Editing Circle (section)

==History==
[[File:2009_07_09_camino_cielo_paradise_137.jpg|thumb|Circular cave paintings in [[Santa Barbara County, California]]]]
[[Image:Shatir500.jpg|right|thumb|200px|Circles in an old [[Arabic]] [[astronomical]] drawing.]]
Prehistoric people made [[stone circle]]s and [[timber circle]]s, and circular elements are common in [[petroglyph]]s and [[cave painting]]s.<ref>{{Cite journal |last1=Simek |first1=Jan F. |last2=Cressler |first2=Alan |last3=Herrmann |first3=Nicholas P. |last4=Sherwood |first4=Sarah C. |date=2013-06-01 |title=Sacred landscapes of the south-eastern USA: prehistoric rock and cave art in Tennessee |url=https://www.cambridge.org/core/product/identifier/S0003598X00049048/type/journal_article |journal=Antiquity |language=en |volume=87 |issue=336 |pages=430–446 |doi=10.1017/S0003598X00049048 |s2cid=130296519 |issn=0003-598X}}</ref> Disc-shaped prehistoric artifacts include the [[Nebra sky disc]] and jade discs called [[Bi (jade)|Bi]].

The Egyptian [[Rhind papyrus]], dated to 1700 BCE, gives a method to find the area of a circle. The result corresponds to {{sfrac|256|81}} (3.16049...) as an approximate value of [[Pi|{{pi}}]].<ref>[http://www-history.mcs.st-andrews.ac.uk/history/Chronology/30000BC_500BC.html#1700BC Chronology for 30000 BC to 500 BC] {{webarchive|url=https://web.archive.org/web/20080322085509/http://www-history.mcs.st-andrews.ac.uk/history/Chronology/30000BC_500BC.html |date=2008-03-22 }}. History.mcs.st-andrews.ac.uk. Retrieved on 2012-05-03.</ref>

Book 3 of [[Euclid's Elements|Euclid's ''Elements'']] deals with the properties of circles. Euclid's definition of a circle is:
{{quotation|A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.|author=[[Euclid]]|title=[[Euclid's Elements#Contents|Book I]] |source=[[Euclid's Elements|Elements]]<ref>{{OL|7227282M}}</ref>{{rp|4}}}}

In [[Plato]]'s [[Seventh Letter]] there is a detailed definition and explanation of the circle. Plato explains the perfect circle, and how it is different from any drawing, words, definition or explanation. Early [[science]], particularly [[geometry]] and [[astrology and astronomy]], was connected to the divine for most [[History of science in the Middle Ages|medieval scholars]], and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles.<ref>[[Arthur Koestler]], ''[[The Sleepwalkers (Koestler book)|The Sleepwalkers]]: A History of Man's Changing Vision of the Universe'' (1959)</ref><ref>[[Proclus]], [https://books.google.com/books?id=E1HYAAAAMAAJ ''The Six Books of Proclus, the Platonic Successor, on the Theology of Plato''] {{webarchive|url=https://web.archive.org/web/20170123072440/https://books.google.com/books?id=E1HYAAAAMAAJ |date=2017-01-23 }} Tr. Thomas Taylor (1816) Vol. 2, Ch. 2, "Of Plato"</ref>

In 1880 CE, [[Ferdinand von Lindemann]] proved that {{pi}} is [[transcendental number|transcendental]], proving that the millennia-old problem of [[squaring the circle]] cannot be performed with straightedge and compass.<ref>[http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Squaring_the_circle.html Squaring the circle] {{webarchive|url=https://web.archive.org/web/20080624144640/http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Squaring_the_circle.html |date=2008-06-24 }}. History.mcs.st-andrews.ac.uk. Retrieved on 2012-05-03.</ref>

With the advent of [[abstract art]] in the early 20th century, geometric objects became an artistic subject in their own right. [[Wassily Kandinsky]] in particular often used circles as an element of his compositions.<ref>{{Cite web |title=Circles in a Circle |url=https://philamuseum.org/collection/object/51019 |access-date=2023-12-28 |website=Philadelphia Museum of Art |language=en}}</ref><ref>{{Cite web |last=Lesso|first=Rosie|date=2022-06-15 |title=Why Did Wassily Kandinsky Paint Circles? |url=https://www.thecollector.com/why-did-wassily-kandinsky-paint-circles/ |access-date=2023-12-28 |website=TheCollector |language=en}}</ref>

===Symbolism and religious use===
[[Image:God the Geometer.jpg|thumb|right|200px|
The [[compass (drafting)|compass]] in this 13th-century manuscript is a symbol of God's act of [[Creation myth|Creation]]. Notice also the circular shape of the [[Halo (religious iconography)|halo]].]]
From the time of the earliest known civilisations – such as the Assyrians and ancient Egyptians, those in the Indus Valley and along the Yellow River in China, and the Western civilisations of ancient Greece and Rome during classical Antiquity – the circle has been used directly or indirectly in visual art to convey the artist's message and to express certain ideas.
However, differences in worldview (beliefs and culture) had a great impact on artists' perceptions. While some emphasised the circle's perimeter to demonstrate their democratic manifestation, others focused on its centre to symbolise the concept of cosmic unity. In mystical doctrines, the circle mainly symbolises the infinite and cyclical nature of existence, but in religious traditions it represents heavenly bodies and divine spirits.

The circle signifies many sacred and spiritual concepts, including unity, infinity, wholeness, the universe, divinity, balance, stability and perfection, among others. Such concepts have been conveyed in cultures worldwide through the use of symbols, for example, a compass, a halo, the vesica piscis and its derivatives (fish, eye, aureole, mandorla, etc.), the ouroboros, the [[Dharmachakra|Dharma wheel]], a rainbow, mandalas, rose windows and so forth.<ref>{{cite encyclopedia | editor-first=Jean-François | editor-last = Charnier | title = The Circle from East to West | first = Yahya | last = Abdullahi | encyclopedia = The Louvre Abu Dhabi: A World Vision of Art | date = October 29, 2019 | isbn=9782370741004 | publisher=Rizzoli International Publications, Incorporated}}</ref> [[Magic circle]]s are part of some traditions of [[Western esotericism]].