Mystical and Religious Significance
The most famous example in nature of the vesica piscis during a total solar eclipse, when Moon's apparent size is the same as that of the Sun. As the Moon moves to cover the Sun, at a certain moment it forms a vesica piscis. In many ancient cultures, the Sun was a male god and the Moon a goddess, and the vesica piscis symbolized an opening or gateway between these two polarities through which creation can take place. The ancient Egyptians practiced sacred geometry based on "As above, so below". Architects and artists copied the solar eclipse/vesica piscis and its mathematics in their sacred buildings and artwork to reflect their religious beliefs. This ancient tradition was passed on through the centuries by the Freemasons.
The mathematical ratio of the width across the center 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 and 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:
The vesica piscis has been the subject of mystical speculation at several periods of history, and is viewed as important in 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.
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