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. kaliprasad

    MHB Points on a Circle: Proving $m_1m_2m_3m_4=1$

    If $(m_r,\frac{1}{m_r})$ for r from 1 to 4 are 4 points that lie on a circle show that $m_1m_2m_3m_4= 1$
  2. prashant singh

    I Why trigonometric ratios were defined for a unit circle

    To make it useful for any angles. I need a good explanation for this.
  3. P

    Glider and vertical circle question

    Homework Statement What is the minimum speed that a glider must fly in order to make a perfect vertical circle in the air if the circle has a radius of 200.0 m? Homework Equations Fc = mv2 / r V = 2(Pi)r / T The Attempt at a Solution I have drawn the free body diagram and I think that the...
  4. Titan97

    Geometry Book for learning properties of triangle and circle

    Can you suggest a book that discusses properties of triangles and circles? (Like properties and theorems on circumcircle, excircle, nine point circle, etc). Most of the geometry books are either to basic or too advanced. I have read a book on complex numbers by Liang Shin Hahn. But the...
  5. P

    I Triangulation of circle and disk in R2

    I am studying topology right now and am a bit confused about the idea of triangulation. The definition is: if a topological space X is homeomorphic to a polyhedron K (union of simplexes) then X is triangulable and K is a (not necessarily unique) triangulation. Apparently ## K_0 \equiv {1} \cup...
  6. G

    Magnitude of avg acc. of train moving in a circle?

    Homework Statement "Assume that a train is traveling at 65 cm/s, and the track has radius 20cm. What is the magnitude of the train's average acceleration as the train goes from the tree marked A to the next tree B, located exactly 1/4 of the way around the track from tree A? [Hint: This...
  7. Eclair_de_XII

    Why do you get the area of a whole circle when you integrate

    Homework Statement Okay, I don't actually have a homework problem that explicitly tells me to find the reason why; it's just something I was wondering while I was trying to integrate circles using trigonometric substitution. But just for reference's sake: "Why does Acircle = ∫√(a2-x2)dx?"...
  8. S

    Trying to prove trigonometric integrals on a quarter of circle

    Homework Statement I want to prove that: Homework EquationsThe Attempt at a Solution I tried using the trigonometric identity: sen2x = senx cosx / 2, so, I got: 1/2m∫(sen2x)mdx, x from 0 to pi/2, but now I don't know how to proceed. Can you help me please?
  9. H

    I How Are Permutations Calculated in a Circular Seating Arrangement?

    2 boys and 3 girls are to be seated round a table with 5 seats. Each child occupies exactly one seat. In how many ways can this be done if (a) the 2 boys must be seated together (b) same as (a) but this time the seats are numbered Solution (a) ##\frac{4!}{4}2!## (b) ##\frac{4!}{4}2!\times 5##...
  10. J

    Normal force of a mass sliding down a quarter circle

    Homework Statement A 22-gram mass is released from rest at position A on a stationary frictionless surface whose shape is that of a quarter circle of radius R = 0.66 m. (b) Determine the magnitude of the normal force that acts on the mass when it is at position B (it is at position B when the...
  11. Matejxx1

    Maxima and minima and finding the radius of the circle

    Homework Statement Find where θ is the biggest (largest) I'll have the picture of the problem included below (pic:1) Homework Equations (x-q)2+(y+5/2)2=r2 answer x= 2 The Attempt at a Solution Hi, so my prefesor gave me this problem and told me to try to solve it. We already did this problem...
  12. MarkCJ

    Problem with length difference through circle

    Moved from non-homework section, so the homework template is missing. Distance difference between A and B must be 0.25 or 0.75, find length of A and B in any possible value within radius of circle. Is there a name of theory to find this problem? here's my try. for A at any point on...
  13. 1

    Why is there "weightlessness" on the top of a verticle circle?

