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. S

    Equations of a line tangent to a circle

    Homework Statement Given the circle (x+1)^2 + (y-3)^2 = 25, determine the equations of the tangents to the circle with the slope -3/4.Homework Equations y = mx + bThe Attempt at a Solution I thought that if I could find the equation of the line that passed through the center of the circle and...
  2. T

    Calculating Hydrostatic Force of a Submerged Semicircle

    Homework Statement There is a semicircle submerged in the water. The distance between the surface and the top of the semicircle is 2 ft, and the radius is 5 ft. Find the hydrostatic force. The answer is 1.2 * 10^4 N. Homework Equations y = sqrt(25 - x2) The Attempt at a Solution...
  3. M

    Help Maths Revsion-Coordinate Geometry of a Circle

    Homework Statement Ok hey guys this is my first post so be nice ;). I just wanted to know how to see if a line only intersects the circle once (ie a tangent) I know about double intersections with the quadratic and no intersection with a negative surd in the quadratic equation but is there a...
  4. B

    Map complex line to complex circle

    Homework Statement Find the Linear Fractional Transformation that maps the line Re\left(z\right) = \frac{1}{2} to the circle |w-4i| = 4. Homework Equations For a transform L\left(z\right), T\left(z\right)=\frac{z-z_{1}}{z-z_{3}}\frac{z_{2}-z_{3}}{z_{2}-z_{1}}...
  5. Femme_physics

    Units for moment of inertia of a circle

    We've always been using mm^4, but I see in my answer book (answer written below) that one solution says R^4. Is it the same thing, just that R^4 is used for a circle? The measurement in my exercise are in mm. I did get the answer, I just wasn't aware I was supposed to write it in terms of R^4.
  6. G

    Equation of circle with arc length

    Homework Statement Equation of a circle is: x^2+(y+a)^2=R^2 x intercepts are +/-\sqrt{3} and arclength above x-axis is \frac{4\pi}{3} Find a and R.
  7. G

    Circumscribed circle - inscribed circle area formula

    I'm looking for a formula that subtracts the area of an inscribed circle of a shape from the circumscribed area of the shape. I've confused myself on this one and can't seem to figure it out. The shape is a regular polygon (all sides and angles are equal). What should be given to "plug in" is...
  8. N

    Finding the circle of least confusion for a multi-element optical system

    Hi, I'm a mechanical engineer that's new to optics. I'm trying to determine the best location to place an image sensor for an optical system with multiple lenses and mirrors. In doing so, I've come to the understanding that the best position to put the sensor is at the circle of least...
  9. S

    Motion in a Circle: Proving the Angular Frequency Equation | Homework Help

    Homework Statement An object is moving counterclockwise in a circle of radius r at constant speed v. The center of the cir- cle is at the origin of rectangular coordinates (x, y), and at t = 0 the particle is at (r, 0). If the “angular frequency” is given by ω = v/r, show that...
  10. M

    Electric potential of the arc of a circle

    Homework Statement I previously calculated the electric field for the the arc of the circle and got Ex= Q/2pi^2 e_0 a^2 sin(theta) Ey= Q/2pi^2 e_0 a^2 (1-cos(theta)) I need the electric potential Homework Equations The Attempt at a Solution V=Edr i got an answer interms of theta and since I...
  11. G

    Michelson Interferometer, circle fringes

    Hello guys! Lets say we have a laser beam and we send it to a michelson interferometer. Why the beam pattern at the screen gives circles and not lines or something else? Thanks P.S. see for instance http://techtv.mit.edu/collections/physicsdemos/videos/9823-michelson-interferometer
  12. Y

    Double Integral bounded by Circle?

    Double Integral bounded by Circle? Double integral of (2x-y)dA bounded by circle of radius 2, centered at origin I just need to figure out the limits for my integrals... I am basically lost, can someone show me how to break this up. I tried doing what I did with the previous triangle bound...
  13. V

    Can you prove the area of a circle by calculus?

    I have the proof for pi r^2 (sorry a bit rusty on latex at the moment) Y'all might want to take a try at it. I'll post the proof in a couple of days thanks vector22
  14. B

    Finding Radius of 3 Congruent Tangential Circles in Larger Circle

    Hello everyone! I'm trying to find out how to precisely construct three congruent circles inside a larger circle, each tangential to both the outer circle and the other two circles. For example: http://img4.imageshack.us/img4/1044/verybasicdrawing.png An image I found on the internet...
  15. M

    Electric field of a semi circle

    Homework Statement [PLAIN]http://img101.imageshack.us/img101/2786/21417885.png [96] Homework Equations The Attempt at a Solution E= kdq/r^2 dq=Q/(pi a) dx Ex = 0 , Ey= E sintheta sin theta = sqrt(a^2 - x^2)/a by Pythagorean theorem Ey = kQ/(pi a* a^3) integral from -a to a sqrt(a^2 - x^2)dx...
  16. F

    Distance between a point on a sphere and a great circle arc

    Hi all, Let me state up front that I'm a math idiot. I minored in it in college 20+ years ago and haven't needed it as a software engineer...until now. I'm trying to solve a problem for work that's got me pulling my hair out, mostly because I'm having to relearn so much math I'd forgotten...
  17. T

