name 'mandorla' was used long before the term 'vesica piscis', which is the Latin translation of the German 'fischblosen' (fish-bladder) used by Albrecht Dürer in his book on geometry. Therefore, the name invented by Dürer was not used by the painter for a sacred form. However, after the middle of the nineteenth century the term 'vesica piscis' exploded in literature. Its use was criticized and, at the same time, it was stressed that the proper term for the symbol is 'mandorla'.  Nonetheless, the 'vesica piscis' continues to be largely used in the sacred geometry, which ascribes symbolic and sacred meanings to certain geometric shapes and proportions. In the proposed discussion, we will also show that, recently, the 2-dimensional lenticular symbol has been related to the Pythagorean philosophy. It is told that the followers of this philosophy had the habit of using an apple for symbolic communications. Sliced across, the core of the apple is displaying a pentagram, but s...