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. F

    How accurate is Mohr's circle?

    I'm getting approximations within 5% of the actual values. Does that sound about right?
  2. J

    Complex Numbers Circle Equation

    Homework Statement Write the equation of a circle in complex number notation: The circle through 1, i, and 0. Homework Equations The Attempt at a Solution I know the equation for a circle with complex numbers is of the form |z-a| = r where a is the center point and r is the...
  3. U

    How to find the radius of a circle by knowing two points and its arc length

    How can I find the radius of a circle by knowing two points and its arc length? Do I have to use a numerical method to solve for a trigonometric equation or is there any algebraic or geometric method?
  4. DryRun

    Area of region between circle and curve

    Homework Statement http://s2.ipicture.ru/uploads/20120107/67Ag24Qb.jpg The attempt at a solution So, i plotted the graphs of the circle and the curve: http://s2.ipicture.ru/uploads/20120107/x32KTV6y.jpg The shaded area is what i need to find. My plan to solve this problem is to find...
  5. R

    What shape results from integrating the area of a circle?

    Hi there, I am trying to understand calculus as concerns circles and I can clearly see that the integral of a circumference is an area: \int2∏r = ∏r^{2} but what do I get if I integrate the area, I get ∏r^{3}/3 I am confused as to what this shape would be, I kind of was expecting a...
  6. R

    Simple Mohr's Circle Question - Axis scales?

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  7. W

    Constant Rate of Change in Area of Circle with Changing Radius?

    Homework Statement A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. Does the area also increase at a constant rate? Homework Equations A = ∏r2 The Attempt at a Solution dA/dt = 2∏r(dr/dt) dA/dt = 2∏r(3ft/s) What now?
  8. A

    Radius of a circle whose area is of 2 other cirlces

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  9. T

    Forces in a circle from similar charges?

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  10. L

    Can a Magnetic Dipole Form a Circle?

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  11. P

    THE CIRCLE HAS RETURNED(Help me please)

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  12. T

    Comparing Volume of Oval vs Circle: Joe's First Post

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  13. R

    Area of a circle and pi and generally area

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  14. R

    Parametric equation for 3D circle that's off-axis

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  15. Z

    Work Done By A Force of Constant Magnitude in Moving an Object in a Circle

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  16. A

    As a gyroscope precesses, its center off mass moves in a circle

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  17. B

    Fun with Dynamic Spirograph - Circle Rolling around Rolling Circle

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  18. L

    Effective Resistance if bent in the form a circle

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  19. P

    Ball Rolls off of a circle :O PROBLEM

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  20. N

    A slingshot rotates counterclockwise on the circle x^2+y^2=9

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  21. S

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  22. M

    Equation of a circle / polar coordinates

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  23. B

    Proving Angle WTU is Twice as Large as WOX with Circle Theorem

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  24. X

    Elastic Problem. Aluminum Wire in Horizontal Circle

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  25. O

    Volume of a substance (in a circle)

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  26. T

    Parameterizing A Circle Projected onto a Plane

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  27. S

    Inequality with Circle and Triangle in Euclidean Geometry

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  28. L

    Using Green's Theorem to Solve a Circle Line Integral

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  29. S

    Kinetic Energy of a mass moving in horizontal circle

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  30. S

    Understanding the Möbius Bundle on a Circle

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  31. X

    Lagrangian Problem. Two masses on a massless circle

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  32. phinds

    How does the twin paradox work in a circular orbit?

    There have been a couple of posts over the last few months that posit a relativistic-speed path in a circle around the Earth and I want to make sure I correctly understand the ramifications. It's the twin paradox in a circle. SO ... here's a scenario that I think will solidify it for me: This...
  33. T

    A pig hanging from a string going in a circle.

    Homework Statement This is me paraphrasing. It's about uniform circular motion. The question involves a pig on a string dangling below a motor. It rotates in a circle below the horizontal. Resolve the tension vector into components. The vertical component of tension is equal to the...
  34. J

    Proving a quadrilateral is cyclic and finding the radius of the circle

    Homework Statement The Attempt at a Solution So my first thought is that the only way to solve this problem is to apply a characterization of a cyclic quadrilateral. We know that the perpendicular bisectors of a cyclic quadrilateral are concurrent. So here's my thoughts: Construct...
  35. G

    Every circle has form |z-a|=k|z-b|

    We can express any circle in the complex plane as |z-a|=k|z-b| where a and b are distinct complex numbers, k > 0 and k \not= 1. Is there an elegant way of showing this fundamental property of the complex plane to be true?
  36. M

    3D Mohr's circle conceptual question

    This is more of a general conceptual question than a specific homework problem. I know how to do these problems, but I'm not understanding part of them. So, with a given stress element, I first look at one specific face, and plot a two-dimensional Mohr's circle. Then, I find the center...
  37. B

    Need math help Tangent to circle question

    The question is: A circle touches the y-axis at the origin and goes through the point A(8, 0). The point C is on the circumference. Find the greatest possible area of ∆OAC I graphed the above situation, and used the equation A=(1/2)bcsinA, but i couldn't muster up an answer. Your...
  38. AGNuke

    Circle and Chords intersected by x-axis

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  39. N

    Find Point on Rect Inside Circle Given Angle

    Alright, this is a bit of a confusing one for me. The problem: The ultimate objective is to get the coordinates of the points on the edge of the rectangle (labeled: (?,?) ), given the angle, and the height and width of the rectangle. The more I think about this problem, however, the more I...
  40. X

    Lagrangian of a Pendulum on a rotating circle

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  41. D

    Is This Physics Calculation Correct for a Decelerating Rotating Ball?

    Homework Statement Can someone check if this is right? The time seems okay, but the work I feel is wrong A ball with moment of inertia 0.1kg · m2 is rotating on a table, but friction is slowing it down with constant angular acceleration. The ball is originally spinning at 2π radians per...
  42. P

    Rotational Motion Tension at the bottom of the circle

    Homework Statement 9. A 0.61 kg mass attached to the end of a 0.50 m cord rotates in a vertical circle. The angular speed of the mass at the bottom of the circle is 2π rad/s. The tension in the string at this point is: a. 18 N b. 21 N c. 12 N *d. 54 N Homework Equations W=mg F=ma...
  43. B

    Euclidian geometry: Construct circle trough point on angle bisector where

    Homework Statement This is part from a larger construction, but I realized if i can construct this, i can do the larger construction. All ofcourse with ruler and compass. I have been given an angle with its bisector and a point on that bisector. I have to construct a circle trough that point...
  44. S

    Uniform circle motion question

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  45. T

    Identifying equivalence classes with the unit circle

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  46. T

    Move tricycle in circle during x sec at speed s

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  47. O

    Triangle tangent to circle problem using derivatives

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  48. T

    Kinetic and potetnial energy in a circle?

    Homework Statement The drawing below shows a person who, starting from rest at the top of a cliff, swings down at the end of a rope, releases it, and falls into the water below. There are two paths by which the person can enter the water. Suppose he enters the water at a speed of 10.0 m/s via...
  49. M

    Do intersecting circles always have equal angles at the circumference?

    I was wondering if the common chord of two intersecting circles subtends an equal angle in both circles at the circumference (in no special cases i.e different radii circles etc) If not, are there any special case(s) where this would work, making these two triangles similar or ABDC is a...
  50. C

    Why the circle can't be homeomorphic to a real interval

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