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Columbia Encyclopedia entry: circle
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 Ar2. 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.
Wikipedia search results for: Circle
From Wikipedia, the free encyclopedia
A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the centre. The common distance of the points of a circle from its centre is called its radius. Circles are simple closed curves which divide the plane into two regions, an interior and an 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. However, in strict technical usage, "circle" refers to the perimeter while the interior of the circle is called a disk. The...more »
Columbia Encyclopedia search results: circle
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  • vertical circle

    Vertical circle, in astronomy, the great circle on the celestial sphere that passes from the observer's zenith through a given celestial body. In the altazimuth coordinate system the altitude ...

  • hour circle

    Hour circle, in astronomy, a secondary axis in the equatorial coordinate system. The hour circle of a celestial body is the great circle on the celestial sphere that passes through both the bo...

  • Antarctic Circle

    Antarctic Circle, imaginary circle on the surface of the earth at 661/2°S lat., i.e., 231/2° north of the South Pole. It marks the southernmost point at which the sun can be seen at the winter...

  • Arctic Circle

    Arctic Circle, imaginary circle on the surface of the earth at 661/2°N latitude, i.e., 231/2° south of the North Pole. It marks the northernmost point at which the sun can be seen at the winte...

  • diurnal circle

    Diurnal circle, apparent path followed by a star due to the earth's rotation on its axis. The stars appear to move on the celestial sphere in concentric circular paths centered at the celestia...

  • Knights of the Golden Circle

    Knights of the Golden Circle, secret order of Southern sympathizers in the North during the Civil War. Its members were known as Copperheads. Dr. George W. L. Bickley, a Virginian who had move...

  • chord, in geometry

    Chord, in geometry, straight line segment both end points of which lie on the circumference of a circle or other curve; it is a segment of a secant. A chord passing through the center of a cir...

  • celestial meridian

    Celestial meridian, vertical circle passing through the north celestial pole and an observer's zenith. It is an axis in the altazimuth coordinate system.

  • sphere

    Sphere, in geometry, the three-dimensional analogue of a circle. The term is applied to the spherical surface, every point of which is the same distance (the radius) from a certain fixed point...

  • pi

    Pi, in mathematics, the ratio of the circumference of a circle to its diameter. The symbol for pi is π. The ratio is the same for all circles and is approximately 3.1416. It is of great import...

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