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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.
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} .
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.
A form of the Triquetra symbol which has the exact geometrical proportions to be composed of three overlapping Vesica piscis symbols — something which is important to a few authors of books on Christian symbolism. (Ribbons version.)
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.
Parts of these same circles are used to form the triquetra, a figure of three overlapping semicircles (each two of which form a vesica piscis symbol) that again has a Reuleaux triangle at its center; [76] just as the three circles of the Venn diagram may be interlaced to form the Borromean rings, the three circular arcs of the triquetra may be ...
Primitive Heronian triangle; Right triangle. 30-60-90 triangle; Isosceles right triangle; ... Lens, vesica piscis (fish bladder) Lune; Quatrefoil; Reuleaux polygon ...