What is Circles: Definition and 308 Discussions

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

    B What would need to be possible to make a cube of circles?

    in what geometry would a cube of circles be possible
  2. S

    Radii of stacked circles inside the graph of y = |x|^1.5

    (a) The hint from question is to used geometrical argument. From the graph, I can see ##r_1+r_2=c_2-c_1## but I doubt it will be usefule since the limit is ##\frac{r_2}{r_1} \rightarrow 1##, not in term of ##c##. I also tried to calculate the limit directly (not using geometrical argument at...
  3. C

    Limit problem involving two circles and a line

    For this problem, The limiting position of R is (4,0). However, I am trying to solve this problem using a method that is different to the solutions. So far I have got, ##C_1: (x - 1)^2 + y^2 = 1## ##C_2: x^2 + y^2 = r^2## To find the equation of PQ, ## P(0,r) ## and ##R(R,0) ## ## y =...
  4. M

    My proof of the Geometry-Real Analysis theorem

    Consider a convex shape ##S## of positive area ##A## inside the unit square. Let ##a≤1## be the supremum of all subsets of the unit square that can be obtained as disjoint union of finitely many scaled and translated copies of ##S##. Partition the square into ##n×n## smaller squares (see...
  5. L

    Work to bring a charge to the center of two quarter circles

    By measuring angle \theta from the positive ##x## axis counterclockwise as usual, I get ##d\vec{E}=k( (\lambda_2-\lambda_1)\cos(\theta)d\theta, (\lambda_2-\lambda_1)\sin(\theta)d\theta )## and by integrating from ##\theta=0## to ##\theta=\frac{\pi}{2}## I get...
  6. karush

    MHB What are the coordinates of points equidistant from (1,0) and (5,4)?

    Find the coordinates of all points whose distance form (1,0) is $\sqrt{10}$ and whose distance is from (5.4) is $\sqrt{10}$ ok assume first we convert the info to (2) general eq of a circle $(x-h)^2+(y-k)^2=r^2$ so we have $(x-1)^2+(y-0)^2=10$ and $(x-4)^2+(y-4)^2=10$edit:took out tikz
  7. M

    MHB Adam's Circles: Splitting & Connecting Segments

    Adam has a circle of radius $1$ centered at the origin. - First, he draws $6$ segments from the origin to the boundary of the circle, which splits the upper (positive $y$) semicircle into $7$ equal pieces. - Next, starting from each point where a segment hit the circle, he draws an...
  8. karush

    MHB 2.4.10 3 circles one intersection

    $\tiny{\textbf{2.4.10}}$ $\begin{array}{rl} (x+4)^2+(y+11)^2&=169 \\ (x-9)^2+(y+5)^2&=100 \\ (x-4)^2+(y-5)^2&=25 \end{array}$ ok i solved this by a lot of steps and got (1,1) as the intersection of all 3 circles these has got to be other options to this. basically I expanded the...
  9. H

    MHB Area of multiple circles inside a rectangle

    Figure shows six identical circles inside a rectangle. The radius of each circle is 24 cm. The radius of the circles is the greatest possible radius so that the circles fit inside the rectangle. The six circles form the pattern shown in Figure so that • each circle touches at least two other...
  10. K

    MHB Distance between the centers of two circles

    Hello, everybody: I am a philologist who is fond of mathematics, but who unfortunately has just an elementary high school knowledge of them. I am translating La leçon de Platon, by Dom Néroman (La Bégude de Mazenc, Arma Artis, 2002), which deals with music theory and mathematics in the works of...
  11. G

    MHB How can I find angles in circles?

    Please Help.. I am struggling to answer this inspite of trying to re read theorems.. I couldn't answer anything.. if you can solve this please teach me the steps. So i could answer them in the future..
  12. M

    MHB How Do Constraints and Graphs Relate to Concentric Circles?

    Two concentric circles have radii x and y, where y > x. The area between the circles is at least 10 square units. (a) Write a system of inequalities that describes the constraints on the circles. What does the word CONSTRAINTS mean here? (b) Identify the graph of the line in relation to...
  13. J

    I Why does wind blow leaves in circles?

    Earlier today I realized that, when a strong gust of wind would blow through my area, it would pick up leaves off the ground and typically blow them in circular patterns, and typically the leaves would go in at least several complete circles before coming to rest back down on the ground. Why is...
  14. STEM_nerd

    A math problem related to circles

    Summary:: If a circle can be inscribed in a parallelogram how will the parallelogram change? Explain. It is a 10th grade math question in case you want to know.
  15. Saracen Rue

    Area remaining of a quarter-circle deprived of these 3 inscribed circles

    Summary:: Calculate the percentage of area remaining when a quarter-cirlce is deprived of 1 large circles and 2 smaller circles. Hi, I'm not sure if this is the right subforum for this question but it seemed to be the one that fit the best. Please consider the following diagram: Before...
  16. O

    MHB Relationship between inner and outer radius of a two concentric circles

    If i have two circles that say 24" apart from each other. one inside the other. and i know the radius of the inside circel, how can i calculate the outside radius
  17. S

    I Is it possible to calculate this geometrical relationship between circles?

