al rings of 1, 7, 19, 37, 61, and 91 circles The
triangular lattice form, with circle
radii equal to their separation is called a
seven overlapping circles grid. It contains six circles intersecting at a point, with a seventh circle centered on that intersection. Overlapping circles with similar geometrical constructions have been used infrequently in various of the
decorative arts since ancient times. The pattern has found a wide range of usage in popular culture, in
fashion,
jewelry,
tattoos and decorative products.
Cultural significance Near East The oldest known occurrence of the overlapping circles pattern is dated to the 7th or 6th century
BCE, found on the threshold of the palace of Assyrian king
Aššur-bāni-apli in
Dur Šarrukin (now in the
Louvre). The design became more widespread in the early centuries of the
Common Era. One early example is a set of 5 patterns of 19 overlapping circles drawn on the granite columns at the
Temple of Osiris in
Abydos, Egypt, and a further five on a column opposite the building. They are drawn in red
ochre and some are very faint and difficult to distinguish. The patterns are
graffiti, and not found in natively Egyptian ornaments. They are mostly dated to the early centuries CE although medieval or even modern (early 20th century) origin cannot be ruled out with certainty, as the drawings are not mentioned in the extensive listings of graffiti at the temple compiled by
Margaret Murray in 1904. Similar patterns were sometimes used in England as
apotropaic marks to keep witches from entering buildings.
Consecration crosses indicating points in churches anointed with holy water during a church's dedication also take the form of overlapping circles. In
Islamic art, the pattern is one of several arrangements of circles (others being used for fourfold or fivefold designs) used to construct grids for
Islamic geometric patterns. It is used to design patterns with 6- and 12-pointed stars as well as
hexagons in the style called
girih. The resulting patterns however characteristically conceal the construction grid, presenting instead a
design of interlaced strapwork.
Europe Patterns of seven overlapping circles are found on
Roman mosaics, for example at
Herod's Palace in the 1st century BCE. The design is found on one of the silver plaques of the Late Roman hoard of
Kaiseraugst (discovered 1961). It is later found as an ornament in
Gothic architecture, and still later in European
folk art of the early modern period. High medieval examples include the
Cosmati pavements in
Westminster Abbey (13th century).
Leonardo da Vinci explicitly discussed the mathematical proportions of the design.
Modern usage : silver
pendant (2013) The name
Flower of Life is modern, associated with the
New Age movement, and commonly attributed specifically to Drunvalo Melchizedek in his book
The Ancient Secret of the Flower of Life (1999). The pattern and modern name have propagated into wide range of usage in popular culture, in fashion, jewelry, tattoos, and decorative products. The pattern in
quilting has been called the
diamond wedding ring or
triangle wedding ring to contrast it from the
square pattern. Besides occasional use in fashion, it is also used in the decorative arts. For example, the album
Sempiternal (2013) by
Bring Me the Horizon uses the
61 overlapping circles grid as the main feature of its album cover, and the album
A Head Full of Dreams (2015) by
Coldplay features the 19 overlapping circles grid as the central part of its album cover. Teaser posters illustrating the cover art to
A Head Full of Dreams were widely displayed on the
London Underground in the last week of October 2015. The
Sun of the Alps () symbol has been used as the emblem of
Padanian nationalism in northern Italy since the 1990s. It resembles a pattern often found in that area on buildings. A seven-circle Flower of Life is also used in the coat of arms of
Asgardia the space nation.
