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. A

    MHB Equation of a line tangent to a circle

    The circle x^2 +y^2 -4x+2y+m=0 is tangent with the line y=x+1.Find m. p.s : I know that o should solve it from the equations of two lines but i really get confused when i substitute the y :/ . Thanx :)
  2. B

    Segment of a circle calculation

    I'm working to calculate the cross-sectional area of a lathe turned feature machined with a radiused insert. My calculations have essentially led me to the equation for the area of a segment of a circle. Area=r^2/2*(∏/180*C-sin(C)) where r is the circle's radius and C is the central angle...
  3. 7

    LaTeX Fill with color three of five sectors in circle with latex.

    Hi every one, here is a question about drawing and filling in Latex (\usepackage{tikz}) I just draw a circle with 5 sectors correctly, and what I need help on please, how I fill 3 sectors with green color and the other 2 sectors with red... please help me with this task...
  4. U

    Circular Motion Dynamics. Car traveling in vertical circle

    Homework Statement A small car with mass .800 kg travels at a constant speed of 12m/s on the inside of a track that is a vertical circle with radius 5.0m. If the normal force exerted by the track on the car when it is at the top of the track is 6.00N, what is the normal force at the bottom of...
  5. S

    Quotient Group is isomorphic to the Circle Group

    A portion of a homework problem was given me to solve for practice. I have solved some but not all of the homework problem and I hope you all can help. Here is the problem: 1. For each x \in R it is conventional to write cis(x) = cos(x) + i sin(x). Prove that cis(x+y) = cis(x) cis(y)...
  6. C

    MHB Circle problem finding coordinates of points

    Continued from; Originally Posted by Jameson http://www.mathhelpboards.com/f2/understanding-how-deal-fractions-using-brackets-2596/#post11674 What is the full problem you are trying to solve? I can't make sense of your post until I know that. I have a circle problem and am trying to find...
  7. A

    Unruh effect and detectors moving in a circle

    Hi all, I have a question about the Unruh effect. I've read that a detector will only register the effect (i.e., the thermal bath) when the Rindler horizon is visible - in turn, a detector accelerating in a circle (changing direction but not speed) would not measure the thermal effect...
  8. A

    Change orbit from circle to parabola

    1(a) Homework Statement A spaceship travels in a circular orbit around a planet. It applies a sudden thrust and increases its speed by a factor f . If the goal is to change the orbit from a circle to a parabola, what should f be if the thrust points in the tangential direction? 1(b) Is...
  9. H

    What is the total energy and velocity of a ball in a vertical circular path?

    A 0.8 kg ball is whirled on a string r = 0.4 meters long in a vertical circular path. At the bottom of the circle, the ball is h = 0.45 meters from the ground. At the top of the circle, the ball has a speed of 3 m/s. Assume that the total energy of the ball is kept constant. a. Calculate...
  10. trollcast

    Show 2 of 3 points on a circle are the diameter

    Homework Statement Points A B and C lie on the circumference of a circle where $$A =(-3,2)\\B=(-1,6)\\C=(7,2)$$ Show that AC is the diameter of the circle. Homework Equations The Attempt at a Solution Would it be sufficient to show that the angle ABC is a right angle and therefore...
  11. K

    The substended angle of a circle

    The subtended angle of a circle Hello! I came across the following formula for the change in the subtended angle (of a circle), when we move our obersvation point \vec{x} by \delta \vec{x}, \delta \Omega = \oint \hat{x} \cdot \frac{(\delta \vec{x} \times d\vec{l})}{|\vec{x}|^2}. The...
  12. M

    Mohrs Circle, Von Mises and Minimum Yield Strength Help

    Hi Wasn't sure where to post this, hope it's ok in here! I've gotten myself very confused as to how to find the minimum yield strength for an element. I have used Mohrs circle to find sigma1 and sigma2, then plugged that into the von mises equation to find sigma-von = 636.8MPa. The...
  13. C