    A large cirlcle with radius 50 m contains a smaller circle with radius 7.4 m that is tangent to its surface internally. Is it possible to calculate what number of the small circle the larger circle can contain iside it in which all are tangent to its surface ... but without using trig. Functions
  18. karush

    MHB -gre.ge.3 Circles Find the shaded area as a fraction

    Ok this is considered a "hard" GRE geometry question... notice there are no dimensions How would you solve this in the fewest steps?
  19. karush

    MHB -3 circles centers on line segment PQ

    it was done by simple observation typos maybe,,,, Also, posted on MeWe and Linkedin
  20. L

    Find the radius of 2 circles

    Middle point of (1,3)(2,4) is (1.5, 3.5) r1 to r2 passing through (1.5, 3.5) I cannot grasp on what should i do to find r1 and r2 from the line Without graph*
  21. karush

    MHB 39 intersection of 3 circles

    studying with a friend there was the intersection of 3 circles problem which is in common usage here is my overleaf output I was wondering if this could be solved with a matrix in that it has squares in it or is there a standard equation for finding the intersection of 3 circles given the...
  22. Z

    MHB Find the exact shaded area of the region in 4 overlapping circles

    So, say you got 4 circles intersecting this way: Now, I am looking for two things: A proof that each part of the circle which is in an intersection is 1/4 the size of the whole circle's circumference The exact area of the non-shaded region. Now, in my search to finding the answer to...
  23. Z

    MHB The height of a section of overlapping circles.

    Say I have two identical circles, both of radii of one, overlapping, as shown in the diagram below: In this diagram, x is the circumference of the circles, and the bit of the bottom circle which is drawn blue (the overlapping bit) is 1/6th of the whole circumference. What I'm looking for is...
  24. Calculuser

    I Family of Circles at Two Points

    As I was flipping through pages of my analytic geometry book from high school, in circle section I stumbled across the formula of "family of circles intersecting at two points" with two circles (##x^2 + y^2 + D_1 x + E_1 y + F_1 = 0## , ##x^2 + y^2 + D_2 x + E_2 y + F_2 = 0##) known to intersect...
  25. W

    MHB Circles in a square and diameter of the circle

    A circle is inscribed in a square with sides = 40. A smaller (of course!) circle tangent to the above circle and 2 sides of the square is inscribed in one of the corners of the square. What is the diameter of this circle?
  26. V

    B Universe Moving in Circles? Exploring 4th Dimension

    Well I was thinking everything is moving in circle or ellipse, is universe also in such motion? If so it may be moving on a different dimension fourth one maybe on time, where time would be a physical quantity, a closed loop on which universe is revolving and repeating every single point as we...
  27. M

    MHB Interval of eigenvalues using Gershgorin circles

    Hey! :o We have the matrix $$A=\begin{pmatrix}2 & 0.4 & -0.1 & 0.3 \\ 0.3 & 3 & -0.1 & 0.2 \\ 0 & 0.7 & 3 & 1 \\ 0.2 & 0.1 & 0 & 4\end{pmatrix}$$ We get the row Gershgorin circles: $$K_1=\{z\in \mathbb{C} : |z-2|\leq 0.8 \} \\ K_2=\{z\in \mathbb{C} : |z-3|\leq 0.6 \} \\ K_3=\{z\in \mathbb{C} ...
  28. S

    Do programming trends just go in circles?

    Latest buzzwords include "functional programming" and "stateless." What's funny is these are not new, just a reversion from OOP back to procedural programming the way you write code in C. Create objects that are just value bags with no behavior and write functions that modify the values. Or...
  29. R

    A non-intersecting family of circles

    Mentor note: Moved from a technical math section. What is the proof that the family of circles out of two non-intersecting circles, no two circles in that family intersect. Say S1 = x^2 + y^2 - 8x + 7 = 0 (i.e center at (4,0) and radius = 3 ) S2 = x^2 + y^2 - 24x + 135 = 0 ( i.e center...
  30. Felipe Lincoln

    Newton's law and double stars moving in circles

    Homework Statement The two components of a double star are observed to move in circles of radii ##r_1## and ##r_2##. What is the ratio of their masses? (Hint: Write down their accelerations in terms of the angular velocity of rotation ##\omega##) Homework Equations ##m\ddot{\vec{x}}=...
  31. G

    Angles inscribed in circles part 1

    Homework Statement OK, I am new to these kinds of problems and I am trying to learn the appropriate properties but they are proving somewhat difficult for me... I hope I am going in the right direction. Homework Equations [/B] The first problem corresponds to the figure with 'Rep' in the...
  32. A

    Which is harder to pull apart, a circle or a triangle?

    In deciding which shape of ring I should use to secure an anchor to an anchor trolley I came across two choices, a circular ring or a triangular ring. While either will surely work, I began to wonder which would be more difficult to pull apart. Most of the information I found is about forces...
  33. C

    MHB Secant and Tangent Angles in Circles, finding an arc length.

