What Is the Circle Grid Line in Art Called

Kind of geometric pattern

Instance overlapping round circumvolve figures
foursquare circle grid
i+
four
9
Centered square lattice forms
5
13

triangular circle grid
i+
3
4
7
19

An overlapping circles filigree 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 blueprint of points.

Patterns of seven overlapping circles appear in historical artefacts from the 7th century BC onwards; they go a oft used ornament in the Roman Empire period, and survive into medieval artistic traditions both in Islamic fine art (girih decorations) and in Gothic art. The name "Bloom of Life" is given to the overlapping circles pattern in New Age publications.

Of special interest is the six petal rosette derived from the "seven overlapping circles" design, too known equally "Sun of the Alps" from its frequent apply in alpine folk art in the 17th and 18th century.

Triangular filigree of overlapping circles [edit]


This design can be extended indefinitely, seen here with hexagonal rings of 1, 7, xix, 37, 61, 91 circles...

The triangular lattice class, with circle radii equal to their separation is called a seven overlapping circles grid.^[ane] Information technology contains vi circles intersecting at a betoken, with a 7th 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 mode, jewelry, tattoos and decorative products.

Cultural significance [edit]

Near Due east [edit]

The oldest known occurrence of the "overlapping circles" pattern is dated to the 7th or 6th century BCE, plant on the threshold of the palace of Assyrian king Aššur-bāni-apli in Dur Šarrukin (now in the Louvre).^[ii]

The pattern becomes more widespread in the early centuries of the Common Era. Ane early on example are v patterns of 19 overlapping circles drawn on the granite columns at the Temple of Osiris in Abydos, Egypt,^[3] and a further v on column opposite the edifice. They are drawn in red ochre and some are very faint and difficult to distinguish.^[iv] The patterns are graffiti, and not establish in natively Egyptian ornaments. They are mostly dated to the early on centuries of the Christian Era^[5] although medieval or even modernistic (early on 20th century) origin cannot be ruled out with certainty, equally the drawings are non mentioned in the all-encompassing listings of graffiti at the temple compiled past Margaret Murray in 1904.^[6]

Similar patterns were sometimes used in England equally apotropaic marks to go on witches from entering buildings.^[7] Consecration crosses indicating points in churches anointed with holy water during a churches dedication too have the course of overlapping circles.

In Islamic art, the blueprint 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 mode called girih. The resulting patterns however characteristically conceal the construction grid, presenting instead a design of interlaced strapwork.^[eight]

Europe [edit]

Patterns of 7 overlapping circles are constitute on a Cypro-Primitive I loving cup of the eighth-seventh century BC in Cyprus^{[ citation needed ]} and Roman mosaics, for example at Herod's palace in the 1st century BC.

The design is plant on ane of the silver plaques of the Late Roman hoard of Kaiseraugst (discovered 1961).^[9] It is later establish as an ornament in Gothic architecture, and yet subsequently in European folk fine art of the early modernistic period.

High medieval examples include the Cosmati pavements in Westminster Abbey (13th century).^[x] Leonardo da Vinci explicitly discussed the mathematical proportions of the design.^[11]

Modern usage [edit]

19-circle with arcs
Pendant, silver, ⌀ 27 mm
(commercial product, 2013)

The name "Blossom of Life" is modern, associated with the New Age motility, and usually attributed specifically to Drunvalo Melchizedek in his book The Ancient Hush-hush of the Flower of Life (1999).^[12] ^[thirteen]

The pattern and modernistic name have propagated into wide range of usage in popular culture, in manner, jewelry, tattoos and decorative products. The pattern in quilting has been chosen diamond wedding ring or triangle wedding band to contrast it from the square pattern. Besides an occasional use in way,^[14] information technology is too 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,^[15] whereas the album A Caput Full of Dreams (2015) by Coldplay features the 19 overlapping circles grid every bit the central office of its album cover. Teaser posters illustrating the cover art to A Head Full of Dreams were widely displayed on the London Hush-hush in the last calendar week of Oct 2015.^[xvi]

The "Sunday of the Alps" (Italian Sole delle Alpi) symbol has been used every bit the keepsake of Padanian nationalism in northern Italian republic since the 1990s.^[17] It resembles a pattern frequently establish in that area on buildings.^[eighteen]

Gallery [edit]

1, 7, and 19-circle hexagonal variant

In the examples below the pattern has a hexagonal outline, and is further circumscribed.

i-circle with completed arcs
7-circle: Mosaic floor from a bathhouse in Herod'south palace, 1st century BCE
19-circle symbol with completed arcs and bounded by a larger circumvolve
19-circumvolve: Two symbols drawn in red ochre Temple of Osiris at Abydos, Arab republic of egypt
19-circle: A window at the southern apsis of the church of Preveli Monastery (Moni Preveli), Crete.

