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. DaveC426913

    Ice circles - and now their jungle cousins

    The article below is tainted with the silliness of woo, but the phenomenon is quite natural - and way cool. It's a tropical verson of an ice circle. I found ice circles hard to believe at first, but I watched a small-scale simulation on an artificial river with just the right flow rate and...
  2. NickTesla

    B Circles -- transform degrees in minute

    A minha pergunta é na divisão 10800/1110 My question is in the division 10800/1110 ?
  3. wolfieon2

    I Fitting circles inside other circles

    I'm working on the following fun problem. I have a circle of a given radius, R0. (Green circle in the image). I want to be able to supply a radius of the first circle that is to fit into this large circle. Let's say R1 is 0.75 * R0. Following this I find the best position of R2 (to maximise...
  4. M

    I Proving Vector Space of Circles is Not Axiomatic

    Hi How can i prove that the set if circles does not form a vector space AXIOMATICALLY . ( i am not considering a circle lives in xy-plane ( subset ) as a subspace of xy-plane
  5. D

    I Family of Circles through Two Points: Exists Any Circle Beyond?

    Supposed 2 circles ##C_1 : x^2 + y^2 + {f_1}x + {g_1}y + h_1 = 0## and ##C_2 : x^2 + y^2 + {f_2}x + {g_2}y + h_2 = 0## through two points. A family of circles can be constructed as ##x^2 + y^2 + {f_1}x + {g_1}y + h_1 + k(x^2 + y^2 + {f_2}x + {g_2}y + h_2) = 0##. By altering the k, an...
  6. H

    I Show the envelope of circles around a circle is a cardioid

    Is there a shorter way to get the answer, the polar equation of a cardioid, directly? My solution involves some tedious work and doesn't give the polar equation directly: The equation of the member curves (circles) is ##f(x, y...
  7. P

    I Great Circles and....Coriolis?

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  8. twistor

    A What's the truth behind CCC's concentric circles prediction for the CMB?

    http://arxiv.org/pdf/1510.06537v1.pdf I found this semirecent paper about CCC's concentric circles prediction for the CMB. Is this just another piece of the debate, or is its significance enough to increase the plausibility of Penrose's model? Thank you in advance for your answers, and please...
  9. E

    Show that the equipotential lines are circles

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  10. O

    Greeks, Circles, Small Straight lines and Calculus

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  11. 24forChromium

    Concentric circles and a certain curve's function

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  12. C

    Why are circles infinitely smooth if they have degrees?

    Because a triangle comes out to 180 degrees, and yet it can only have three sides. A circle has 360 degrees, but its number of "sides" are uncountable. Can someone explain this?
  13. C

    B Do curves, circles and spheres really exist?

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  14. T

    Math & David Hume: Tangents & Circles

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  15. gracy

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  16. T

    Area of A Segmented Circle Cut By A Chord

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  17. S

    About the formation of crops circles.

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  18. W

    MHB Circles and parallel Lines

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  19. PhysixChick

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  20. AdityaDev

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  21. A

    Why Cherenkov light leave rings instead of full circles?

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  22. ArcanaNoir

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  23. Dethrone

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  24. S

    MHB Finding the area of a region which is inside two circles (II)

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  25. S

    Circles vs an infinitely n-sided polygon.

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  26. L

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  27. C

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  28. C

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  29. srfriggen

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  30. L

    Drawing circles with different distance functions

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  31. A

    Change of speed of a car turning in circles

    My textbook says : "The friction force on a car turning a corner does no work." I agree somewhat. However, if there is no work, there is no change of speed, aka no change of kinetic energy. How can a car in a real-life stop if it is doing perfect circles with forces pointing towards the...
  32. T

    Surveying Problem Relating To Circles & Lines

    Hello all I am hoping someone could help shed some light on a surveying problem I am having. The problem is this:- • A circle is centered at point B with Known co-ordinates (X2,Y2) • The circle has a radius which is known (R). • Point A lays outside of the circle with known...
  33. Saitama

    Where Do Chords of Circles Through A(3,7) and B(6,5) Intersect?

