What is Circle: Definition and 1000 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. B

    Map complex line to complex circle

    Homework Statement Find the Linear Fractional Transformation that maps the line Re\left(z\right) = \frac{1}{2} to the circle |w-4i| = 4. Homework Equations For a transform L\left(z\right), T\left(z\right)=\frac{z-z_{1}}{z-z_{3}}\frac{z_{2}-z_{3}}{z_{2}-z_{1}}...
  2. Femme_physics

    Units for moment of inertia of a circle

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  3. G

    Equation of circle with arc length

    Homework Statement Equation of a circle is: x^2+(y+a)^2=R^2 x intercepts are +/-\sqrt{3} and arclength above x-axis is \frac{4\pi}{3} Find a and R.
  4. G

    Circumscribed circle - inscribed circle area formula

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  5. N

    Finding the circle of least confusion for a multi-element optical system

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  6. S

    Motion in a Circle: Proving the Angular Frequency Equation | Homework Help

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  7. M

    Electric potential of the arc of a circle

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  8. G

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  9. Y

    Double Integral bounded by Circle?

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  10. V

    Can you prove the area of a circle by calculus?

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  11. B

    Finding Radius of 3 Congruent Tangential Circles in Larger Circle

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  12. M

    Electric field of a semi circle

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  13. F

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  14. T

    Hough Transform for circle detectoin - getting information out

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  15. B

    Magnetic field of a goffered circle

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  16. MacLaddy

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  17. P

    Solving a Circle Problem: Finding Radius and Center | Math Forum Help

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  18. D

    Airplane flying in a horizontal circle

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  19. D

    Shadow of vertical circle on wall?

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  20. P

    Finding Equation of Smallest Circle Containing 3 Circles

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  21. M

    Area of a Segment of a Circle, when only the radius is known.

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  22. N

    Symbol Meaning: "+" Enclosed in a Circle

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  23. M

    How do you find the center of a circle using only a compass?

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  24. M

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  25. T

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  26. M

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  27. J

    Calculating Tension in a Vertical Circle

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  28. L

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  29. J

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  30. Demon117

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  31. S

    Why is the Unit Circle Important in Teaching Trigonometry?

    Ok- I am teaching trigonometry to low level students right now and I am trying to figure out why they need to know the unit circle. Are there some interesting things they can learn about by using a unit circle? So far, we pretended it was a magic-barbie-sized-half-underground-ferris-wheel...
  32. C

    Finding a second point on a circle

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  33. X

    Center of mass of a semi circle using polar coordinates

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  34. M

    Prove that a great circle is a geodesic

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  35. E

    Value of 0 on X-Axis for Circle Problem (r=2)

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  36. J

    Sound wave interfernce on a large circle

    Homework Statement Given two isotropic point sources of sound \[s_{1}\] and \[s_{2}\]. The sources emit waves in phase at wavelength 0.50m; they are separated by D = 1.75m. If we move a sound detector along a large circle centered at the midpoint between the sources, at how many points do...
  37. I

    Average Velocity of a particle moving in a circle over a given interval

    Homework Statement Homework Equations d = 2.5 c = pi*d = 7.854 velocity/s ?= c * 2 = 15.7079The Attempt at a Solution Since PR is 1/4 of the circle and the particle moves around the circle 2 times per second, I thought the average velocity would be 1/8th of the velocity that it's traveling...
  38. T

    Equation of an Oscillating Circle

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  39. P

    Smooth Mapping Between Unit Circle and Curve in R^2?

    Hi, I have been told that in R^2 the unit circle {(x,y) | x^2 + y^2 = 1} is smoothly mappable to the curve {(x,y) | x^4 + y^2 = 1}. Can someone please tell me what this smooth map is between them? I can only think of using the map (x,y) --> (sqrt(x), y) if x is non-negative and (sqrt(-x), y)...
  40. icystrike

    Can we ever construct a perfect circle? (Curiousity)

    Homework Statement As stated abv. Since \pi can only be established by infinite sum and according to zeno's paradox we can never break a finite length into infinite pieces (loosely speaking)
  41. S

    Frictional work inside a circle

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  42. Q

    Block sliding down incline shaped as circle

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  43. Q

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  44. X

    Find the radius of the middle circle

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  45. T

    Electric Point Forces in a Circle

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  46. U

    What are the constraint forces on a circle with a particle?

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  47. P

    Radius of A Circle inside a Sphere

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  48. A

    Find Length of Segment AB in Circle Co-ordinate Question

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  49. W

    Proof of Monge's circle theorem

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  50. N

    Geometry problem. Circle and parallel lines to a circle.

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