Similar patterns

In the examples below the pattern does not have a hexagonal outline.

Loving cup with mythological scenes, a sphinx frieze and the representation of a king vanquishing his enemies. Cypro-Archaic I (8th–7th centuries BC). From Idalion, Cyprus.
Flooring ornament from the northern Iraq palace of King Ashurbanipal, visible in the Museum of Louvre, dated 645BC.
"Sun of the Alps" emblem used by the Lega Nord

Construction [edit]

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 i-[inch; 25 mm] radius, with each betoken of intersection serving as a new center. The design tin be expanded advertising infinitum depending upon the number of times the odd-numbered points are marked off."

The pattern figure tin can be drawn by pen and compass, by creating multiple series of interlinking circles of the same diameter touching the previous circle'south center. The 2d circumvolve is centered at any signal on the first circumvolve. All following circles are centered on the intersection of two other circles.

Progressions [edit]

The pattern can exist extended outwards in concentric hexagonal rings of circles, as shown. The kickoff row shows rings of circles. The second row shows a three-dimensional interpretation of a ready of n×north×n cube of spheres viewed from a diagonal centrality. The third row shows the pattern completed with partial circle arcs within a set of completed circles.

Expanding sets have 1, vii, 19, 37, 61, 91, 127, etc. circles, and continuing ever larger hexagonal rings of circles. The number of circles is n ³-(n-i)³ = 3n ²-3n+1 = 3n(n-1)+1.

These overlapping circles can likewise exist seen as a projection of an north-unit cube of spheres in 3-dimensional space, viewed on the diagonal centrality. There are more than spheres than circles considering some are overlapping in 2 dimensions.

Rosette figures including fractional circles
1-circle	7-circle (8-ane)	19-circle (27-eight)	37-circle (64-27)	61-circle (125-64)	91-circle (216-125)	127-circle... (343-216)

1-sphere (1×1×1)	eight-sphere (2×2×2)	27-sphere (iii×three×3)	64-sphere (4×four×4)	125-sphere (v×v×5)	216-sphere (half dozen×half-dozen×half-dozen)	343-sphere (7×seven×vii)

+12 arcs	+24 arcs	+36 arcs	+48 arcs	+threescore arcs	+72 arcs	+84 arcs

Other variations [edit]

Some other triangular lattice form is common, with circle separation as the square root of iii times their radius. Richard Kershner showed in 1939 that no arrangement of circles tin can cover the aeroplane more than efficiently than this hexagonal lattice system.^[19]

Two showtime copies of this circumvolve blueprint makes a rhombic tiling pattern, while iii copies make the original triangular pattern.

19 circle example
2 offset copies of the minimal covering circle pattern (left) make a rhombic tiling pattern, like this cherry-red, blueish version.
Three start copies of the minimal roofing circle blueprint (left most image) make the seven-circle pattern, like this scarlet, green, bluish version.

[edit]

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 circumvolve and outside the other circle is called a lune.

The three-circle effigy resembles a depiction of borromean rings and is used in three-set theory Venn diagrams. Its interior makes a unicursal path called a triquetra. The centre of the 3-circumvolve figure is called a reuleaux triangle.

Vesica piscis	Borromean rings	Venn diagram	Triquetra	Reuleaux triangle

Some spherical polyhedra with edges forth corking circles tin be stereographically projected onto the airplane as overlapping circles.

Polyhedra in stereographic project
octahedron	Cuboctahedron	Icosidodecahedron

The 7-circle pattern has also been chosen an Islamic vii-circles pattern for its apply in Islamic art.

Square grid of overlapping circles [edit]

Square lattice form
The circle radius is foursquare root of two times their separation.	A quilt design called a double nuptials ring design.

Centered square lattice form
It can be seen as ii one-half-offset square grids of tangent circles.	Egyptian blueprint, from Owen Jones's The Grammar of Ornament (1856)

The foursquare lattice form tin can be seen with circles that line upwards horizontally and vertically, while intersecting on their diagonals. The pattern appears slightly different when rotated on its diagonal, also chosen a centered foursquare lattice grade because it tin be seen every bit ii square lattices with each centered on the gaps of the other.

