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. A

    Forces acting on a half circle by a standstill wire

    Hello I have a problem where a wire is pulled around a half circle (disc) and then both ends pulled. The force in both ends are equal (F1 + F2). The disc must in total put up a force (F3) equal to F1 + F2 to not be pulled along by the wire. My question is how does the force of the...
  2. MarkFL

    MHB Find Where Two Tangent Lines Intersect on a Circle | Math Help

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  3. Arkavo

    Central Force with application at circle

    Homework Statement An object of mass 'm' if revolving in a circular path of radius 'R', this is analogous to a gravitational motion except that the force is applied from a point on the circle itself, it is required to find the force law Homework Equations from the point of application...
  4. karush

    MHB How is the IBV3 Vector Applied in a Circle?

    (a) if $r=6$ and $\displaystyle \pmatrix { 6 \\ 0 } $ then $A$ is $6$ from $0,0$ on the $x$ axis and if $\displaystyle \pmatrix { -6 \\ 0 }$ then $B$ is $-6$ from $0,0$ on the $x$ axis and if $\displaystyle \pmatrix { 5 \\ \sqrt{11} }$ implies $\sqrt{5^2 + 11}=6 = OC$ (b) I presume...
  5. Chris L T521

    MHB Involute of a Circle and Grazing Area

    Thanks again to those who participated in last week's POTW! Here's this week's problem! ----- Background Info: A string is wound around a circle and then unwound while being held taut. The curve traced by the point $P$ at the end of the string is called the involute of the circle. If the...
  6. M

    Determining whether the unit circle group is a cyclic group

    1. Homework Statement Let S be the set of complex numbers z such that |z|=1. Is S a cyclic group? 3. The Attempt at a Solution I think this group isn't cyclic but I don't know how to prove it. My only idea is: If G is a cyclic group, then there is an element x in G such that...
  7. M

    MATLAB Geographical points + great circle = ellipse? (Matlab)

    I'm doing this in Matlab but it's not restricted to any particular software. I have a bunch of geographical points (x,y coordinates for each) and I want to take all the points that are 50 km or closer to the reference point. I took the great-circle equation to convert geographical longitude...
  8. L

    Derive the general formula of the equation of a circle for the points

    Homework Statement 1. (a) Find the equation of the circle with the straight line joining A(1;-1) and C(3; 4) as diameter. (b) Hence or otherwise, derive the general formula (x - x1)(x - x2) + (y - y1)(y - y2)=0 of the equation of a circle for the points A(x1; y1) and C(x2; y2): Homework...
  9. G

    MHB How to Calculate the Radius of a Circle Tangent to Two Lines?

    I'm having some difficulty with this problem and any help would be appreciated. What is the radius of a circle tangent to the lines y = 3x + 7 and y = .5x - 3 and containing the point (8,1)? I've determined that the given point (8,1) is the point of tangency of the line y = .5x - 3 and the...
  10. T

    General equation for light intensity entering half circle

    Hello, I am currently working on a problem to calculate the light that makes it through a half circle. For example, say I put a cylinder out in the sun, where the intensity is known to be 1030 W/m^2. I would like to compute the intensity/energy/power that makes it into this. Now, given the...
  11. D

    Distance of a ball in a circle

    Homework Statement In the figure on the right, a 4.0 kg ball is attached to the end of a 1.6 m rope, which is fixed at O. The ball is held at A, with the rope horizontal, and is given an initial downward velocity. The ball moves through three quarters of a circle and arrives at B, with the...
  12. MarkFL

    MHB Ivyrianne's question at Yahoo Answers regarding finding a circle

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  13. karush

    MHB Triangle and circle length and areas

    the following diagram shows a circle with center O and a radius 4cm The points A, B, and C Lie on the circle. The point D is outside the circle, on (OC) Angle ADC=0.3 radians and angle AOC=0.8 radians (a) find AD I used law of sines \frac{4}{\sin{0.3}}=\frac{x}{\sin{0.8}} x \approx...
  14. H

