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. murshid_islam

    A paragraph on circles and cylinders

    Homework Statement My niece has to write a paragraph on circles and cylinders. This is the exact question: "How are circles and cylinders related? Write a paragraph to explain what you learned about circles and cylinders." Homework Equations The Attempt at a Solution I am...
  2. B

    Lines and circles having rational operations

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  3. J

    Does the Higgs field explain anything or go in circles?

    This might be a bit of a naive question but I am only just starting to learn the very basics of this stuff. I'm hearing about being able to account for the mass of, well, massive particles, by saying that in our cool universe, there is this field pervading all of space that certain...
  4. M

    Circles and Triangles: Solving for X with Geometry

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  5. A

    Capacitance of concentric circles

    Homework Statement i have a graph or r against V and to make it a straight plot i then plotted ln(r) against V, Homework Equations The Attempt at a Solution the problem is i dnt know how to find the capacitance from the graph. it definitely isn't the gradient or the point of...
  6. J

    Geometry of circles and polygons.

    I have found an equation which deals with regular polygons touching circles tangentially with each of their sides. P=Dn\tan(\frac{180}{n}) where P is the perimeter of the polygon. D is the diameter of the circle. n is the number of sides on the polygon. i originaly thought it would be...
  7. B

    Finding Connected Components of a Set of Circles

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  8. R

    Solve Vertical Circles: Force, Velocity, Acceleration, Mass, Reaction

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  9. andrewkirk

    Existence of square circles

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  10. B

    Finding Radius of 3 Congruent Tangential Circles in Larger Circle

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  11. D

    Triangle and two circles theorem

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  12. F

    Naming Concentric Circles: What's the Best Approach?

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  13. G

    Drawing Mhor's Circles: Orientation Angles on One Axes

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  14. D

    Geometry Homework: Sum of Circles and Triangles in Figure

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  15. D

    Method to parameterize circles in R3 laying in a plane

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  16. binbagsss

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  17. binbagsss

    Vertical Circles: mg vs Resultant Force

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  18. X

    What is the solution to Problem 88?

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  19. nicksauce

    No evidence for circles in the CMB; contrary to claims by Penrose and Gurzadyan

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  20. R

    5 circles inside 1 large circle

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  21. M

    Three mutually tangent circles

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  22. T

    Geometry with circles, triangles and squares

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  23. DaveC426913

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  24. C

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  25. S

    Finding normal vector on circles

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  26. H

    If I spin in circles, am I accelerating?

    Homework Statement If I spin in circles, in place, am I accelerating? Homework Equations If acceleration is a change in velocity, which is a vector quantity, does only a change in direction count as acceleration? The Attempt at a Solution
  27. M

    Solving Equations of Circles: Finding Center and Radius | Homework Help

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  28. M

    Find Area of Circle Segments: Chord Length 4cm, Radius 3.3cm

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  29. C

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  30. Z

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  31. wolram

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  32. F

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  33. P

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    The straight line parallel to each other is parallel. Concentric circles are parallel,too. As shown in figure, There is a big circle,Oa，Another one is small, Oc.They are concentric circles. AB is a straight line. AB and Oa are intersections D, AB and Oc are intersections C. EF is a straight...
  34. A

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    Homework Statement I don't know why but my brain is having one of its moments and I can't work through this. Not even on paper anymore. Okay so I have 3 intersecting circles. Like a Venn Diagram. How do I find the area of all three minus the instersecting parts. I know how to do two...
  35. R

    How many circles can be placed inside another circle?

    We have a circle of certain radius.How many circles of smaller radius(we are provided with the ratio of radius) can be placed within the larger circle? Help me to determine the least number of the smaller circles that can be filled?? I am trying to generate a generalized solution, and looking...
  36. B

    A. 2 circles that have the same center have their radiuses

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  37. M

    Euclidean geometry proof concerning circles

    i really need help with this proof. suppose two circles intersect at points P and Q. Prove that the line containing the centers of the circles is perpendicular to line segment PQ
  38. X

    Parametric equations and finding tangents from circles

    Homework Statement A circle has the parametric equations: x=1+2cos\theta y=3+2sin\theta dy/dx= -1/tan\theta Find the tangent equation at the point with parameter \theta Homework Equations y-y1=m(x-x1) The Attempt at a Solution I've tried putting dy/dx in as the gradient and...
  39. S

    Mobius Maps: Parallel and Perpendicular Lines, Disjoint Circles

    Homework Statement Suppose T is a Mobius map take Real -> Real and infinite infinitely to 0 a) What's the image of the family of lines parallel to Real? b) What's the image of the family of lines perpendicular to Real? c) Show the Mobius map take D = {z :|z|<1} onto itself iff Tz =...
  40. E

    Total area of circles infinitely inscribed in isosceles triangle

    1. The base of the yellow triangle has length 8 inches; its height is 10 inches. Each of the circles is tangent to each edge and each other circle that it touches. There are infinitely many circles. The radius of the largest of them is __________ and the total area of all the circles is...
  41. C

    Potential Difference between Concentric Circles

    Homework Statement Three concentric circles of radii 1.5m, 2.5m, and 4m are filled with a gas that breaks down in electric fields greater than 1.6 x 10^7 volt/meters. What is the highest potential difference that can be maintained between the innermost circle and the outermost circle. (Hint...
  42. K

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    (keep in mind, its circle math.. :/) Write the equation (x+9)2+(y-5)2=12 in general form.
  43. T

    Ferris wheel problem - vertical circles and centripetal acceleration

    Homework Statement Given a Ferris wheel that rotates 5 times each minute and has a diameter of 19 m, with the acceleration of gravity as 9.8 m/s^2, what is the centripetal acceleration of a rider? Answer in units of m/s^2. (There's a diagram that shows a ferris wheel with radius 9.5 m spinning...
  44. S

    Relation between two circles sets

    Good day all I have two lists of data A & B. The max & min for A is different from B. I want to draw circles, by specific software, representing each one of the two list of data. The max of both A&B should have the large circle and the min of both of them should have the smallest...
  45. P

    What is the area of a slice of a disk with angle theta?

    Homework Statement Draw a circle of radius R with the center at the origin. Get the function that represents the top half of the circle. Let d be between 0 and R. State the definite integral that gives this area. Let P be the point were x=d intersects the curve. Let theta be the angle...
  46. L

    Solve "Circles and Sectors: 3θ=2(π−sinθ)

    Homework Statement The diagram shows a semicircle APB on AB as diameter. The midpoint of AB is O. The point P on the semicircle is such that the area of the sector POB is equal to twice the area of the shade segment. Given that angle POB is \theta radians, show that 3\theta =...
  47. M

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  48. C

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  49. A

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  50. Q

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    Hi everyone, I'm new and this is my first post here. I'm 37 yo, I'm italian so forgive my english. My question is about the law of relativity that says that an object moving is shorter, when I observe it. The shortening is the famous sqrt(1-square(v/c)). Ok, but now imagine this: I have 2...
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