A circle is every plane point at one fixed distance from a center
A circle is every point in a plane lying at one fixed distance from a centre, an idea people knew before recorded history. The full moon and a sliced fruit show it in nature. The shape underlies the wheel and the gear, and its study helped spark geometry, astronomy and calculus.
The fixed distance is the radius, and a segment through the centre joining two points on the curve is the diameter, twice the radius and the longest chord the circle has. Any chord splits the figure into two segments, and a straight line meeting the curve at exactly one point is a tangent. Strictly, the circle is only the boundary line; the region inside is a disc, though everyday speech blurs the two. An annulus is the ring between two circles sharing a centre, and a lens is where two overlapping discs meet.
The name comes from Greek kirkos or kuklos, a rearrangement of Homeric krikos, a hoop or ring, and circus and circuit share the root. Prehistoric builders raised stone and timber circles, and disc-shaped objects include the Nebra sky disc and Chinese jade bi discs. Egypt's Rhind papyrus of about 1700 BCE gave a rule for the area that amounts to taking pi as 256/81, roughly 3.16.
Book 3 of Euclid's Elements is devoted to circles, and Archimedes showed that the enclosed area equals a triangle whose base is the circumference and whose height is the radius, which works out to pi times the radius squared. Pi itself, the ratio of circumference to diameter, is irrational at about 3.14159. In 1880 Ferdinand von Lindemann proved pi transcendental, settling that squaring the circle with straightedge and compass is impossible.
Many medieval scholars saw something divine in the shape, and Plato's Seventh Letter distinguishes the perfect circle from any drawing of one. Halos, mandalas, the ouroboros, the Dharma wheel and rose windows carry that symbolism, and Wassily Kandinsky made circles a recurring element of his abstract paintings.
Source: Circle
