Circle Definition and 1000 Threads

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. H

    Why there are 360 degress in a circle

    Mentor comment: Harmony360 original post violated our rules. The new wording is mine. D H So, why there are 360 degress in a circle?
  2. U

    How can a 1-dimensional being prove they live on a circle?

    How could i mathematically proove that I am living on a circle. Almost got it last night , just need an insight to figure out an equation. Ty.
  3. P

    What Determines the Detachment Point of a Ball Rolling on a Circle?

    Homework Statement A ball on top of a circle is acted on by a FG. The ball rolls to a certain point on the circle, and detaches. Ffr Is negligable. Given info: Diameter Of the circle, Mass of ball no ffr x = the distance from the balls posistion to the top of the big circle. x is what is...
  4. F

    Is Mohr's Circle Accurate in Real-Life Applications?

    I'm getting approximations within 5% of the actual values. Does that sound about right?
  5. 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...
  6. 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?
  7. 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...
  8. 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...
  9. R

    Simple Mohr's Circle Question - Axis scales?

    I'm just wondering about using a Mohr's Circle, do I need to use the same scale for the x and y axes, as surely otherwise my choice of scale greatly impacts the results. I am using one to get my principle second moment of areas, Ix and Iy, for an equal L section. Ix and Iy are where the...
  10. 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?
  11. A

    Radius of a circle whose area is of 2 other cirlces

    Homework Statement --SOLVED-- It seems, that you just apply the pythageos thereom to 'A' and 'B' =)--------------- Lets say I have a circle 'A' with radius 6cm, and a circle 'B' with radius 6cm. These two circles would have an area of 113.097cm^2. When both are combined they would have an...
  12. T

    Forces in a circle from similar charges?

    Hey guys, New here. It's been a while since I've done any physics. I've been playing around with some mental work in my head and I am trying to figure out why something doesn't work. I know it shouldn't work, but I can't figure out the why. What I am talking about is utilizing similar charges...
  13. L

    Can a Magnetic Dipole Form a Circle?

    Sorry for my lack of knowledge, I'm in Grade 7 I just learned that Magnets have dipoles--like this: If those dipoles formed a circle, wouldn't it be possible to create perpetual motion?
  14. P

    THE CIRCLE HAS RETURNED(Help me please)

    Homework Statement PICTURE: http://imageshack.us/photo/my-images/21/circls.png/ A Force of gravity acts upon a ball on top a circle. The ball rolls a down the curve of the circle until a CERTAIN POINT. at this CERTAIN POINT the ball detaches from the circle and travels until it his the ground...
  15. T

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

    This is my first post here and any help is appreciated. I belong to a drag racing forum and this has been a hot topic of discussion. If you have a 4 inch round pipe by 2 inches tall and insert the pipe into a vice and make it oval shaped it would somehow change the volume. Please see...
  16. R

    Area of a circle and pi and generally area

    So I always wondered why you multiply by pi when you're finding an area of a circle, for a rectangle you multiply by length and width, I guess that makes sense... How I see multiplying a length and width is if you have a length of 5 cm and a width of 4 cm, I imagine you just stack 4, 5 cm...
  17. R

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

    Hi. I want to know the equation to draw a circle that's a bit tilted. Imagine a 3D circle that's parallel with the Y axis. Now I want to take that circle and have its center cross through the origin still, but I want it to be θ degrees titled from the Y Axis. I'm using the following...
  18. Z

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

    Homework Statement A wagon is drawn by a student pulling with a constant force of F Newtons applied at an angle of θ° to the horizontal. If the wagon is drawn in a circle with radius r meters, how much work is done on the wagon? (I don't remember the actual numbers) Homework Equations...
  19. A

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

    my textbook says: "As a gyroscope precesses, its center off mass moves in a circle with radius r in a horizontal plane. Its vertical component of acceleration is zero so the upward normal force exerted by the pivot must equal mg." Now wouldn't this always be true. I mean if u have a...
  20. B

    Fun with Dynamic Spirograph - Circle Rolling around Rolling Circle

    Circle Rolling around Rolling Circle (1) Circle 1 rolls around inside of the fixed base circle. Circle 2 rolls around inside of Circle 1.
  21. L

    Effective Resistance if bent in the form a circle

    Homework Statement A wire of resistance 8R is bent in the form of a circle. What is the effective resistance between the ends of a diameter AB? Homework Equations I have attached the image and my attempt to solve it as told by my teacher. Homework Equations The Attempt at...
  22. P

    Ball Rolls off of a circle :O PROBLEM

    Ball Rolls off of a circle :O! PROBLEM! So the problem is, a ball at zero velocity begins to roll on a circle. At a certain point the ball and the circle "DISCONNECT". There is a height x from the roof to the point it disconnects. Given Information. Height X, Diameter D of circle, Vi=0...
  23. N

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

    Homework Statement Suppose a slingshot rotates clockwise along the circle x^2 + y^2 = 9 and the rock is released at the point (2.99,0.77). If the rock travels 200 feet, where does it land? Homework Equations The Attempt at a Solution I think you might have to find the tangent at...
  24. S