    Hough Transform for circle detectoin - getting information out

    Hi, I am using the hough transform to perform circle detection. I am able to perform a hough transform and plot the results, but how exactly do I now take my hough transform to actually get meaningful information. I know the size of the my circle (it's radius), but what information am I looking...
  18. B

    Magnetic field of a goffered circle

    Homework Statement There is a constant current I = 10A in a conductor shaped as a “goffered” circle. Find the magnetic induction B at the center of the conductor. [The equation for the curve of the conductor, in polar coordinates, is {\textstyle{1 \over r}} = {\textstyle{1 \over a}} + b\cos...
  19. MacLaddy

    Is the Circle Division Math for the Stator Correct?

    Not a homework question, I was just hoping someone could assist me with understanding some math. Actually, more accurately, I was wondering if someone could double check the math on the following website. http://www.otherpower.com/statormold.shtml If you scroll down you will see some...
  20. P

    Solving a Circle Problem: Finding Radius and Center | Math Forum Help

    Hi, Math forums! I need some help with a circle question. 3x^2 + 12x + 3y^2 - 5y = 2 And I was supposed to find the radius and center of the circle, So I first divided by 3: x^2 +4x + y^2 - 5/3y = 2/3 And then I complete the square x^2 + 4x + 4 + y^2 - 5/3y + 25/36 = 2/3 + 12/3 +...
  21. D

    Airplane flying in a horizontal circle

    Homework Statement An airplane is flying in a horizontal circle at a speed of 410 km/h (Fig. 6-41). If its wings are tilted at angle a = 42° to the horizontal, what is the radius of the circle in which the plane is flying? Assume that the required force is provided entirely by an...
  22. D

    Shadow of vertical circle on wall?

    A ball is spun in a vertical circle on a string. A light is shining from the side of the circle so that a shadow of the balls motion is shown on a wall behind it. The shadow is simply a circle moving up and down in a straight line (I can't attach the image). The amplitude of the shadow is 0.5m...
  23. P

    Finding Equation of Smallest Circle Containing 3 Circles

    Homework Statement if equation of 3 circles is given then find the equation of the smallest circle containing all 3 circles Homework Equations The Attempt at a Solution i can do this question for 2 circles , please give a hint for 3 circles
  24. M

    Area of a Segment of a Circle, when only the radius is known.

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  25. N

    Symbol Meaning: "+" Enclosed in a Circle

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  26. M

    How do you find the center of a circle using only a compass?

    Years ago my high school math teacher showed us how to find the center of a given circle using only a compass, nothing else. I can't remember how. I need to do it now. Does anyone have the answer?
  27. M

    Why Does Parallel Transport on a Circle Cause Vector Field Rotation?

    I'm trying to understand parallel transport and I'm stuck. The example given is if you have a unit sphere and you take one of the latitudes (not the equator), take at a point on the latitude the tangent vector to the curve, and parallel transport it around the curve. I don't understand why the...
  28. T

    How to express a circle in spherical coordinates

    I've got a unit sphere sitting at the origin. This sphere is cut by an arbitrary plane. I'm looking to find the equation of the circle that results from the intersection in spherical coordinates. This is for a computer program I'm writing, and I've already set it up to approximate this by...
  29. M

    Find the Proof: Tangent Lines & a Circle w/ Square Root of 3 Radius

    Homework Statement Our teacher was talking about something regarding two tangent lines on a circle who distance between the tangent lines is square root of 3 times the radius of the circle... She wanted us to find the proof of this but I am stumped on where to even look... Does anyone know...
  30. J

    Calculating Tension in a Vertical Circle

    1. A string 1.5 m long is used to whirl a 1.5 kg stone in a vertical circle to that its velocity at the top is 6 m/s. What if tension in the string when it is horizontal? (g = 9.8 m/s2) 2. Centripetal acceleration = mv^2/r 3. i don't get what they mean by vertical circle...
  31. L

    What Is the P-adic Volume of the P-adic Circle x² + y² = 1?

    Find the p-adic volume of the p-adic circle x^2 + y^2 = 1. This isn't hw.
  32. J

    Layperson asking about circle sides (Warning may not make sense)

    God knows if I'm posting this in the right place on physics forum but here goes... If a circle can be thought of as a shape with an infinite number of sides does this then therefore mean that each side would have to be infinitely small? Within a large circle you can draw a smaller circle...
  33. Demon117

    Show that the unit circle is connected

    1. Show that S:= {(x,y)an element of R^2 : x^2 + y^2 =1} is connected. 2. Relevant theorems 1. Path-connected implies connected. The Attempt at a Solution Define f: [0,2pi] --> R^2 by f(x) = (cos(x),sin(x)). This map is continuous, and its image is S^1. The interval [0,2pi]...
  34. S

    Why is the Unit Circle Important in Teaching Trigonometry?