    Homeomorphism of Unit Circle and XxX Product Space

    Is there atopological space X such that XxX (the product space) is homeomorphic to the unit circle in the plane
  15. C

    Intuition why area of a period of sinx =4 = area of square unit circle

    Homework Statement This isn't really homework, but I've been reviewing calc & trig and realized that the area of one period of sin(x) = 4. Since sin(θ) can be understood as the y-value of points along a unit circle, I noticed that the area of a unit square that bounds the unit circle is...
  16. MarkFL

    MHB Jalen's question at Yahoo Answers regarding finding the equation of a circle

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  17. J

    Car Traveling the Circle - Kinematic Quiz

    Good evening. I'd like to first start by saying I am new to this forum, and I am a physics noob. I know that very fact will help people shy away from trying to help me answer this question. This problem (which an image is posted) is 1 of 5 questions on a take home kinematic quiz. I've managed to...
  18. R

    Airplane diving with a circle radius

    1. A 55 kg airplane pilot pulls out of a dive by following, at constant speed, the arc of a circle whose radius is 320 m. At the bottom of the circle, where her speed is 230 km/h, what is the magnitude of her acceleration? Homework Equations v^2= vi^2 +2a(x-xi) The Attempt at a...
  19. H

    Particle going in a circle with speed U problem

    Homework Statement Hello all, I am having some trouble with answering the problem below, mostly because I do not know what the letters stand for and what kind of graph is meant to be drawn. Any help on this would be greatly appreciated. Thanks For a particle going in a circle with speed U...
  20. S

    Calculating the Area of a Circle Segment with Given Radius and Angle

    Hi all, I am having an issue trying to solve the following problem Homework Statement I know that the radius of the circle is 7 and the angle of the segment is 150° Homework Equations Area of a circle: A = \pi{r}^2 Area of the sector of the circle: A = \frac{n}{360}\pi r^{2} Area...
  21. G

    The vicious circle of standard redshift explanations

    We should all know that photons only exist in quantum mechanics. In fact, the idea that energy comes bundled in discrete units is what actually caused QM in the first place. For some reason, however, I've spent my entire life under the assumption that cosmologists make true statements about...
  22. M

    Point of Contact Between Arc and Circle

    Hello, I have an arc with an arc length = 46.88 mm and radius = 44 mm. I have an intersecting arc with an arc length = 26.69 mm and radius = 43.4 mm. A circle with radius = 24 mm fits between the two arcs. How can I determine the contact points of the circle and the two arc lines?
  23. CrimsonFlash

    Contour integral of e^(-1/z) around a unit circle?

    Homework Statement What is the integral of e-1/z around a unit circle centered at z = 0? Homework Equations - The Attempt at a Solution The Laurent expansion of this function gives : 1 - 1/z + 1/(2 z^2) - 1/(3! z^3) + . . . . . The residue of the pole inside is -1. So the integral...
  24. J

    Line integral around a circle in polar coordinates

    I know that \oint_{C}\mathrm{d}\vec{l} = 0, for any closed curve C. But when i try to calculate the integral around the unit circle in polar coordinates, I get a result different from zero. Here is my approach : \oint_{C}\mathrm{d}\vec{l} = \int_{0}^{2\pi}\hat{\phi}\mathrm{d}\phi =...
  25. D

    Equation of circle in 3 dimensions

    Homework Statement Hi, I am trying to find the general formula of a circle in 3D Let's consider a sphere centred at (x1,0,0),with radius x1 It's equation is (x-x1)^2 + y^2 + z^2 = (x1)^2 If there is a plane x = x1 intersects with the sphere A equation of a circle is formed,which is y^2 +...
  26. nomadreid

    Lattice on the closed unit circle?

