# Questions tagged [circles]

For questions concerning circles. A circle is the locus of points in a plane that are at a fixed distance from a fixed point.

685 questions
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### How to calculate the fundamental group of $S^3$ without two linked cirles

I need to find: the fundamental group of the space obtained by cutting out the three-dimensional $S^3$ sphere of two circles, once linked with each other. Can you help me? I have no idea about it, i ...
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### Comparing The Rates at Which Squares and Circles Fill Large Similar Areas.

Consider these two search patterns. ${\square}$ A square moves in straight lines forming what you might call a "square-spiral" pattern as it covers a much larger square space. ${\bigcirc}$ A circle ...
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### Inverse with respect to a given circle

Determine the inverse with respect to a given circle $g:\mathbb{R}^{2} \to \mathbb{R}^{+}, g(x,y)=x^{2}+y^{2}$. I have looked around for non geometric derivations without finding any of value. Anyone ...
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### Proof: At most 3 circles of radius 1/2 fit into the interior of a halfcircle of radius 1

It is a well known fact that at most 7 interior disjoint circles of radius 1/2 can be centered in a circle of radius 1; note that they don't need to be fully contained in the radius 1 circle. I am ...
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### Pre calculus Unit Circle

Suppose that you did not have the Unit Circle on Circle A, but rather a circle of radius $5$. Will the angle measures in degrees and/or radians change? Why or why not? Suppose that you did not have ...
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### Count balls to put in triangle

Given balls of radius $R$ we need to find how many balls can be put into a triangular container with sides $a,b$ and $c$. Example : Let $R=1$ and $a=3,b=4$ and $c=5$ then answer is $1$, as only one ...
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### Equation for Circle in 3D Space Given Center, Radius, and Point

I'm looking for how to derive the equation of a circle, in 3D space, given the following information: The Center Point The Radius One point on the circle I understand that this is functionally the ...
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### Trilateration question help

Kind of stuck n this question, I just got the circle equation written down for the robot don't know what to do from here. A bicycle robot is travelling on a circle centred at the origin and with a ...
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### arrange div elements in circle and square

I n number of divs which are arranged in a circle using javascript. Right now i set the dimension of each div to 40*40. Below is what i am able to achieve so far. This is how i find X & Y of each ...
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### Family of circles touching a line

I found this in a book but I am not able to understand how they got this result. It goes the equation family of circles touching a given line $(y-y_1)=m(x-x_1)$ at $(x_1,y_1)$ for any value of $m$ is ...
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### angles subtending arcs at the circumference and centre

$A$ and $B$ are two points on the circumference of a circle center $O$. $C$ is a point on the major arc $AB$. Draw the lines $AC$, $BC$, $AO$, $BO$, and $CO$, extending the last line to a point $D$ ...
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### draw a circle using beizer curve and co-ordinate of control points

I want to draw a circle of radius R centered at the origin using Bezier Curve Segments. I have to draw the circle using four Bezier Curve segments - one for each quadrant as shown in the following ...
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### Grid overlay on an annulus. Move n squares to create a sector that is closest to the area of the original.

I want to create an image in photoshop, and need to break an annulus, pictured below, into smaller segments. I can use other methods to find the solution, but I'm interested to see how mathematicians ...
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### Is there a relation for when a circle intersects more than half the perimeter/circumference of another circle?

Is there some nice formula or algoritm for determining when a circle "hides"/intersects more than half of the perimeter of another circle, in a circle-circle interaction. Example image: Two example ...
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### (PA)^2 + (PB)^2 +(PC)^2 + (PD)^2 is equal to?

A circle is inscribed into the rhombus ABCD with one angle 60. The distance from the centre of the circle to the narest vertex is equal to 1. If P is any point of the circle ,then (PA)^2 + (PB)^2 +(...
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### Problems with Circles and Lines on a Cartesian Plane

(a) Find the equations of the two circles each of which touches both coordinate axes and passes through the point $(9,2)$. (b) Find the coordinates of the second point of intersection of the two ...
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### Apollonius Circle help

I have been given a question which is very similar to this: Apollonius circle, its radius and center However, I have been told to translate and scale the given circle to give a unit circle centred ...
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### Optimization and derivatives homework

Find the dimensions of a right circular cylindrical can with both a top and a bottom that holds 8 cubic cm and is constructed with the least amount of material possible. Radius of can= cm Height ...
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### Best path for finding within a radius of x units from this point

Say i am standing at a point and knew there is one thing within a radius of x units from this point. What is best path to find that thing. Best can mean shortest, but the discussion can be more open.
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### Is there a continuous version of $tan^{-1}(\frac{y}{x})$ for the entire unit circle?

The fact that $tan^{-1}(\frac{y}{x})$ only "works" for the upper-right quadrant makes some calculations (for a physics simulator) impossible. I of course use $atan2(y,x)$ in the code, that's not what ...
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### Given 2 outer points of a perfect circle, find the centerpoint

Alright, I hope this makes some sense. I am using a software that can create arcs. This arc is defined by: Begin point End point Center of "circle" The center is supposed to be the center of the ...
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### Maximum latitude of a great circle

1 - I am trying to figure out the longitude at which a geodetic great circle reaches its apex. (I have a point and the azimuth at that point identifying the circle) I have found a good resource that ...
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### Finding tangent points of circle inside a triangle

Hi, This is really a part 2 of a previous questions of finding intersecting points of a circle and triangle. I'd like to run my approach by you all to see if I'm thinking correctly. Maybe there's a ...
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### Completelly cover area with minimum number of maxed circles NP-completeness (or harder) proof

everyone. I'm looking for paper with proof of NP-completeness following, or similar problem. Given: Area $S \subset \mathbb{N}^2$, let it be convex or rectangular, I believe it doesn't matter ...
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### Area of ring section closed within a rectangle

I wish to find out the area of a section of a ring which can be acted on my a rectangle 100mm wide by 60mm height. I know the inner diameter,ID and outer diameter,OD of the ring and the width of the ...
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### What “boundary conditions” can make a rectangle “look” like a circle?

I posted the question below in Stackoverflow but then realized that it perhaps would find a better audience here. I am solving a fourth order non-linear partial ...
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### How to find the center of a circle moving and rotating in space having the coords of 3 points on the circle?

consider a circular plate with radius R , with three points on it at arbitrary coordinates on the plate area that form a triangle. Just imagine 3 holes on the plate area If I can have the new ...
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### Three circles inscribed in a rectangle as shown in the diagram

3circles in a rectangle of width 6cm. The first circle of radius 3cm touches the three sides of the rectangle. The second of radius 2cm touch one side of the rectangle and touches the former and the ...