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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 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.
An overlapping circles grid is a geometric pattern of repeating, overlapping circles of an equal radius in two-dimensional space.Commonly, designs are based on circles centered on triangles (with the simple, two circle form named vesica piscis) or on the square lattice pattern of points.
Interlaced triquetra which is a trefoil knot. The triquetra (/ t r aɪ ˈ k w ɛ t r ə / try-KWEH-truh; from the Latin adjective triquetrus "three-cornered") is a triangular figure composed of three interlaced arcs, or (equivalently) three overlapping vesicae piscis lens shapes.
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>.
For any edge of any Euclidean minimum spanning tree, the lens (or vesica piscis) formed by intersecting the two circles with as their radii cannot have any other given vertex in its interior. Put another way, if any tree has an edge u v {\displaystyle uv} whose lens contains a third point w {\displaystyle w} , then it is not of minimum length.
A mandorla is a vesica piscis shaped aureola which surrounds the figures of Christ and the Virgin Mary in traditional Christian art. [4] It is commonly used to frame the figure of Christ in Majesty in early medieval and Romanesque art, as well as Byzantine art of the same periods.