Gallery 1, 7, and 19-circle hexagonal variants In the examples below the pattern has a hexagonal outline, and is further circumscribed. File:Leonardo da Vinci - Codex Atlanticus folio 309v detail1.png|Drawing in Leonardo da Vinci's
Codex Atlanticus, between 1478 and 1519 File:Leonardo da Vinci – Codex Atlanticus folio 307v.jpg|Drawing by
Leonardo da Vinci (Codex Atlanticus, 307v) File:RozetaSymbol.svg|1-circle with completed arcs File:Mosaic floor from a bathhouse in Herod's palace - Google Art Project.jpg|7-circle mosaic floor from a bathhouse in
Herod's Palace, 1st century BCE File:Flower-of-Life-small.svg|19-circle symbol with completed arcs and bounded by a larger circle File:Temple-of-Osiris Flower-of-Life 02.jpg|Two 19-circle symbols drawn in red ochre at the Temple of Osiris in Abydos, Egypt File:Moni Preveli Church Apsis Window South.JPG|19-circle window at the southern apsis of the church of
Preveli Monastery (Moni Preveli), Crete File:Flower of life ephesos square.jpg|19-circle pattern from
Ephesus, Turkey
Similar patterns In the examples below, the pattern does not have a hexagonal outline: File:Cup Idalion Louvre N3454.jpg|Cup with mythical scenes, a
sphinx frieze, and a king defeating his enemies. From the Cypro-Archaic I period (8th–7th centuries BCE) of
Idalion, Cyprus. China-beijing-forbidden-city-P1000157-detail.jpg|Ball held by the male
Guardian Lion at the
Gate of Supreme Harmony, Forbidden City, Beijing, China, showing the pattern on its surface File:Floor decoration from the palace of King Ashurbanipal.jpg|Floor decoration from the northern Iraq palace of King
Ashurbanipal, visible at the Louvre Museum, dated 645 BCE File:Coffee cup with overlapping circles grid ornament (Germany, 2022).jpg|Coffee cup (Germany, 2022) File:Sun of the Alps.svg|
Sun of the Alps emblem used by the
Lega Nord Construction Martha Bartfeld, author of geometric art tutorial books, described her independent discovery of the design in 1968. Her original definition said, "This design consists of circles having a 1-[inch; 25 mm] radius, with each point of intersection serving as a new center. The design can be expanded
ad infinitum depending upon the number of times the odd-numbered points are marked off." The figure can be drawn by
pen and
compass, by creating multiple series of interlinking circles of the same diameter touching the previous circle's center. The second circle is centered at any point on the first circle. All following circles are centered on the intersection of two other circles.
Progressions The pattern can be extended outward in concentric hexagonal rings of circles, as in the following table. The first row shows rings of circles. The second row shows cubes of stacked spheres in
isometric projections. The third row shows the pattern completed with partial circle arcs within a set of completed circles. Expanding sets have 1, 7, 19, 37, 61, 91, 127 circles, and continuing ever larger hexagonal rings of circles. The number of circles is n^3-(n-1)^3=3n^2-3n+1=3n(n-1)+1, where
n is the number of rings, forming the
centered hexagonal numbers. These overlapping circles can also be seen as a
projection of an
n-unit
cube of spheres in 3-dimensional space, viewed on the diagonal axis. There are more spheres than circles because some are overlapping in 2 dimensions.
Other variations Another
triangular lattice form is common, with circle separation as the
square root of 3 times their radius. Richard Kershner showed in 1939 that no
arrangement of circles can cover the plane more efficiently than this hexagonal lattice arrangement. Two offset copies of this circle pattern makes a
rhombic tiling pattern, while three copies make the original triangular pattern. File:Flower of life 0577-19-circle.svg|A 19-circle example, the minimal covering circle pattern File:Flower of life 0577-2compound.png|Two offset copies of the pattern (left) make a
rhombic tiling pattern File:Circlemesh hexagonal tiling compound.svg|Three offset copies of the pattern (leftmost image) make the seven-circle pattern File:Jar Met 56.185.15.jpg|Example on an
Ayyubid-era
Raqqa ware stoneware glazed jar, Syria, 12th or 13th century File:Pavement Hospitalia Villa Hadriana n8.jpg|Black and white
mosaic pavement at
Hadrian's Villa, Tivoli, 2nd century CE
Related concepts The center
lens of the two-circle figure is called a , from the mathematician
Euclid. Two circles are also called
Villarceau circles as a plane intersection of a
torus. The area inside one circle and outside the other is called a
lune. The three-circle figure resembles the
Borromean rings and is also used in the
three-set variant of
Venn diagrams. The combined path of the intersections forms a
unicursal path called a
triquetra. The center of the three-circle figure is called a
Reuleaux triangle. Some
spherical polyhedra with edges along
great circles can be stereographically projected onto the plane as overlapping circles. The seven-circle pattern has also been called an
Islamic seven-circles pattern for its use in
Islamic art. ==Square grid of overlapping circles==