    Probability that n points lie on one side of a circle

    Homework Statement Suppose that n points are independently chosen at random on the circumference of a circle and we want the probability that they all lie in some semicircle. Let ##P_1...P_n## denote the n points. Let A denote the event that all the points are contained in some semicircle and...
  14. R

    Geometrical (circle) Proofs - Help

    Q1 Two circles intersect at P and Q. Two parallel line segments APC and BQD are drawn to meet one circle at A and C, and the other circle at B and D. PB and PD are diameters of their respective circles. Prove that points B, Q and D are collinear. Q2 AB and CD are two parallel chords of a...
  15. C

    [Differential Geometry of Curves] Prove the set f(p) = 0 is a circle

    Homework Statement Consider a function f that can be put in the form f(p) = g(|p|) where g : [0,+∞) -> ℝ is C1 with g(0) < 0 and g'(t) > 0 for all t ≥ 0 Assume that |∇f(p)| = 1 for all p ≠ 0 and prove that the set f(p) = 0 is a circle. Homework Equations Given above The Attempt at a...
  16. J

    Since the earth orbits in an ellipse, not a circle

    doesn't that mean that one hemisphere would have a hotter summer than the other hemisphere and the opposite would have a colder winter? if so, which is which. I am willing to guess the northern hemisphere has the colder winter and southern has the hotter summer.
  17. C

    Making a cylinder into a circle?

    Hi I don't understand how you can take a cylinder with equation x2+y2=2x And rewrite it to (x-1)2+y2=1 And then it suddenly becomes the equation for the base circle of the cylinder. Would it not usually require that you remove some variable to transform it from 3D to 2-dimensional...
  18. T

    Solving Mohr's Circle Problem: Is My Solution Correct?

    Homework Statement Here is the question with the solution from the textbook and my solution: I don't understand the textbook solution because in their Mohr's circle the max shear stress is 65 Mpa. However, as stated in the problem, the max shearing stress is 80Mpa and this occurs 45...
  19. 5

    Expressing geometrically the nth roots of a complex number on a circle

    Homework Statement Let z \in \mathbb{C}. Prove that z^{1/n} can be expressed geometrically as n equally spaced points on the circle x^2 + y^2 = |z|^2, where |z|=|a+bi|=\sqrt{a^2 + b^2}, the modulus of z. Homework Equations // The Attempt at a Solution My problem is that I am...
  20. D

    MHB Equations of Sides of Square Inscribed in Circle

    Find the equations of the sides of square inscribed in the circle $3(x^2+y^2)=4$, one of whose sides is parallel to the line $x-y=7$.
  21. F

    Lattice Points on Circle: Determining the Number of Points on the Boundary

    Does any circle having irrational radius have no lattice points on its boundary ? Extended question: Is there any way to determine the number of lattice points lying on the boundary of a given circle ? *The centres of these circles are all (0,0) *
  22. D

    The circle as a set closed and bounded

    Hi guys, I would like to understand why a circle (and in general a n-sphere) as a subset of R^2 (in general R^(n+1)) with the standard topolgy is considered a closed and a bounded set. I think that this can be a closed set because its complement (the interior of the circle and the rest of...
  23. H

    Centripetal acceleration A jet flies in a vertical circle

    Homework Statement A pilot, whose mass is 96.0 kg, makes a loop-the-loop in a fast jet. Assume that the jet maintains a constant speed of 225 m/s and that the radius of the loop-the-loop is 2.064 km. What is the apparent weight that the pilot feels (i.e., the force with which the pilot...
  24. S

    Rotate a Circle Around the X/Y Axis - Cylindrical Shells

    Homework Statement Rotate the region bound by the given curve by about the x and y axis. Find the volume through the cylindrical method. x^2 + (y-1)^2 = 1 Homework Equations Cylindrical method: ∫2∏xf(x)dx Slice Method: ∫A(x)dx The Attempt at a Solution x^2 + (y-1)^2 = 1 x =...
  25. P

    How Do You Apply Mohr's Circle to Geotechnical Engineering Problems?

