Circles Definition and 310 Threads

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted.
Specifically, a circle is a simple closed curve that divides 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; 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.

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  1. S

    A pair of two-dimensional supercompressed circles

    Imagine a two dimensional universe, a plane. We take two perfect circles on this plane; they are uncompressable, being elementary particles or some such thing (whatever they are, the important thing is that they cannot be compressed). We take these two circles and set them on a collision...
  2. C

    Who Really Knows the Truth About Crop Circles?

    Does anyone know it, or have good guesses? I'm not particularly interested in the subject per se, but I find it strange that the skeptical explanation (that it is a hoax) is as phoney as the claims that ET's do it. As far as I can tell no one seems to know what is going on, and yet everyone...
  3. J

    Discovering the Radius of a Planet with a Man, a Parachute, and a Satellite

    a man jumps out of a plane w/ a parachute at 1000m above a spherical planet (point A). He sees a satellite rise at the eatern horizon. Standing 2 m above surface of the planet (equator)(point B), the satellite re-appears 1.5 minutes after he saw it at 1000 m above sea level. From this point, the...
  4. Ivan Seeking

    Are Crop Circles a Natural Phenomenon or Elaborate Hoaxes?

    Crop Circles We all know that many to most circles are hoaxed. It is my understanding that beyond any doubt, this phenomenon predates modern reports by at least decades. Some years ago I watched a Nova or similar that discussed this subject purely in meteorological terms. It was shown that...
  5. Ivan Seeking

    Mysterious Circles Appear In Ohio Soybean Field

    http://www.newsnet5.com/news/2524748/detail.html
  6. Ivan Seeking

    Is This Mysterious Circle in a Vacant Lot Evidence of Paranormal Activity?

    I'm thinking Hall of Fame? http://www.paratexas.com/Vacantlotcircles.htm
  7. C

    Why does a circles angles equal up to 2pi? Wouldn't it be 1?

    Why does a circles angles equal up to 2pi? Wouldn't it be 1pi? Please help. My geometry teacher (last year - and now he's gone) drew a circle for me and defined all the points in terms of pi (is there an ASCII character for pi, by-the-way, on the keyboard?). Where the 90 degree point would be...
  8. Ivan Seeking

    MICHIGAN CROP CIRCLES: Farmer raises a mystery

    "HOWELL TOWNSHIP -- They've come late at night, holding flashlights, their beams cutting the dark in the middle of 1,000 acres of wheat fields. They've come in the afternoon under blue sky to lift their arms and pray." http://www.freep.com/news/mich/signs5_20030805.htm
  9. Ivan Seeking

    Dodge County Man Sees Crop Circles Form

    ""The holes appeared and there it was but you couldn't see what made it, but I seen it right when it happened," farm owner Arthur Rantala said." http://www.themilwaukeechannel.com/news/2342726/detail.html
  10. S

    What is the radius of a circle represented by the equation |z - z1|=k|z - z2|?

    In general, |z - zo|=r, where z_o is a fixed point and r is a positive number, represents a circle centered at z_o and with radius r. |z - z1|=k|z - z2|, where z_1 and z_2 are fixed points, also apparently represents a circle, except maybe in the case where k=1. Then we have a line, or a...
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