    I got 138.17, but that isn't correct. I don't know how to do it, since the only way I thought, gave me the wrong answer. Can anyone help?
  34. V

    B Two waves moving at right angles go in circles?

    ylet x = Asinx, y = Acosx, apparently x^2 + y^2 = A^2 so this combination goes in circles. wot? creating waves in a pool 90 degrees off and out of phase by 90 will make it move in circles? I'm skeptical, anyone have a video of an experiment that demonstrates this?
  35. Pedgepoke

    Vertical Circles Centripetal Acceleration

    Homework Statement A jet pilot takes his aircraft in a vertical loop. V is 840 km/hr (233.3 m/s) find the min. radius of the loop to that the centripetal acceleration at the bottom does not exceed 6 Gs. Homework Equations a = v^2 / r F = ma The Attempt at a Solution I don't know where to...
  36. R

    Intersecting circles using Newton's Method

    Homework Statement Homework EquationsThe Attempt at a Solution My initial thought was to set the two equations equal to each other but the resulting equation is linear which gives a constant for a Newton iteration. I thought about Taylor's theorem in 2-d but I'm not so sure about that as far...
  37. C

    I keep runing in circles around this optic fiber question....

    Hi everyone I can not seem to get the right formulas to finish this question. I keep on beating my head against a wall for hours now. It just feels like I can not get the right formula to help me out...Is this some sort of trick question? Note if the image does not load here is the link ->...
  38. M

    I Calculating area of multiple connected circles

    Hopefully this is a challenging maths problem for someone. This problem is to compare the surface area of the 4 identical circles with the circle overlayed drawn in pencil. The attached image shows 4 circles, each with diameter x. To solve the problem, I need to calculate the maximum separation...
  39. H

    How to find the radii of these 2 circles given 2 known points

    Homework Statement Homework Equations y-y1 = m (x-x1) ---> line equation $$ (x - a)^2 + (y-b)^2 = r^2 $$ ---> circle equationThe Attempt at a Solution I tried to draw the triangles using, (1, 3) (2, 4) and (0, b) (0, b) is the tangent point to y-axisand used those points for making...
  40. R

    B Dimension of subset containing two circles

    So I am reading a calculus book, and went online to find explanations for why a circle is 1D. Theres the explanations that say something about zooming in very close and seeing that it's indistinguishable from a Real line. Or you can specify any point on it with only one variable Or if there was...
  41. jamalkoiyess

    MATLAB How to create distinct circles in Matlab?

    I want to create a plate of distinct circles on Matlab where their radii are generated by randn(1,p) and centers are random. I am currently doing the circles using viscircles, but some of them are overlapping, and since I want approximately 100 ones, this problem only gets worse. How can I make...
  42. Mario

    Circles and Euler spiral (repost from general math)

    Hi, i have this problem..., giving two circle (example radius 1 = 500 units, radius 2 = 200 units, distance between centers = 275.73 units) find Euler Spiral (aka Cornu spiral, aka Clothoid https://en.wikipedia.org/wiki/Euler_spiral) tangent giving circle (unknown tangent points). For this...
  43. Z

    Java Draw circles at end Point of Line with End Points as Centre

    Hi, I am trying to draw circles at the end points of a line but circle centre is not exactly on the end point of the line. Can somebody please guide me. import java.applet.Applet; import java.awt.*; import javax.swing.*; public class JCircle extends Applet{ int x1=30; int y1=30...
  44. ThunderLight

    MATLAB How to spin the colormap in 2 different circles in matlab

    Hi, I'm trying to rotate 2 different plotted circles in matlab, which have the Jet colourmap. Colormap has the Spinmap function, but when I use it, it only spins the Jet colormap in 1 circle, leaving out the other. I would like to spin the Jet colormap in2 different circles in opposite...
  45. D

    What is the angle of perspective for circles in a view of The London Eye?

    Good Morning everybody. I hope that this thread is of interest. I am a retired architect with an interest in Mathematics. My picture shows a view of The London Eye. We know that it views as an ellipse but the major axis (drawn), clearly is not at right angles to the axis of the wheel and if you...
  46. FritoTaco

    How can I prevent overlapping circles in a JApplet program?

    Hello, I have this program where you run the JApplet and it makes circles at random. When you click the "Generate" button, it makes another set of random circles. The problem is, it overlaps the previous set of circles. I want the program to get rid of the previous set and I can't figure out...
  47. R

    B Do all auroras occur in circles?

    Do the formation of auroras always occur in circles/ovals/ellipses?? What causes the shape of their formation?
  48. caters

    Solve for unknown radius without trig

    Homework Statement What is the next radius outwards of this Apollonian gasket? R = radius of outer circle = 5 r1 = radius of largest inner circle = 3 r2 = radius of second largest inner circle = 1 a = unknown radius Homework Equations C = 2πr A = πr2 d = 2r The Attempt at a Solution Make a...
  49. Monoxdifly

    MHB [ASK] About Circles in Coordinates

    3. A(a,b), B(-a,-b), and C is plane XOY. P moves along with curve C. If the multiplication product of PA's and PB's gradients are always k, C is a circle only if k = ...? 4. The radius of a circle which meets X-axis at (6,0) and meets the curve y=\sqrt{3x} at one point is ... 5. A circle meets...