    Homework Statement http://imageshack.us/a/img27/6347/screenshot20121023at125.png Uploaded with ImageShack.us This is for a class on Geotechnical Engineering for those who are interested.Homework Equations Basic understanding of Mohr's Circle concepts and general knowledge on subject. Kind of...
  26. D

    Why fish under water see a circle surrounded by darkness

    A fish looking straight up to the surface of a pond receives a cone of light filled with images. This bright field is surrounded by darkness. Explain what is happening and compute the cone angle. No given data but ##n_w=1.33## No give equations but I anticipate Snell's law and maybe the...
  27. iVenky

    Differential equation of a circle

    Consider a circle of radius 'a' and centre (h,b) then the equation of the circle is given by (x-h)2 + (y-b)2 = a2 I expressed this in terms of differential equations which is - a= {[1+(dy/dx)2]3/2}/{d2y/dx2} According to my book - this equation indicates that 'a' is a...
  28. J

    Graphical solution to an equation relating tan(x) to a semi semi circle

    Homework Statement Using graphical means, determine how many positive roots exist, as a function of a, the the following equation. Homework Equations √(a2-x2) = tan(x) The Attempt at a Solution I've sketched graphs showing tan(x) and the semi circle overlapping for various radii...
  29. R

    Homeomorphism between the open sets of the circle and the open sets of real line

    I'm trying to prove the homeomorphism between the open intervals of the real line and the open sets of the circle with the induced topology of R^2. Notice that the open sets of the circle is the intersection between the open balls in R^2 and the circle itself. Anyone can help me...
  30. J

    Converting 2D density (circle) to 3D density (sphere)

    Hi All, I'm looking for help in converting 2D density (objects/area) in a circle to 3D density (objects/volume) in a sphere, the circle and sphere having the same radius and distribution of objects being uniform. To make this problem more intuitive, here's a sample application: both crabs and...
  31. W

    Finding coordinates of a point on a circle( angle and distance from O known)

    1. I basicly have to find the coordinates of P. All the pink lines are know, coordinates of points A and centre of circle are know. 2. (x-a)^2 + (y-b)^2 = r^2 [b]3. I try to substitute mx+c into the equation and get (x-a)^2 + (y-mx-c)^2 + r^2= 0 but I can't work out what m and c...
  32. N

    Comp Sci Finding circle zero-points with C++

    Hi everyone! My primary question is below the problem. My problem: Circles The standard form of an equation for a circle is (x − h)2 + (y − k)2 = r2 where (h,k) represents the center of the circle and r is the radius. The y-value of the equation becomes zero at the point of intersection with...
  33. J

    Showing a polynomial has at least one zero outside the unit circle.

    The first thing that we should notice is that the leading coefficient $a_n = 1$. I was thinking about considering the factored form of p. I googled, and there is an algorithm called the "Schur-Cohn Algorithm" that is suppose to answer exactly this, but I can't find any information on it or...
  34. johann1301

    Non-trigonometric parametric equation of a circle

    I wish to write this equation: 1=√(x2+y2) as a parametric equation but WITHOUT the use of sine and cosine. Is this possible?
  35. D

    Integration of a Circle in Polar Coordinates

    Homework Statement Hi, I'm trying to find the area of a circle in polar coordinates.I'm doing it this way because I have to put this into an excel sheet to have a matrix of areas of multiple circles. Here is an example of the problem. a= radius of small circle (gamma, r0) = polar coordinate...
  36. D

    What is the Integration Formula for a Polar Circle?

    Hi, I'm not sure how to integrate this equation where a, r0 and γ are constants.
  37. S

    Triangle inscribed on circle proof I am missing something

    Triangle inscribed on circle proof...I am missing something :( Homework Statement I have provided a link to the problem below http://imageshack.us/a/img854/4143/photo1lsd.jpg I need to prove AE is an altitude on this proof Homework Equations all radii are congruent, cpctc, ASA...
  38. P

    Finding intersection of line and circle.

