Vesica piscis: Difference between revisions

The vesica piscis is a type of

This figure appears in the first proposition of

Mathematically, the vesica piscis is a special case of a lens, the shape formed by the intersection of two disks.

The mathematical ratio of the height of the vesica piscis to the width across its center is the

The area of the vesica piscis is formed by two equilateral triangles and four equal circular segments. In the drawing one triangle and one segment appear in blue.

One triangle and one segment form a sector of one sixth of the circle (60°). The area of the sector is then: ${\displaystyle {\frac {1}{6}}\pi r^{2}}$.

Since the side of the equilateral triangle has length r, its area is ${\displaystyle {\frac {\sqrt {3}}{4}}r^{2}}$.

The area of the segment is the difference between those two areas: ${\displaystyle {\frac {1}{6}}\pi r^{2}-{\frac {\sqrt {3}}{4}}r^{2}}$.

By summing the areas of two triangles and four segments, we obtain the area of the vesica piscis:

${\displaystyle {\frac {1}{6}}(4\pi -3{\sqrt {3}})r^{2}\approx 1.2284r^{2}}$

Uses

The two circles of the vesica piscis, or three circles forming in pairs three vesicae, are commonly used in Venn diagrams. Arcs of the same three circles can also be used to form the triquetra symbol, and the Reuleaux triangle.

In

The cover of the Chalice Well in Glastonbury (Somerset, United Kingdom) depicts a stylized version of the vesica piscis design (see picture).

The vesica piscis has been used as a symbol within Freemasonry, most notably in the shapes of the collars worn by officiants of the Masonic rituals.^[6] It was also considered the proper shape for the enclosure of the seals of Masonic lodges.^[7][8]

The vesica piscis is also used as proportioning system in architecture, in particular Gothic architecture. The system was illustrated in Cesare Cesariano's Vitruvius (1521), which he called "the rule of the German architects".

Gallery

• 
  Christ in Majesty within a mandorla-shaped aureola in a medieval illuminated manuscript
• Church of Scotland logo
  Church of Scotland logo
• 
  Coat of arms of Guam
• Perth College (Western Australia) logo
  Perth College (Western Australia) logo

See also

• Flower of Life
  , a figure based upon this principle
• Villarceau circles, a pair of congruent circles derived from a torus that, however, are not usually centered on each other's perimeter

References

External links

Wikimedia Commons has media related to Vesica piscis.

• Weisstein, Eric W. "Vesica Piscis". MathWorld.