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The vesica piscis is the intersection of two congruent disks, each centered on the perimeter of the other. The vesica piscis is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other. [1]
The center lens of the 2-circle figure is called a vesica piscis, from Euclid. Two circles are also called Villarceau circles as a plane intersection of a torus. The areas inside one circle and outside the other circle is called a lune. The 3-circle figure resembles a depiction of Borromean rings and is used in 3-set theory Venn diagrams.
The number 153 is associated with the geometric shape known as the Vesica piscis or Mandorla. Archimedes , in his Measurement of a Circle , referred to this ratio (153/265), as constituting the "measure of the fish", this ratio being an imperfect representation of 1 / 3 ≈ 0.57735 {\displaystyle 1/{\sqrt {3}}\approx 0.57735} .
Example of two asymmetric lenses (left and right) and one symmetric lens (in the middle) The Vesica piscis is the intersection of two disks with the same radius, R, and with the distance between centers also equal to R. If the two arcs of a lens have equal radius, it is called a symmetric lens, otherwise is an asymmetric lens.
This had great significance to the ancients! In many ancient cultures, the Sun was a male god and the Moon a goddess, and the vesica piscis symbolized the opening or gateway between these two polarities through which creation can take place <ref>Nicholas R. Mann, The Sacred Geometry of Washington, D.C. p. 92 (Barnes & Noble, 2006)</ref>.
Articles relating to sacred geometry, which ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. ... Vesica piscis;
A geometrical hexafoil. The hexafoil is a design with six-fold dihedral symmetry composed from six vesica piscis lenses arranged radially around a central point, often shown enclosed in a circumference of another six lenses.
The aureola, when enveloping the whole body, generally appears oval or elliptical in form, but occasionally depicted as circular, vesica piscis, or quatrefoil. When it appears merely as a luminous disk round the head, it is called specifically a halo or nimbus, while the combination of nimbus and aureole is called a glory.