    Would either or both of these work as a lattice on the closed unit circle in the plane? (1) Using a linear order: Expressing points in polar coordinates (with angles 0≤θ<2π), define: (r,α) < (s,β) iff r<s or (r=s & α<β) (r,α) ≤ (s,β) iff (r,α) < (s,β) or (r=s & α=β) The meet and join...
  27. G

    Solving for the Radius of a Circle in a Sector

    Hi all, I have found this formula being used but I am not sure what it means. It is used to find the radius of a circle in a sector. Hope you can help me understand it. sin(π/6) = r/(6-r) r is the radius of the circle itself and 6 is the radius of the sector or the circle of the sector...
  28. adjacent

    Centripetal Force and radius of the circle

    When the radius of the circle decrease the object moves faster(With the same force) I believe this is a misconception .In common sense the object revolves around more,This leads us to think that it is moving fast but actually the object moves the same distance.Am I right?
  29. J

    Finding the center of mass of an incomplete circle

    Homework Statement Locate the x coordinate of the center of mass of the homogeneous rod bent into the shape of a circular arc. Take r = 170 . The arc goes from (-5/6) to (5/6)pi (counterclockwise). It has a radius of 170mm.Homework Equations x=rcosθ, y=rsinθ, dL=r*dθThe Attempt at a Solution...
  30. J

    Fidning the center of mass of an incomplete circle

    Homework Statement Locate the x coordinate of the center of mass of the homogeneous rod bent into the shape of a circular arc. Take r = 170 . The arc goes from (-5/6) to (5/6)pi (counterclockwise). It has a radius of 170mm.Homework Equations x=rcosθ, y=rsinθ, dL=r*dθThe Attempt at a Solution...
  31. F

    Particle on a Circle Homework: Solving with Newton's Law

    Homework Statement Homework Equations I suppose Newtons third and second law. centripetal acceleration = v^2 /R The Attempt at a Solution I'm thinking that the force due to weight, should be exceeded by the centripetal acceleration? I couldn't get the calculations to add...
  32. M

    How To Create An Arc Of A Circle As A Straight Line?

    How do you construct the arc of the circle as a straight line by geometry not by an equation? Thank you
  33. T

    Scaling of a Circle or a Straight Line Using Complex Numbers

    I'm working on an assignment that is due in roughly two weeks and I'm stuck on a problem. I have what I believe may be a solution but am unsure whether or not it is 'complete'. Here is the problem: "Let C be a circle or a straight line. Show that the same is true of the locus of points...
  34. C

    Charged mass connected to spring, swung in circle in mag. field

    Homework Statement A spring with an unstretched length of 20 cm and a force constant of 100 N/m is attached to a 2-kg mass with a charge of 3.0 C. The mass is swung in a circle in a zero gravity environment, so that the spring is perfectly horizontal and is parallel to the radius of the...
  35. E

    Little confusion regarding centripetal force in vertical circle

    consider a pendulum. The mass 'm' is hung and now we are interested in finding the velocity so that it completes one circle. Clearly we can do it easily by conserving energy. Now my problem is with the top most point. Clearly the tension is minimum at this point so that string becomes slack...
  36. K

    Graphs of Frequency for Car Moving in a Circle

    Homework Statement A car with a horn making a frequency of 'f' Hz is driven in a circle with a radius of 'r' m. The uniform velocity of the car is v ms-1. Draw graphs showing the frequency observes by the observer who is standing on; a) Position A b) Position B (Position B is very far...
  37. O

    Solve Equation of a Circle: Get Help Now!

    I'm having some difficulty with this question. Can anyone help me out, please? Many thanks. Homework Statement A circle of radius length \sqrt{20} contains the point (-1, 3). Its centre lies on the line x + y = 0. Find the equations of the 2 circles that satisfy these conditions...
  38. P

    Statistics expectation problem involving circle.

    Hi, Homework Statement A circle of radius r is as shown in the attached diagram. I am asked to first express X as a function of θ, then to compute E(X). It is also stated that θ obeys U[0,2π]. Homework Equations The Attempt at a Solution Through simple trigonometry I have found X...
  39. Saitama

    What is the value of alpha + beta + gamma?