    Homework Statement Consider a family of circles passing through two fixed points A(3,7) and B(6,5). Show that the chords in which the circle ##x^2+y^2-4x-6y-3=0## cuts the members of the family are concurrent at a point. Find the coordinates of this point. Homework Equations The...
  34. Q

    Related Rates: Circles and Changing Circumference

    Homework Statement The circumference of a circle is increasing by 4 inches per second. What is the rate of change of the diameter with respect to time if the radius is 2 inches? Homework Equations C = 2∏r = ∏d. The Attempt at a Solution dC/dt = 4 = ∏dd/dt. dd/dt = 4/∏ Is this it? It...
  35. D

    Find Direct Common Tangent of 2 Circles without Complexity

    Homework Statement Is there any direct formula for calculating the direct common tangent of two circles without having to go all the trouble of using y-y1=m(x1-x2) to derive it for two separate tangents t1 and t2. If there is could anyone explain to me how it is derived? Homework...
  36. E

    How to determine the area of intersecting circles?

    I've been wondering how to calculate the area of intersection of two overlapping circles in terms of their radii. There's two cases I'm interested in: The easier case: Suppose there are two circles of radius R and r (R > r). The center of the larger circle is at the origin, and the center...
  37. nomadreid

    Circles in Minkowski space: unknown notation

    I am reading an article about Minkowski space (as a vector space, which is why I am putting my question in this rubric) which is poorly translated from the Russian, and have come across several notational curiosities, most of which I have been able to figure out. However, there is one that I do...
  38. nomadreid

    What Are 'M-M' and 'N-N' Circles in Russian Physics?

    In a paper translated from the Russian, the author refers to "m-m" and "n-n" circles (including Minkowski circles) and orbits. When I first came across "n-n", I thought it was "non-negative" until I came across the "m-m". In one of the references I went to a diagram referred to, and saw an arc...
  39. K

    Circle inside of circles

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  40. A

    Electric Field at a point inside 2 semi circles

    Homework Statement I have this picture http://i.imgur.com/ek2N1dL.png I have to find the electric field at the point inside 2 semi circles. The left semi circle has a charge of -3 micro Coulombs and the right one has +3 micro coulombs. The radius between the point and the circle is 0.2...
  41. A

    Is there a formula for these circles?

    I have six 2x2 complex matrices from the group SL(2,C). Each line is a matrix: first row, second row. \left( \begin{array}{cc} \left\{\frac{1}{\sqrt{1-k^2}},\frac{k}{\sqrt{1-k^2}}\right\} & \left\{\frac{k}{\sqrt{1-k^2}},\frac{1}{\sqrt{1-k^2}}\right\} \\ \left\{\frac{1}{\sqrt{1-k^2}},\frac{i...
  42. z.js

    Finding Common Area of Two Circles

    Homework Statement Two circles with radii 12 cm and 10 cm respectively have their centers 14 cm apart, find the area common to both circles. (note : This is in radians.) Homework Equations Area of a sector = 0.5r2θ - 0.5r2sin θ The Attempt at a Solution None. :confused:
  43. U

    Finding the Length of QP in a Circle-Triangle Problem

    Homework Statement Q)A circle C whose radius is 1 unit touches the x-axis at 'A'.The centre Q lies in 1st quadrant.The tangent(other than x-axis) from origin touches the circle at T and a point P lies on it such that OAP is a right angled triangle with right angle at 'A' and its perimeter is 8...
  44. S

    Area of intersection between two circles

    Hi, I would very much like someone to help me solve the area of intersection between to intersecting circles (one with the radius r, and one with the radius 1). Tangents at the intersecting point form a 120 degree outer angle. 1. Homework Statement , 2 Relevent equations Here is a...
  45. marcus

    Meissner sees Penrose-type circles in Planck CMB map

    Meissner et al just posted a paper where they see those circles in the high res. microwave sky of Planck. Who knows if this is real, or what it would mean if it were confirmed? Meissner has a followup paper in preparation with Penrose and others. Either way I think it's pretty interesting...
  46. S

    What is the area between two circles with a diameter of 10m?

    Homework Statement Homework Equations The area of a circle: A_c = \pi r^{2} The Attempt at a Solution I know that the diameter of the oval shape is 10m since the problem says that it touches the circumference of the center of each circle. I am not sure how to approach the problem...
  47. O

    Solve Circles & Chords: Find Equations to Satisfy Conditions

    With this question, I have worked out the correct answers (see the section bordered by BBB), but my original approach was to go by the 1st attempt (bordered by AAA). In the 1st attempt, the h/ k equation results in a single centre, rather than the 2 required to form the 2 separate circle...
  48. M

    The region within circles r=cosθ and r=sinθ

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  49. C

    Geometry Problem involving packing Hexagons into Circles

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  50. E

    Using radians to discover the lengths of geometric shapes (circles)

    Homework Statement refer to question image Homework Equations refer to question image againThe Attempt at a Solution refer to working out image This is my brothers maths homework. He normally doesn't use online methods to request help and this is his first time.
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