circle (redirected from going round in circles)

circle, closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone. The term circle is also used to refer to the region enclosed by the curve, more properly called a circular region. The radius of a circle is any line segment connecting the center and a point on the curve; the term is also used for the length r of this segment, i.e., the common distance of all points on the curve from the center. Similarly, the circumference of a circle is either the curve itself or its length of arc. A line segment whose two ends lie on the circumference is a chord; a chord through the center is the diameter. A secant is a line of indefinite length intersecting the circle at two points, the segment of it within the circle being a chord. A tangent to a circle is a straight line touching the circle at only one point, the point of contact, or tangency, and is always perpendicular to the radius drawn to this point. A circle is inscribed in a polygon if each side of the polygon is tangent to the circle; a circle is circumscribed about a polygon if all the vertices of the polygon lie on the circumference. The length of the circumference C of a circle is equal to π (see pi) times twice the radius distance r, or C=2πr. The area A bounded by a circle is given by A=πr². Greek geometry left many unsolved problems about circles, including the problem of squaring the circle, i.e., constructing a square with an area equal to that of a given circle, using only a straight edge and compass; it was finally proved impossible in the late 19th cent. (see geometric problems of antiquity). In modern mathematics the circle is the basis for such theories as inversive geometry and certain non-Euclidean geometries. The circle figures significantly in many cultures. In religion and art it frequently symbolizes heaven, eternity, or the universe.

---

circle

Geometrical curve, one of the conic sections, consisting of the set of all points the same distance (the radius) from a given point (the centre). A line connecting any two points on a circle is called a chord, and a chord passing through the centre is called a diameter. The distance around a circle (the circumference) equals the length of a diameter multiplied by π (see pi). The area of a circle is the square of the radius multiplied by π. An arc consists of any part of a circle encompassed by an angle with its vertex at the centre (central angle). Its length is in the same proportion to the circumference as the central angle is to a full revolution.