Circles Definition and 310 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. C

    Geometry Problem involving packing Hexagons into Circles

    Hello All, I have been give a particular task with packing hexagonal shapes with radius 0.105m, into different circular areas. This is not a 3D problem, and I have been trying to search for answers on the topic of "packing" but haven't seemed to find any that fit my requirements. So the idea...
  2. E

    Using radians to discover the lengths of geometric shapes (circles)

    Homework Statement refer to question image Homework Equations refer to question image againThe Attempt at a Solution refer to working out image This is my brothers maths homework. He normally doesn't use online methods to request help and this is his first time.
  3. R

    Calculation of circles parameters embedded in 2 rotating discs?

    The next situation is presented 2 big circles (blue ones) are rotating in different directions. The left one is rotating clockwise and the right one rotates counter clockwise. Inside the 2 big circles, 2 small circles (pink ones) are embedded...
  4. A

    MHB Two different circles in the plane with nonempty intersection

    Hi. Here is a problem I've been trying to solve for some time now. Maybe you could help me. We have two sets \mathcal {Q} is a set of those circles in the plane such that for any x \in \mathbb{R} there exists a circle O \in \mathcal {Q} which intersects x axis in (x,0).\mathcal {T} is a set of...
  5. N

    Linear regression to radii of multiple circles

    Hi, I am trying to simulate muon paths through drift tubes and I have ran into a problem performing a linear regression. I have generated simulated muon trajectories in 2 dimensions and they passes through my simulated drift tubes represented as black circles with a '+' in the center. As the...
  6. F

    Focusing at infinity for a camera and circles of confusion

    Hello Forum, when a camera is focused at "infinity", everything from infinity on is in focus (acceptable). How is that possible? Every plane that is not in perfect focus has a certain circle of confusion that gets larger (more blurring) as we move away from the best focus plane... Also...
  7. S

    Circles on XY, YZ and XZ planes from a Sphere

    I want to find the equations for the circles (formed on the planes) when a sphere cuts the XY, YZ and XZ planes. What I am trying to achieve is a software application that will have a 3D cuboid and inside this cuboid there will be many spheres. Now I want to find the circles created by these...
  8. caffeinemachine

    MHB Two circles intersecting, a lot of lines.

    Let two circles $T_1$ and $T_2$, ($T_1$ is smaller than $T_2$), intersect at points $C$ and $E$. Let the tangent to $T_1$ at $C$ meet $T_2$ at $A$. From $A$ another tangent to $T_1$ is drawn which touches $T_1$ at $B$ and meets $T_2$ again at $D$. Let $F$ be the foot of perpendicular from $B$ to...
  9. R

    Irrational circles about the orgin

    I recall a post previously where the Op was wondering if any circle about the orgin having an irrational radius could pass through a rational point. The answer then was if the irrational radius was the square root of the sum of two rational squares then of course. Now I am wondering what if...
  10. S

    Are my postulates true regarding circles?

    If we know the exact radius of a circle, then we can't have an exact circumference, and if we know the exact circumference, then we can't know the exact radius. If these postulates are true, then I realize that this idea is not original but probably known since B.C.
  11. D

    MHB Optimizing Triangle Area on a Circle: Finding the Minimum with Tangents

    Tangents are drawn to the circle $x^2+y^2=32$ from a point $A$ lying on the x-axis. The tangents cut the y-axis at a point $B$ and $C$, then find the coordinate(s) of $A$ such that the area of $\Delta ABC$ is minimum.
  12. L

    Double integration of circles, spheres etc

    Homework Statement So I have three questions. The first one is the double integration of x+2 from y=0 to y=sqrt(9^2-x^2). The second question is the double integration of sqrt(r^2-x^2-y^2) where the domain is in the circle of radius R and origin 0. And the last question is the double...
  13. S

