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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.
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.
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} .
Vesica piscis This page was last edited on 17 May 2021, at 07:51 (UTC). Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional ...
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The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.