    i'm ashamed, that i never understand this, eventhough I'm studying quantum mechanics... so... why is there "weightlessness" on the top of a verticle circular motion? ie, if a plane if flying in verticle circles, why is there weightlessness while on the top of a circular path? i mean, if it's...
  14. akashpandey

    I Understanding the Physical Meaning of Pi in a Circle

    I want to know that how to imply π in a circle. as we know that circumference/diameter= π . so how π has physical meaning in circle. as it condstant.
  15. G

    Cars: Wheel Angle & Turning Circle Radius

    My question is, if a car is moving at speed V, and its front wheels are at an angle (theta), what is the relationship between the angle of the wheels relative to them being parallel with the car and the radius of the circle at which the car goes around. Thanks.
  16. onemic

    B Unit Circle and Other Trig Questions

    When creating a right triangle in a unit circle how do you know where to place the leg from the terminal side? My textbook and Khan academy don't really explain this and it's just sort of assumed that I'd know. For example, If theta is equal to 135 degrees, where does the leg to complete the...
  17. S

    MHB Adjustments to lie within a circle

    Hello! In the topic I'm working on, I derived that the parameter $\sigma>0$ satisfies $$\sigma = \sqrt{\frac{\nu}{T} - \lambda(\mu^2+\delta^2)},$$ where $\nu>0$ denotes the variance and $T>0$ denotes the time. The parameters $\mu \in \mathbb{R}, \delta>0$ and $\lambda>0$ are parameters that I...
  18. Lucas94

    Make a circle in square that is split 8x8 parts?

    Sorry if i may sound little unclear, english is not my first langue. I I am looking for a way to create a circle that is in a square cut in 8x8 in matlab. I would be glad if someone could give me a hand. Thanks!
  19. P

    Mass moving back and forth at the bottom of a circle (Polar)

    Homework Statement A mass ##m## at the bottom of a circle of radius R moves back and forth with no friction and the follows the equation (where ##\alpha(t)## is small) ##\theta(t)=\frac{3\pi}{2}+\alpha(t)##. Find a differential equation using polar coordinates for ##\alpha(t)## which is linear...
  20. G

    Orthoprojection of circle onto a plane

    Homework Statement Show that the orthoprojection of a circle onto a plane is an ellipse Homework Equations Let's say the circle ##{\cal C}## of center ##O## and radius ##R## lies on plane ##P## and we want to orthoproject ##{\cal C}## onto ##P'## The Attempt at a Solution We can say that...
  21. sa1988

    Finding centre of (moving) circle

    Homework Statement Find the co-ordinate of the centre of the following circle as a function of time: x2+y2 = C + 2 t x Homework EquationsThe Attempt at a Solution No idea..! It's part of a fluid dynamics problem, which I don't need to explain here, other than to say I plotted it on...
  22. T

    Create Concentric Circles with Equal Distances

    Is it possible to create a concentric circles whereby all the objects on it have equal distance from each other? where the squares/rectangles are object and are equal distance from each other regardless on what circle they are on. Thanks!
  23. R

    Can Uniform Points on a Circle be Derived from the Standard Normal Distribution?

    Is it possible to derive the standard normal distribution from using polar form p = r*e^(i*v) to distribute uniform points along the contour of a circle? I've read that it is possible to randomize points like that using X and Y values with normal distribution by normalizing each point, but I...
  24. stvrbbns

    Relationship between velocity, acceleration, and a circle?

    The perimeter of a circle is 2πR (R=radius). [ref] Acceleration = Δv/Δt (v=velocity, t=time). [ref] Motion mathematics can always be reduced to multiple independent one-dimensional motions. [ref] The distance an object travels while accelerating = vit + at2/2 (a=acceleration, vi=initial...
  25. Cosmophile

    Kleppner/Kolenkow: Two Points Around a Circle

    Hey, all. I've decided to go back and work on some old K&K problems that I didn't finish last time. Here's a neat one that's been giving me trouble. I hadn't attempted problem a yet (I admittedly completely overlooked it by accident!). For b, I had a difficult time finding a good starting...
  26. E