    Small mass attached to a string sliding between two circles

    Homework Statement A small mass M attached to a string slides in a circle (Y) on a frictionless horizontal table, with the force F providing the necessary tension (see figure). The force is then decreased slowly and then maintained constant when M travels around in circle (X). The radius of...
  14. V

    Tangent Lines of Two Circles Intersect At Point

    Homework Statement The tangent lines of two circles intersect at point (11/3,2/3). What are the two points that each tangent line touches on its respective circle? Homework Equations Circle 1: x^2 + (y-3)^2 =5 Circle 2: (x-2)^2 + (y+3)^2 = 2 The Attempt at a Solution I found the...
  15. D

    How can I plot a perfect circle in a 2D array using Visual Basic?

    hi,I am learning visual basic as a pastime. I have a question,I can plot positions in a 2 dimensional array e.g:- dim test(100,100) as integer for cox as integer = 40 to 60 for coy as integer = 40 to 60 test(cox,coy)=1 next cox next coy My question is how can I plot positions to make...
  16. O

    Equation of osculating circles

    Homework Statement Find equations of the osculating circles of the ellipse 9x^2 + 4y^2 = 36 at the points (2,0) (0,3) as far as I understand I need to get T and N at some point on the curve, cross them to get B and use that + a point to write a equation of plane i don't know know...
  17. L

    Hypocycloid Equations required to form system of three rotating circles

    Hi there, I have never worked with Hypocycloids before so I'm unsure which equations I should be using; but I'll try and get across what I am trying to build. Essentially I am trying to create a series of hypocycloids that act in a similar manner to the "spirograph". Goal: Three circles...
  18. nukeman

    Quick question about finding distance between the centres of 2 circles?

    Homework Statement Lets say you have the equation of 2 circles ok, and it asks you to find the distance between the centres of the 2 circles. Is that what you do...? 1) Find the center of each circle by completing the sqaure. 2) Enter those 2 centres into a distance formula: d =...
  19. D

    Finding equation of osculating circles of ellipse

    Homework Statement Find the equations of the osculating circles of the ellipse 9x^2 + 4y^2 =36 at the points (2,0) and (0,3) Homework Equations The Attempt at a Solution I honestly have no idea what to do here. This problem is in the chapter relating to curvature and arc length...
  20. K

    Finding the Area of a Triangle Inside a Circle and Parallel Line: How to Solve?

    1.There is a circle with the equation x^2 + y^2 - 2ax = 0. A line is drawn through the centre of the circle which is parallel to the line x+2y=0. and also intersects the circle at A and B. Find the area of the triangle AOB. My attempt- I calculated the slope of the given line(-1/2).So the...
  21. T

    Have crop circles been debunked yet?

    How could such large intricate patterns spring up overnight? If humans are doing them, which kind of machines could they possibly be using? These circles usually have the cut crops removed.
  22. G

    How to Find the Normal Force of a Spring on a Ball in a Non-Concentric Slot?

    Hey guys, i'm building an apparatus with a sliding pin containing a spring and a ball. I want to lock in two different positions so I've rounded two slots in the housings. I would like to know what is the equation two find the normal force of the spring on the ball depending on the displacement...
  23. A

    Calculating the points of tangency for two circles given a picture

    I have two circles with the same radius and I want to calculate the points of tangency. For example, in the picture below, I want to calculate (x3,y3) and (x4,y4). I have the radius and the distance between the two circles as shown below:
  24. M

    Equations of alternating half circles

    I working on a final project for vector calculus and am stuck on the equation of my line. I have made a 3d model of -sin (sqrt(x^2+y^2) on top of a circle with D 10.3125 the kicker is instead of a sin I made it with connecting half circles with D 47/32. I need help with the formula before I...
  25. R

    Convergence of Circle Areas in a Boundary Defined by y=1/x and x=0, y=0

    I thought of a problem a few days ago and I have no idea as to its solution. I posted this on Reddit and xkcd forums earlier but not much has been solved apart from the area of one circle. Suppose you have a boundary formed by the curve y=e^(-x), and the lines x=0 and y=0. In this boundary you...
  26. G

