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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]
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.
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} .
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.
Among all shapes of constant width that avoid all points of an integer lattice, the one with the largest width is a Reuleaux triangle. It has one of its axes of symmetry parallel to the coordinate axes on a half-integer line. Its width, approximately 1.54, is the root of a degree-6 polynomial with integer coefficients. [17] [19] [20]
Vesica piscis, a shape formed by the intersection of two circles of the same radius Topics referred to by the same term This disambiguation page lists articles associated with the title Vesica .
It is the distance between parallel sides of a regular hexagon with sides of length 1. It is the length of the space diagonal of a unit cube. The vesica piscis has a major axis to minor axis ratio equal to :. This can be shown by constructing two equilateral triangles within it.