    Integrals to Solve Area and Center of Mass of a Cut Circle

    Homework Statement I am after finding the centroid of the remaining area (hatched) when a circle is cut by a line. I made a diagram in CAD that demonstrates the problem. The idea is that, starting from the bottom of the circle, a cut is taken leaving a remaining shape whose area and...
  27. PhysicsBoyMan

    Area of circle using integration

    Homework Statement http://postimage.org/][/PLAIN] free picture upload 2. The attempt at a solution I want to go width times delta height. To do this I must describe width in terms of height. Here they used the Pythagorean theorem which is weird to me because I don't see a nice triangle...
  28. Arman777

    Moment of Inertia of Half Ring (Half Circle)

    Homework Statement Theres an object which makes a pendulum motion.Lets suppose we hang the mass to the ceiling.We released the object with inital angle 0 to the ceiling.(I mean the angle between the object and the ceiling is zero).Whats the moment of the Inertia to the point A. A is a...
  29. Jessica01

    Want to talk about unit circle

    Hi all, I was wandering on the web to collect some solid and justifiable reasons to answer a question "Why we always choose a unit circle."? I saw several websites and meanwhile I saw this post https://www.physicsforums.com/threads/trig-unit-circle-why.475575/. I saved it. But overall, I...
  30. droidofthevoid

    Velocity and Acceleration of a particle around a circle

    Homework Statement A particle moves with constant speed around a circle. When it is at the top of the circle, its coordinates are x=0 and y=2 and its velocity is 4(m/s) i. When it reaches the left hand of the circle, where its coordinates are now x=2 and y=0, what is its velocity and...
  31. S

    Average current by particle moving in circle

    Homework Statement A particle having charge 8 nC moves in circular orbit with angular speed of 100 π rad/s. Find the average current produced! a. 0.2 μA b. 0.3 μA c. 0.4 μA d. 0.5 μA e. 0.6 μA Homework Equations Q = I.t The Attempt at a Solution The equation I can think of is Q = I.t. I don't...
  32. S

    Circle/Sphere Touching: Perfection & Friction

    Theoretically, if you had a perfect circle, and a perfectly flat surface, wouldn't only one atom touch at a time (assuming friction can't take away the perfect circle/flat surface)? Personally this doesn't sound right, but I can't think of why it wouldn't.
  33. C

    Deriving the Equation for 2-D Elastic Collision Circle

    Homework Statement Hi there! In this exercise, we are supposed to derive this formula for a 2-D elastic with two different masses: (x-U*v1)^2 + y^2 = (Uv1)^2 (example, two billiard balls), the second mass is at rest. It's a equation which leads to a circle where all of the possible p2' lie...
  34. S

    Circle or polygon for charged particle in magnetic field....

    ...perpendicular to its path? OK; let's say you have any charged particle moving perpendicular to a magnetic field; does it describe a gigantic polygon or a perfect circle? I think it's a polygon; the particle absorbs a "quantum of force" from the magnetic field, so to speak, and changes...
  35. astrololo

    Simple circle problem involving area and circumference

    Homework Statement A stone is thrown into still water, forming ripples which travel from the center of disturbance in the form of circles. If the circumference of the circle which bounds the disturbed area is 10 ft and the circumference is increasing at the rate of 3 ft. per second, how fast is...
  36. Iconoclast

    B A circle in the Hubble Ultra Deep Field picture?

    I was analyzing the Hubble Ultra Deep field image and I realized that if you look at the image from a certain distance from your monitor, you can notice there is a ring of galaxies, forming a circle. The following are the HUDF image and an image where I try to show where I see the circle (it is...
  37. tomdodd4598

    Pendulum with Pivot Moving in Horizontal Circle

    Homework Statement The problem is the following: Using a Lagrangian, find the equations of motion of a mass hanging from a massless string, with the pendulum pivot moving in a horizontal circle at constant angular velocity. I take the mass to be m, the length of the string L, the radius of the...
  38. J

    Length of a line between origin and edge of a circle

    For a circle with radius R centered at R along the X-axis so that the edge of the circle touches the origin, what is the length of a line drawn between the origin and an edge of the circle in terms of the angle between that line and the X-axis? This isn't a homework problem, just something I'm...
  39. 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?
  40. C

    B Do curves, circles and spheres really exist?