    Prove some relations but going round in circles

    Homework Statement I need to prove some relations but going round in circles. ## [\hat{J}_z, \hat{J}_+] = \hbar J_+ ## I've got this: ##\left(a_+^{\dagger }a_+-a_-^{\dagger }a_-\right)\left(a_+^{\dagger }a_-\right)-\left(a_+^{\dagger }a_-\right)\left(a_+^{\dagger }a_+-a_-^{\dagger...
  27. S

    Bizarre Oscillating Circles Above US

    Greetings to all! I bring you all very strange and very peculiar tidings! I'll jump right into it: Over the course of the last two days, a small group of friends have been examining what appears to be a collection of magnetic disturbances over the south-eastern region of the United States...
  28. L

    Circular Motion,Uniform motion in Vertical Circles

    Homework Statement If the object is at the top, the centripetal force (pointing as always towards the centre) is down and negative. ● If the object is at the bottom, the centripetal force is pointing up and positiveThe Attempt at a Solution I thought any force towards the center is always...
  29. F

    Plan Sprinkler System Layout: Minimize # Circles for Max Coverage

    I have to plan the layout of a sprinkler system. Basically, each sprinkler shoots a radius of 7.5 feet water, and I want every part of the floor covered with water. How can I use the least number of sprinklers?
  30. C

    Transforming Lines to Circles in the w-plane

    Homework Statement "The transformation T from the z-plane to the w-plane is given by w=\frac{1}{Z-2} where Z=x+iy and w=u+iv Show that under T the straight line with equation 2x+y=5 is transformed to a circle in the w-plane with centre \left ( 1,-\frac{1}{2} \right ) and radius...
  31. J

    Calculating Tension of a bob moving in horizontal circles

    Could someone please look at the problem below and see if i am on the right lines of solving it? I am finding the whole subject of circular motion hard to get my head around and therefore not 100% confident in my workings. I have also attached my free body diagram. Homework Statement...
  32. S

    Motion in circles mechanical engineering

    first time guys. i have a disc with a bearing and a shaft through it. the disc is rotating in simple harmonic motion with a dynamic force of 14400N and speed of 2.43 rpm. i need to use electromagnets to stop this disc from rotating. questions. -where or can can i get electromagnets to stop...
  33. T

    Finding the Length of a Vector using Inner Products and Circles

    Mostly I'd like to look at the third part of the problem. I'm not sure if this is the correct way to derive the equation: So, finding the length of a given vector given this inner product: <(x,y),(x,y)> = 5x^2 + y^2. Taking the length, we have |(x,y)| = \sqrt{5x^2 + y^2}, which we define as...
  34. Evo

    History 12,000 year old megalith circles turn knowledge of ancient humans upside down

    This is incredible. This archaeological find predates Stonehenge and the Great pyramids by 6,000 years and makes Stonhenge look like rubble in comparison to this 12,000 year old find. It's before stoneage man had agriculture, before the wheel, a time of hunter gatherers. This site brings up...
  35. D

    What is the Overlapping Range of Two Radio Transmitters?

    Homework Statement Two radio transmitters, one with a 40 mile range and one with a 60 mile range, stand 80 miles apart. you are driving 60 miles per hours on a highway parallel to the line segment connecting the two towers. How long will you be within the range of both transmitters...
  36. S

    Efficiently Calculate Radian Circles | Part B Explanation

    for part b I'm not sure how to do it any hints on how to do it? I've tried using sine rule etc but I'm just guessing, and I'm pretty sure there is a more simple method.
  37. S

    MHB Geometry: Integrating the Seed of Life with Circles

    Identify one (1) lesson on circles that could integrate the Seed of Life in the delivery of the lesson. I need help on this urgently
  38. P

