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The vesica piscis in Euclid's Elements. This figure appears in the first proposition of Euclid's Elements, where it forms the first step in constructing an equilateral triangle using a compass and straightedge. The triangle has as its vertices the two disk centers and one of the two sharp corners of the vesica piscis. [4]
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.
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.
Primitive Heronian triangle; Right triangle. 30-60-90 triangle; Isosceles right triangle; ... Lens, vesica piscis (fish bladder) Lune; Quatrefoil; Reuleaux polygon ...
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.
Whenever two edges of a Euclidean minimum spanning tree meet at a vertex, they must form an angle of 60° or more, with equality only when they form two sides of an equilateral triangle. This is because, for two edges forming any sharper angle, one of the two edges could be replaced by the third, shorter edge of the triangle they form, forming ...
The main reason Pisces and Libra find success in a romantic relationship is their commitment to find common ground. Pisces tends to struggle with being forthcoming, but Libra puts them so at ease ...
The lens shape formed by such an intersection is called vesica piscis when two same-radius circles overlap, with the center of each lying on the perimeter of the other, [124] which is not the case on the monument grounds.