    Homework Statement A variable line ax+by+c=0, where a,b,c are in A.P (arithmetic progression), is normal to a circle ##(x-\alpha)^2+(y-\beta)^2=\gamma##, which is orthogonal to circle ##x^2+y^2-4x-4y-1=0##. The value of ##\alpha+\beta+\gamma## is equal to A)3 B)5 C)10 D)7 Homework...
  40. S

    Radial Distribution of Points over the Area of a Circle

    This is a tiny part of a presentation I am giving Friday, any and all help is appreciated. Homework Statement Suppose we have a circle centered on O. We are looking for the distribution of the points generated by the following method: We choose a random radius of the circle, and then choose...
  41. U

    Great Circle Problem: Derive Equation for Route from A to B on Sphere

    Homework Statement derive/create an equation for a "great circle" route r(t) from a given point A to a given point B along the surface of the sphere with center (0,0,0) and radius = 15 test point 1: A=(2,10,11) to B(14,5,2) test point 2: A=(10,5,10) to B(0,-12,9) Homework Equations...
  42. N

    Find the Maximum Angular Velocity of the Quarter Circle with Energy

    Homework Statement The uniform quarter-circular sector is released from rest with one edge vertical as shown. Determine its subsequent maximum angular velocity. The distance b is 560 mm. Homework Equations The Attempt at a Solution I know that I need to use: T1 + V1 + U'1-2...
  43. R

    MHB Most efficient way to identify a circle

    A friend's homework problem (Prove any five points in the plane determines a possibly degenerate conic section) led us to a different problem that we found more interesting. We can identify a circle with three points on the circle, or six parameters $(x_1,y_1,x_2,y_2,x_3,y_3)$ where, keeping...
  44. B

    Chromatic image through a double circle aperture

    Hi, I am conducting an experiment and i am displaying diffraction images of light through 2 pinholes on a DSLR camera. I get a good image with lasers but when I capture images of chromatic light i only get the top half (semi circle) image. can someone explain to me why this occurs? I think...
  45. anemone

    MHB Calculating the Radius of a Circle Using Point Ratios

    Points A, B, C, D are on a circle with radius R. |AC| = |AB| = 500, while the ratio between |DC|, |DA|, |DB| is 1, 5, 7. Find R.
  46. T

    Angular Oscillation of a rod in a circle

    Homework Statement A uniform rod moves in a vertical circle .Its ends are constrained to move on the track without friction.Find the angular frequency of small oscillation .Homework Equations The Attempt at a Solution Suppose the rod of length L moves in a circle of radius R . Let the...
  47. Q

    Using Centripetal Forces to find the radius of a circle

    Homework Statement A 100g (0.1kg) rock is attatched to a 1.0m rope and spun around in a circle with a period of rotation of 1.0s. What is the Radius of the circle that it forms? Homework Equations Fc = (mV^2) / r V= (2∏r/T) LCosθ = r The Attempt at a Solution Im quite stick...
  48. N

    Topology of punctured plane vs topology of circle?

    So how does the topology of R^n minus the origin relate to that of the (n-1)-dimensional sphere? I would think the topology of the former is equivalent to that of an (n-1)-dimensional sphere with finite thickness, and open edges. But I suppose that is as close as one can get to the...
  49. A

    MHB Find the Radius of 4th Circle When All are Tangent: Hint d/2

    The centers of three circles are situated on a line. The center of the fourth circle is situated at given distance d from that line. What is the radius of the fourth circle if we know that each circle is tangent to other three. Please give me a hint, if you can. Answer: d/2.
  50. Saitama

    Vectors and points on a circle

    Homework Statement Let A, B, C, D be distinct points on a circle with centre O. If there exists non zero real numbers x and y such that ##|x\vec{OA}+y\vec{OB}|=|x\vec{OB}+y\vec{OC}|=|x\vec{OC}+y\vec{OD}|=|x \vec{OD}+y\vec{OA}|##, then which of the following is always true? A)ABCD is a trapezium...
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