What is Circles: Definition and 308 Discussions

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. R

    Calculation of circles parameters embedded in 2 rotating discs?

    The next situation is presented 2 big circles (blue ones) are rotating in different directions. The left one is rotating clockwise and the right one rotates counter clockwise. Inside the 2 big circles, 2 small circles (pink ones) are embedded...
  2. A

    MHB Two different circles in the plane with nonempty intersection

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  3. N

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  4. F

    Focusing at infinity for a camera and circles of confusion

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  5. S

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  6. caffeinemachine

    MHB Two circles intersecting, a lot of lines.

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  7. R

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  8. S

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  9. D

    MHB Optimizing Triangle Area on a Circle: Finding the Minimum with Tangents

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  10. L

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  11. S

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  12. V

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  13. D

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  14. O

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  15. L

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  16. nukeman

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  17. D

    Finding equation of osculating circles of ellipse

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  18. K

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  19. T

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  20. G

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  21. A

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  22. M

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  23. R

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  24. G

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  25. S

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  26. L

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  27. F

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  28. C

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  29. J

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  30. S

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  31. T

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  32. Evo

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  33. D

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  34. S

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  35. S

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  36. P

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  37. Y

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  38. Y

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  39. D

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  40. S

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  41. R

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  42. T

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  43. J

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  44. J

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  45. S

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  46. V

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  47. P

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  48. J

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  49. F

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  50. R

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