It is called a Kawung motif in Indonesian batik, and is found on the walls of the eighth century Hindu temple Prambanan in Java.

Information technology is called an Apsamikkum from ancient Mesopotamian mathematics.^[20]

The related five overlapping circles grid is synthetic by from two sets of overlapping circles half-offset.^[21]
Kawung or "Coffee Edible bean" Batik sarong (detail), Java, Indonesia

Meet also [edit]

Uniform tiling symmetry mutations - pattern mutations in 3D space
Knot theory

References [edit]

^ Islamic Fine art and Geometric Design: Activities for Learning
^ Louvre Inv.-Nr. AO 19915. Georges Perrot, Charles Chipiez, A History of Art in Chaldæa and Assyria, vol. 1, London 1884, Southward. 240, (gutenberg.org)
^ Weisstein, Eric W. "Flower of life". MathWorld.
^ Stewart, Malcolm (2008). "The "Flower of Life" and the Osirion – Facts are more interesting than Fantasy". Egyptian Bout (David Furlong) . Retrieved November 8, 2015.
^ Furlong, David. "The Osirion and the Flower of Life". Retrieved November viii, 2015. Furlong states that these engravings can date no earlier than 535 BCE and probably date to the second and 4th century CE. His research is based on photographic testify of Greek text, yet to be fully deciphered. The text is seen alongside the designs and the position close to the summit of columns, which are greater than 4 meters in peak. Furlong suggests the Osirion was one-half filled with sand prior to the circles existence drawn and therefore likely to have been well after the terminate of the Ptolemaic dynasty.
^ Murray, Margaret Alice (1904). The Osireion at Abydos London. p. 35. Retrieved November four, 2015.
^ Kennedy, Maev (October 31, 2016). "Witches' marks: public asked to seek ancient scratchings in buildings". The Guardian. Retrieved October 31, 2016.
^ Broug, Eric (2008). Islamic Geometric Patterns. Thames and Hudson. pp. 22–23 and passim. ISBN978-0-500-28721-seven.
^ Hans Ulrich Instinsky: Der spätrömische Silberschatzfund von Kaiseraugst. Mainz 1971, plaque 85.
^ The Cosmati Pavements in Westminster Abbey. Abgerufen am 14. September 2013.
^ Codex Atlanticus, foll. 307r–309v, 459r (dated between 1478 and 1519).
^ Bartfeld, Martha (2005). How to Create Sacred Geometry Mandalas. Santa Fe, NM: Mandalart Creations. p. 35. ISBN9780966228526. OCLC 70293628.
^ Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics, Second Edition. CRC Printing. p. 1079. ISBN1420035223.
^ E.g. Zaman, Sana (May 14, 2013). "Zaeem Jamal Launches New Drove on Board a Individual Yacht in Dubai Marina". Haute Living. Retrieved November 9, 2015.
^ Cooper, Ed (February 25, 2013). "Bring Me The Horizon: This album needs to be the one that lasts forever". The Independent. Archived from the original on Oct 23, 2015. Retrieved November 8, 2015.
^ Denham, Jess (November vi, 2015). "Coldplay new anthology: Beyonce and Noel Gallagher to characteristic on A Head Full of Dreams". The Independent. Retrieved Nov eight, 2015.
^ "Il significato del simbolo del Sole delle Alpi" (in Italian). Lega Nord. Archived from the original on January 12, 2014. Retrieved December ane, 2014.
^ Ivano Dorboló (June six, 2010). "The church of S.Egidio and the Sun of the Alps symbol". Storia di Confine – Valli di Natisone . Retrieved November 9, 2015.
^ Sphere Packings, Lattices and Groups, John Conway, Neil J. A. Sloane, Chapter 2, section 1.1, Covering space with overlapping circle. pp. 31-32. Figure two.i Covering the aeroplane with circles (b) The more than efficient or thinner covering in a hexagonal lattice. [1]
^ Mesopotamian Mathematics 2100-1600 BC: Technical Constants in Bureaucracy and Education (Oxford Editions of Cuneiform Texts), Eleanor Robson, Clarendon Press, 1999, ISBN 978-0198152460 [2] at books.google.com
^ Creating Square Grids from Circles

External links [edit]

Weisstein, Eric W. "Circle-circle intersection". MathWorld.
The bloom of life article from The Mystica

bondladdelf.blogspot.com

Source: https://en.wikipedia.org/wiki/Overlapping_circles_grid