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.

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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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100 views

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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72 views

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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472 views

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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197 views

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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879 views

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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58 views

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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736 views

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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759 views

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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692 views

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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185 views

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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87 views

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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81 views

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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535 views

(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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378 views

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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143 views

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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525 views

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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138 views

Circle in a simplex

Let $T$ be a $2$-dimensional simplex in $\mathbb{R}^2$. A circle $C(x,y,r) \subset \mathbb{R}^2$ is given by its center $(x,y) \in \mathbb{R}^2$ and radius $r\ge 0$. Show that the set of circles in $...
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206 views

Circle Geometry and Conic Section textbook

I seek a textbook for good conic section and circle geometry questions. Slightly above introductory level. - slightly. But I wouldn't mind introductory level questions to consolidate my knowledge. I ...
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54 views

Zero cell formed by connecting n random points on a circle by chords

To start, think of a regular n-gon inscribed in a circle. If the vertices of the n-gon are all connected by drawing cords between the other vertices, then another smaller n-gon is created at the ...
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255 views

family of circles in bipolar coordinate system

I don't get the idea how the equation for this family of curve is $\displaystyle y^2 + (x - a \coth v)^2 = \frac{a^2}{\sinh ^2v}$ from this article on Wikipedia. Suppose, the equation is $\...
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144 views

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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167 views

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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737 views

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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916 views

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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409 views

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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318 views

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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451 views

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 ...
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49 views

Prove that $AR$ passes through midpoint of $BC$

Consider $\Delta ABC$ is acute triangle, $O$ is circumcircle of $\Delta ABC$. $AD$ is angle bisector of $\angle BAC(\text {D} \in \text {BC})$, $E;F$ are respective in $CA,AB$ such that $CE=CD$ and $...
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25 views

Compute the radius and the central coordinate (x, y) of a circle constructed by three given points on the plane surface

I need you to explain the mathematics behind the code bellow. What is s, what are those formulas for px and py and generally, what logic are we following to find the answer here? ...
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24 views

Radius of a circle in terms height of right triangle

Here are the constants and the arc length s=R*theta is considered constant Given only H and the arc length between theta How can you find the radius of a circle? I was able to find a relationship ...
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Checking circle theorems question

I was just wondering if these answers were right. I am pretty sure that part a is correct, but part b I am not as confident with.
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How does one find a circle which intersects only once with three other circles?

Say I have the equations of three different circles on a plane. How would I proceed to create a fourth circle, which intersects only once with each of these known circles? Would that be possible at ...
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21 views

Find a point on a circle which contains a rectangle using another point, the angle between the two and the rectangle's dimensions

I'm trying to construct a mathematical formula that will calculate a point (x,y) on a circle which contains a rectangle with a width ...
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49 views

Points uniformly distributed on a circle

We select randomly two points in the circumference (with length equal to 1) of a circle. Let $X,Y$ be those points (independent and uniformly distributed) and $D$ the arc distance between them. Since ...
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Finding trig solution to locate the center of an arc that intersects a given arc in the upper right quadrant

Circles with colinear (on X axis) centersWorking entirely in the quadrant where x and y are positive, I'm looking for a trig-based solution for something I can easily construct with a compass but can'...
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27 views

Is this formula correct or best practice?

I have used the formula $((x*x)/(y*2))+(y/2)$ to find the radius of a circle given values x and y on a cartesian plane. I cannot find this formula anywhere and while i know it works, is there a ...
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20 views

Optimal covering with $n$ non-necessarily equal discs

What kind of algorithm can I use to search for an optimal (minimum area) covering of a limited region of the 2d plane with $n$ discs $(x_i, y_i, r_i)$? I've found many investigations on fixed radius ...
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Computational geometry relationship between 2 arcs

I'm writing a program which is making offsets for provided shapes. On the attached picture you can see example of my arc object and all known values. Let's assume that a direction is CW. $O$ - ...
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Find a parametric equation that draws a quarter circle of radius 9 that crosses the y-axis and is as much in quadrant III as it is in quadrant IV.

In preparation for my precalculus test, I was assigned many challenge problems, including this one. I have been struggling to find a solution to this question, as when I graphed my solution, it seemed ...
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27 views

Definition of constant-curvature curve embedded on an Ellipsoid of revolution

I am interested in identifying a type of curve so I can do literature review on it. What is the name of a curve embedded on an ellipsoid of revolution in which the curvature of the embedded curve is ...
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54 views

Gauss Circle problem upper bound derivation

On this page, http://mathworld.wolfram.com/CircleLatticePoints.html It says that |E(R)|<2sqrt(2)piR, how did Gauss show this?
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Calculate the area of a parametric sector

I encountered the following definition: $\forall tD_t=\{(x,y)\in R^2:\theta(x,y) \in [-\pi,t]\}$ where $\theta(x,y)$ is the angle in $[-\pi,\pi)$ that the vector $(x,y)$ forms with the x-axis. ...
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Generalizing computation of number of pixels in inscribed circle to axis-aligned ellipses at arbitrary points

This answer really nicely sums up the question of how to compute the number of pixels inside an inscribed circle. However, I am looking for a more generalized version of this in two ways. 1) I would ...
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36 views

Show that $AB=AA_1$

Let $ABC $ a triangle with $ A_1$ the middle of the edge $[BC] $ and $BAA_1=30°$. $ Let D\in [AB] $ s.t. $CD=AB $. I have to show that $AB=AA_1$. This conclusion seems to be wrong because I can ...
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Calculate new velocity of a ball when colliding with a circle in 2D

I'm currently making a 2D game in C++ but i've come across a problem while doing collisions. I have a ball free falling The above example shows what's going on in my game, I can detect when the two ...