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A circle is the curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre. The radius is the distance between any point on the circle and the center. Except when otherwise specified, this article is about circles in Euclidean geometry, specifically the Euclidean plane.

A circle, in particular, is a closed curve that splits the plane into two regions: inner and exterior. In everyday use, the term “circle” may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a disc.

A circle may also be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations.

The term circle comes from the Greek o/ (kirkos/kuklos), which is a metathesis of the Homeric Greek (krikos), which means “hoop” or “ring.” The words circus and circuit have a tight relationship in their origins.

Since before the beginning of recorded history, the circle has been known. Natural circles such as the Moon, Sun, and a short plant stalk blowing in the wind over sand, which produces a circle shape in the sand, would have been seen. The circle is the foundation for the wheel, which, together with related developments like gears, allows for much of contemporary equipment. The study of the circle has influenced the development of geometry, astronomy, and calculus in mathematics.

For most medieval scholars, early science, particularly geometry, astrology, and astronomy, was linked to the divine, and many felt that circles contained something fundamentally “divine” or “perfect.”

300 BCE ” The features of circles are discussed in Book 3 of Euclid’s Elements.
A full description and explanation of the circle may be found in Plato’s Seventh Letter. Plato describes how the perfect circle differs from any depiction, words, definition, or explanation.
1880 CE ” Lindemann establishes that is transcendental, thereby resolving the millennia-old problem of circle squaring.

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