    What is the distance of the tangent between two circles

    related equations and formulas http://en.wikipedia.org/wiki/Belt_problem#Pulley_problem image http://upload.wikimedia.org/wikipedia/en/0/07/Straight_Belt_pully_diagram.GIF so, i need to know the equation for finding the length of the tangent. please read...
  39. Y

    Resulting directions and velocities of two circles colliding

    Homework Statement I am trying to find the resulting x and y velocities when two moving circles (particles) which are exactly the same in mass and size and are in the same plane, collide, given the x and y velocities and coordinates of the two particles. What is the formula for the resulting...
  40. Y

    Resulting directions and velocities of two circles colliding

    Hi everybody, I am trying to find the resulting x and y velocities when two moving circles (particles) which are exactly the same and are in the same plane, collide. They are not (necessarily) hitting head on. I am trying to implement this in a 2d computer simulation. I have the x and y...
  41. D

    Caluclating tension in string that is moving in horizontal circles.

    Hi all, First of all I'd like to say thank you to you all for providing a great forum which has been a great help to me working through my ics home learning course. As i have learned on here and other places on the internet the information I have in my course materials is not always...
  42. S

    Rotating Tangent Circles: How Many Revolutions to Return to Same Position?

    I've been thinking about these problems for a long time but I really can't wrap my mind around them. Please share your insights! Consider a circle of radius R/8 internally tangent (inside) a circle of radius R. How many rotations does it take for small circle to return to the same position...
  43. R

    Magnetism and Circular Motion: Exploring IronMan's Technology

    I was watching some FX yesterday and Robert Downey's best, IronMan was on. I got to thinking, if possible, how does his little energy producing circle actually works. The idea is this: Picture a circle lined with magnets all facing negatively inward. In the center is a blade with parallel...
  44. T

    Complex Matrices and Unit Circles

    Homework Statement What can you say about a. the sum of a complex number and its conjugate? b. the conjugate of anumber on the unit circle? c. the product of two numbers on the unit circle? d. the sum of two numbers on the unit circle? Homework Equations The Attempt at a...
  45. J

    Question on 3 circles with changing values

    Hey everyone, my friend found this math problem that he couldn't figure out and gave to me. I thought it was quite interesting. So far I haven't been able to find a way to get into it though. There's a circle, C1, with centre O and radius r. Point Y is anywhere outside the circle. Circle C3 has...
  46. J

    Proving two circles are orthogonal

    Homework Statement Homework Equations The Attempt at a Solution Here's an image of what I need to show. I know I need to show that the segment from the center of the smaller circle to F forms a right angle with line segment CF. Alternatively I could show that line segment CH forms a right...
  47. S

    Circles in an equilateral triangle.

    Homework Statement Three triangles are placed into a circle; The vertices of the triangle are tangential to each circle. How do you find the ratio of the area of the circles to that of the triangle? Homework Equations pi r^2, 1/2(b)(h), sqrt3/4 * a^2 (2r^2). The Attempt at a...
  48. V

    Proof in circles and tangents?

    there is a circle say S1,there is a point P outside circle. Two tangents are drawn from the point P to the circle. These two tangents touches circles S1 at Q and R. A circle is made through P,Q,R. proof that circle is passing through center of S1. I have tried to put some triangles congruent...
  49. P

    Homemorphism between the set of circles with rational points and rectangles

    I am trying to solve a problem in which we need to prove that the set of all circles with rational points and radii is homemorphic to the set of all rectangles with vertices at rational points with the length of the diagonals as rational number. I am not able to figure out what the approach...
  50. J

    Tension in a string attached to a bob moving in horizontal circles

    Homework Statement Calculate the tension in a 2m string attached to a 2kg bob that is moving in horizontal circles of 0.5m radius. Homework Equations I thought it was F=MA but the working out shows all sorts The Attempt at a Solution I know the answer is 78.4N but don't know...
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