    Ok- I am teaching trigonometry to low level students right now and I am trying to figure out why they need to know the unit circle. Are there some interesting things they can learn about by using a unit circle? So far, we pretended it was a magic-barbie-sized-half-underground-ferris-wheel...
  35. C

    Finding a second point on a circle

    Hey, I have scoured the interned for an answer to this question, but so far my search has been uneventful. Given a circle with center point (h,k), radius r, and a point on the circle (x,y), I need to find the point on the circle at angle a from (x,y). Any thoughts? Attached is a...
  36. X

    Center of mass of a semi circle using polar coordinates

    Homework Statement Semi circle of Radius R given. Find center of mass using polar coordinates, not double integrals. Homework Equations .5 intergral(r^2dpheta) (1/M) integral y dm r=R The Attempt at a Solution .5(2/piR^2) integral(R^3sinpheta do pheta) from 0 to pi, when I evaluate it I...
  37. M

    Prove that a great circle is a geodesic

    Homework Statement L = R \int \sqrt{1+ sin^2 \theta \phi ' ^ 2} d\theta from theta 1 to theta 2 Using this result, prove that the geodesic (shortest path) between two given points on a sphere is a great circle. [Hint: The integrand f(\phi,\phi',\theta) in the result is independent of...
  38. E

    Value of 0 on X-Axis for Circle Problem (r=2)

    if you have a quadrant sitting on top of the x-axis and on the right of the y axis, when you draw a line perpendicular to the x-axis that splits the circle into two equal parts, then what is the value of 0 on the x-axis to the line mark when r=2? too bad i don't have a diagram to show you
  39. J

    Sound wave interfernce on a large circle

    Homework Statement Given two isotropic point sources of sound \[s_{1}\] and \[s_{2}\]. The sources emit waves in phase at wavelength 0.50m; they are separated by D = 1.75m. If we move a sound detector along a large circle centered at the midpoint between the sources, at how many points do...
  40. I

    Average Velocity of a particle moving in a circle over a given interval

    Homework Statement Homework Equations d = 2.5 c = pi*d = 7.854 velocity/s ?= c * 2 = 15.7079The Attempt at a Solution Since PR is 1/4 of the circle and the particle moves around the circle 2 times per second, I thought the average velocity would be 1/8th of the velocity that it's traveling...
  41. T

    Equation of an Oscillating Circle

    Homework Statement Find an equation of the oscillating circle to y=ln(x) at the point (1,0) Homework Equations p will = the 2nd derivitive of y u will = the 1st derivitive of y i will = the 2nd derivitive of x o will= the 1st derivitive of x (po - ui)/(|V|^3) = k(curvature)...
  42. P

    Smooth Mapping Between Unit Circle and Curve in R^2?

    Hi, I have been told that in R^2 the unit circle {(x,y) | x^2 + y^2 = 1} is smoothly mappable to the curve {(x,y) | x^4 + y^2 = 1}. Can someone please tell me what this smooth map is between them? I can only think of using the map (x,y) --> (sqrt(x), y) if x is non-negative and (sqrt(-x), y)...
  43. icystrike

    Can we ever construct a perfect circle? (Curiousity)

    Homework Statement As stated abv. Since \pi can only be established by infinite sum and according to zeno's paradox we can never break a finite length into infinite pieces (loosely speaking)
  44. S

    Frictional work inside a circle

    Homework Statement You push an object of mass m slowly, partway up a loop-the-loop track of radius R, starting from the bottom, where the normal force to the track is vertically upward, and ending at a point a height h< R above the bottom. The coefficient of friction between the object and the...
  45. Q

    Block sliding down incline shaped as circle

    Homework Statement A 2-kilogram block is released from rest at the top of a curved incline in the shape of a quarter circle of radius R. The block then slides onto a horizontal plane where it finally comes to rest 8 meters from the beginning of the plane. The curved incline is frictionless...
  46. Q

    Circle in plane parameterization

    Homework Statement parameterize the following a circle with radius 2 , centered at 1,2,3 and lies on the plane x+y+z=6 The Attempt at a Solution ok i think i know how to get radius 2, centered 1,2,3 namely, r(t) = (1,2,3) + (2cos(t),2sin(t),t) but how do i fit into the plane...
  47. X

    Find the radius of the middle circle

    Homework Statement There are 3 circles, each tangent to 2 lines and to each other (as in the picture). The radius of the right (largest) circle is 8, and the radius of the left (smallest) circle is 4. What is the radius of the middle circle? The Attempt at a Solution I tried using...
  48. T

    Electric Point Forces in a Circle

    Homework Statement Twelve identical point charges are equally spaced around the circumference of a circle of radius 'R'. The circle is centered at the origin. One of the twelve charges, which happens to be on the positive axis, is now moved to the center of the circle. Part A Find the...
  49. U

    What are the constraint forces on a circle with a particle?

    when a particle is constraint to move on a circle, what are the constraint forces
  50. P

    Radius of A Circle inside a Sphere

    Homework Statement Say you have a sphere of radius r centered at the origin, and a vector v <r,0,0>. Let v' be the vector v rotated about the y-axis by angle theta. What is the shortest distance between the end of the vector and the z-axis? Homework Equations The Attempt at a Solution I...
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