    Homework Statement I have a line obtained from using a slope of 1 and point (-sqrt(2),sqrt(2)): y - sqrt(2) = 1 (x+sqrt(2)) y = 2*sqrt(2) + x and a circle with radius 5 centered at origin. My thought was to solve this parametrically The line is the tangent line (blue...
  39. D

    Area of a Circle in Polar Coordinates

    Hi, I'm trying to find the area of a segment of a circle that is not at the origin. It will look similar to this picture below but I need to find the area enclosed by a circle. Using the polar equation of a circle provided by wikipedia: and integrating to find the area of a...
  40. C

    Calculating Arc Length of a Circle with Radius 6 and Center (4,1,5)

    Homework Statement Find an arc length parametrization of the circle in the plane z=5 with radius 6 and center (4,1,5) Homework Equations ||r'(t)||=r'(u) s=integral r'(u)du The Attempt at a Solution I get the equation of the circle to be (x-4)^2+(y-1)^2+(z-5)^2=6^2 Not sure where...
  41. S

    What is the proper form for Mohr's Circle (rotation of axes) calculation?

    I'm getting conflicting information on the proper form of Mohr's Circle for the stress of a system at a rotation from nominal. Actually it seems that Mohr's Circle is not a tool for just stress or moment if area/stress calculation, but in general for a 2-D simple symmetric form eigenproblem...
  42. A

    Find point coordinate on 3D circle knowing three points

    I would like to find a 3D coordinate of a point (X) on a circle, knowing two points on the circle (P1,P2) which represent the circle diameter and another point (P3) NOT on the circle but on its plane. Also known the length of the line from P2 to X, for example d. Another thing that may help, the...
  43. B

    Finding the Correct Acceleration in a Spinning Circle: What Am I Doing Wrong?

    Homework Statement See image. Homework Equations ωx (ωx r) = anormal αx r =atangent x=rcos*theta y=-rsin*thetaThe Attempt at a Solution I solved for w=2 k rad/s and α= -1.5 k rad/s I also got the correct answer using the cross products. My problem is I am trying to do this problem in...
  44. V

    A circle tranforming into ellipse

    I don't know what category this question falls into. I have two parallel planes, on one I draw a circle and on the other I project it orthogonally. Now I incline the plane with the circle. The projection on the other plane will be an ellipse. I need to find out, the relationship between the...
  45. N

    Electric field from a circle arc

    Homework Statement Find the x-component of the electric field at the origin due to the full arc length for a charge of 3.8 μC and a radius of 1.9 m. The value of the Coulomb constant is 8.98755 × 109 N · m2/C2. Homework Equations E = kq/r^2 dq = q dθ λ = Q/ (R θ) The Attempt...
  46. O

    Circumference of a circle (in strange coordinates)

    Homework Statement We are given a function defined by x = uv, y = 1/2 (u^2-v^2)Homework Equations I derived the line element ds^2 = (u^2+v^2) dv^2 + (u^2+v^2) du^2 However I decided this was to unwieldy to derive our circumference where C = 2*{R}\oint_{-R}^{R} ds So I decided to try to...
  47. R

    Prove roots lie inside the unit circle

    Homework Statement Let P(z)=1+2z+3z^2+...nz^(n-1). By considering (1-z)P(z) show that all the zeros of P(z) are inside the unit disk Homework Equations None given.. The Attempt at a Solution Well (1-z)P(z) = 1+z+z^2+...+nz^n and to find roots I set it to 0: 1+z+z^2+...+nz^n = 0...
  48. A

    Leaves have formed the circumference of the circle

    Sometime in the afternoon or in evening i see some leaves caught in something like air current which i feel that there some thing more. The leaves (tiny fallen leaves and some dust particles) revolve around a center. It looks like the leaves have formed the circumference of the circle and they...
  49. edward

    Was the Ab Circle Pro Refund Due to Deceptive Advertising?

    When I first saw the infomercial I knew this Chinese manufactured piece of junk was worthless. http://www.washingtonpost.com/business/companies-marketing-ab-circle-pro-to-pay-up-to-25-million-in-refunds-to-settle-ads-charges/2012/08/23/77799a20-ed33-11e1-866f-60a00f604425_story.html...
  50. A

    Find radius if a circle is inscribed in quadrilateral

    :cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry:
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