    How to calculate arc length in unit circle

    http://www.up98.org/upload/server1/01/z/cllb59cvnwaigmmar6b5.jpeg What is the method of calculating arc length in In the image above . x & y is known Thanks .
  25. M

    Equation of a circle / polar coordinates

    I was looking at the equation of a circle in polar coordinates on wikipedia, http://en.wikipedia.org/wiki/Polar_coordinate_system and I understand that a is the radius of the circle, and that (r0, phi) is the center of the circle. But I don't see what the r and theta refer to :(.
  26. B

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

    Prove that angle WTU is twice as large as angle WOX. Any help would be greatly appreciated.
  27. X

    Elastic Problem. Aluminum Wire in Horizontal Circle

    Homework Statement An aluminum wire is 0.850 m long and has a circular cross section of diameter 0.780 mm. Fixed at the top end, the wire supports a 1.20-kg object that swings in a horizontal circle. Determine the angular velocity required to produce a strain of 1.00  10–3. Homework...
  28. O

    Volume of a substance (in a circle)

    Hi I just want to check that I am doing this math problem correctly. We were given a density function for review for an upcoming math test. We were then asked to find the volume in a circular radius given this density function. I will post the exact problem now then explain the steps I...
  29. T

    Parameterizing A Circle Projected onto a Plane

    Homework Statement Find a vector function that parameterizes a curve C which lies in the plane x-y+z=2 and directly above the circle x2 + (y-1)2 = 9 The Attempt at a SolutionSo, in order to parameterize the circle, I simply use x=cos(t), y = sin(t) with some adjustments. Namely, I let...
  30. S

    Inequality with Circle and Triangle in Euclidean Geometry

    Homework Statement Please see below... Homework Equations Please see below... The Attempt at a Solution Hi. This question is on geometry with circle and triangle. I am stuck only on 2 parts of the solution and not the whole solution... Thank you...
  31. L

    Using Green's Theorem to Solve a Circle Line Integral

    Homework Statement Use greens theorem to solve the closed curve line integral: \oint(ydx-xdy) The curve is a circle with its center at origin with a radius of 1. Homework Equations x^2 + y^2 = 1 The Attempt at a Solution Greens theorem states that: Given F=[P,Q]=[y, -x]=yi-xj...
  32. S

    Kinetic Energy of a mass moving in horizontal circle

    Homework Statement A mass moves in a circular path that has a radius of 24.6cm on a horizontal frictionaless surface. If the centripetal force acting on the mass is 96.5N, what is the kinetic energy of the mass? r=0.246m Fc=96.5N Homework Equations He told us to use these and "play...
  33. S

    Understanding the Möbius Bundle on a Circle

    Hi, i can not understand how circle has a nontrivial bundle, Möbius bundle. Can you say me what is its transition function on it.
  34. X

    Lagrangian Problem. Two masses on a massless circle

    Homework Statement Two equal masses are glued to a massless hoop of radius R that is free to rotate about its center in a vertical plane. The angle between the masses is 2*theta. Find the frequency of small oscillations.Homework Equations \frac{d}{dt} \frac{∂L}{∂\dot{q}}=\frac{∂L}{∂q} The...
  35. 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...
  36. 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...
  37. 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...
  38. 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?
  39. 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...
  40. 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...
  41. AGNuke

    Circle and Chords intersected by x-axis

    Let a circle be given by 2x (x-a) + y(2y-b) = 0; (a≠0, b≠0). Find the condition on a and b if two chords, each bisected by the x-axis, can be drawn to the circle from (a, b/2) My attempt in this question is not quite relevant at this moment. I just found that (a,b/2) will lie on circle and...
  42. 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...
  43. X

    Lagrangian of a Pendulum on a rotating circle

    Homework Statement Find the Lagrangian of a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant angular velocity. (So basically there is a circle around the origin that spins with a constant angular velocity and the pendulum is attached to the...
  44. 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...
  45. 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...
  46. 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...
  47. S

    What Range of Speeds Can an Object Have Before a String Breaks?

    Homework Statement A light string can support a stationary hanging load of 25.0kg before breaking. An object of mass m = 3.00kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.800m, and the other end of the string is held fixed. What range of...
  48. T

    Identifying equivalence classes with the unit circle

    Homework Statement Define a relation on R as follows. For a,b ∈ R, a ∼ b if a−b ∈ Z. Prove that this is an equivalence relation. Can you identify the set of equivalence classes with the unit circle in a natural way? Homework Equations The Attempt at a Solution I have already proven that this...
  49. T

    Move tricycle in circle during x sec at speed s

    Homework Statement I need to get a tricycle to move around a circle (depending on the angle of the front wheel) in MATLAB (but any mathematical formulae would help). I have the variables: M (x, y, theta) which is the center point between the 2 back wheels and the angle of the tricycle, the...
  50. O

    Triangle tangent to circle problem using derivatives

    Homework Statement A metal bar of length l in the figure below has one end attached at a point P to a circle ofradius a < l. Point Q at the other end can slide back and forth along the x–axis. (a) Find x as a function of θ (θ=angle POQ). (b) Assume the lengths are in centimeters and the...
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