    Obviously, they exist as mathematical concepts, and those concepts are real, but in physical reality, everything is made up of subatomic particles and, if the theory is ever verified, strings. So if you try to construct a curve, circle or sphere, you are necessarily stacking a bunch of subatomic...
  41. M

    MHB Inscribed circle in the triangle

    In the triangle a point I is a centre of inscribed circle. A line AI meets a segment BC in a point D. A bisector of AD meets lines BI and CI respectively in a points P and Q. Prove that heights of triangle PQD meet in the point I. I've tried to show that sides of triangle PQD are parallel to...
  42. B

    Question About Unit Circle (CircularFunction) of a Trig Func

    Please take a look below example (the attached image below). How do I know that the angle ##\sin (\frac{7π}{4})## is corresponds to the coordinates ##(\frac{\sqrt {2}}{2}, -\frac{\sqrt{2}}{2})##? I know that ##\frac{7π}{4}## is 315°.
  43. J

    A circle in a non-euclidean geometry

    Homework Statement Consider a universe described by the Friedmann-Robertson-Walker metric which describes an open, closed, or at universe, depending on the value of k: $$ds^2=a^2(t)[\frac{dr^2}{1-kr^2}+r^2(d\theta^2+sin^2\theta d\phi^2)]$$ This problem will involve only the geometry of space at...
  44. adi adi

    Arc Length Circle Quadrant 1: Solve ∫√(1+(dy/dx)2)dx

    Homework Statement find the arc length of a circle in the first quadrant with an equation x2 + y2 = a2 Homework Equations arc length = ∫ √(1 + (dy/dx)2) dx The Attempt at a Solution i got stuck on how to solve the integral
  45. C

    Two blocks connected by springs moving in a circle

    Homework Statement Block A and block B are on a frictionless table as shown in Figure 2. Spring 1 connects block A to a frictionless peg at 0 and spring 2 connects block A and block B. Their masses are respectively mA=0:45 kg and mB=0:32 kg. When the blocks are in uniform circular motion about...
  46. A

    Centripetal Forces and the Bucket in a Circle

    Homework Statement I was watching a video on centripetal forces, and at one point in the video, the instructor poses a question where he shows a bucket filled with water which requires an Fnet of 3N towards the center to keep the water in the bucket. At one point in the video (please seek to...
  47. D

    Can a Charge in a Wire Move in a Circle Due to Lorentz Force?

    There is a frame that circles around a point because of the Lorentz force. Frame is placed between North and South magnets and there is s current flowing in a frame. My question is - can a charge in a wire move in a circle - for instance clockwise? I mean, if the square frame turns, then the...
  48. S

    Can a 4 base circle camshaft affect rocker ratio and lobe profiles?

    Hi can anyone help me with info on the cause & effects of using a large 4" vs small 2" base circle camshaft. I want to know if I can use less rocker ratio and what software is used to look at lobe profiles- example a .5 inch lift lobe with a 2 inch base circle and a 1.75 rocker ratio (.875 lift)...
  49. I

    Rock Mechanics: Mohrs Stress Circle - Principal Stresses

    Homework Statement A series of shear tests were performed on a weak rock. Each test was carried out until the sample sheared, and the principal stresses for each test were: S. No.--- σ3 (KN/m2) --- σ1 (KN/m2) 1 --- 200 --- 570 2 --- 300...
  50. R

    MHB Angle between the tangents to the circle

    Hi everyone, I need further explanations about the answer of this problem. The answer is angle T = 87.9 degrees. Thanks.
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