Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.

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2
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1answer
187 views

Interval and Circle

Can anyone give me a proof of why the circle $S^1$ and the closed interval $[0,1]$ are not homotopically equivalent? (Using the basic definition and not the fundamental group!)
0
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1answer
110 views

Finding a function that computes a point on the unit-circle

I can't find the definition of a function $f(x); x \in [-1;1]$ where $(x|f(x))$ is a point on the unit-circle. Can you please give me a hint? ---------- Edit ----------- Background: I want to ...
2
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3answers
451 views

How to normalize this circle equation?

I am given a circle described by the equation below. Is there any way I can bring it to the form $(x-a)^2 + (y-b)^2 = c^2$ to have it be normal? My intent is to translate it to polar coordinates and I ...
1
vote
1answer
109 views

Circle locus, how to satisfy the equation.

$A(-3,1), B(0,-5), P(X,Y)$ If $|AP| = 2|BP|$ prove that $x$ and $y$ satisfy the equation: \begin{aligned} \ x^2+y^2-2x+14y+30 =0 \end{aligned} I get as far as determining the ...
1
vote
1answer
94 views

$D^n\times D^m\cong D^{n+m}$?

Let $D^n=\{x\in \mathbb{R}^n : ||x||\le 1\}$ the unit closed ball in dimension $n$, and $I=D^1=[0,1]$. We have $D^1\times D^1=I\times I\cong D^2$. Is it true that $$D^n\times D^m\cong D^{n+m}$$ ...
2
votes
3answers
844 views

Finding location of a point on 2D plane, given the distances to three other know points

I need to find location of the point $s_0$; the locations of other three points ($s_1$, $s_2$, $s_3$) are known. $d_i$ are known distances. Given: $x_1$, $x_2$, $x_3$, $y_1$, $y_2$, $y_3$, $d_1$, ...
0
votes
1answer
73 views

Unknowns in Circle Equation

The circle $x^2-y^2 + ax -2y -15 = 0$ contains the point $P(-6, 5)$. How would I find a?
2
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2answers
1k views

Area of shaded portion

Problem: To find area of shaded portion (AOB) in the below figure. Description of Figure: ABCD is a square of side 14 cm AOCD and BODC are quadrants
7
votes
3answers
207 views

Is there a simple formula for this simple question about a circle?

What is the average distance of the points within a circle of radius $r$ from a point a distance $d$ from the centre of the circle (with $d>r$, though a general solution without this constraint ...
2
votes
2answers
5k views

Get the size of an area defined by 2 overlapping circles

I have two circles, like this: I know the radii of the circles, and I know the X + Y of the center of both circles. Can I get the size of the area that is black in my picture?
2
votes
5answers
2k views

finding center of circle

How can I calculate center of a circle $x,y$? I have 2 points on the circumference of the circle and the angle between them. The 2 points on the circle are $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$. The ...
2
votes
3answers
4k views

Finding the center and radius of a circle given a general degree 2 equation

I am trying to find the center and radius of the circle with equation $x^2 + y^2 -6x + 10y + 9 = 0$
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vote
6answers
52k views

Finding an equation for a circle given two points

No idea how to do this, I used to have these conic shapes committed to memory but I forget them already. I am supposed to find an equation for the circle that has center $(-1, 4)$ and passes through ...
1
vote
1answer
184 views

Ancient astronomers, planetary conjunctions, and epicycles

How did ancient astronomers predict planetary conjunctions? I know they used a system of epicycles to represent the path of planets, but finding the point and time of alignment of two planets still ...
1
vote
1answer
245 views

Find the position of a beacon using lat/lng/signal strength data

Let's assume, hidden in a forest, there's a beacon. I walk in the forest and, at random intervals, ping the beacon. For each ping I get a lat/lng pair and the signal strength of the ping at that point ...
3
votes
6answers
2k views

calculating angle in circle

How to calculate angle in a circle. Please see the diagram to get the idea what I want to calculate? I have origin of circle that is $(x_1,x_2)$. I have a point on circumstance of circle that is ...
5
votes
1answer
190 views

What is the geometrical representation of $1/R$?

Sorry if this is too elementary, if $R$ is the radius how do I visualize $1/R$? Thanks.
3
votes
1answer
128 views

circles tangent to exponential curve

Circle $C_1$ is tangent to the curves $y=e^x$ and $y=-e^x$ and the line $x=0$, and for $n>1$ circle $C_n$ is tangent to both curves and to $C_{n-1}$, how can I find the radius of any circle $C_k$? ...
3
votes
1answer
134 views

summing series using circles inside curves

After watching the infinity elephants video http://www.youtube.com/watch?v=DK5Z709J2eo and seeing how a geometric series could be represented by drawing a circle between a pair of lines, then the ...
2
votes
2answers
178 views

Area of a circle portion

Say I have the following circle and I want to find the area bound between the axis and p, is there an easy way to do it? I tried using an integral but for some reason it doesn't have a nice clean form ...
2
votes
1answer
206 views

Area of a portion of an arbitrarily-placed circle?

I have a circle that's off-center, but I want to find out the area of the part of the circle in the positive x and y region. Not sure how to do this because of the multiple variables involved.
8
votes
2answers
691 views

Sangaku: Show line segment is perpendicular to diameter of container circle

"From a 1803 Sangaku found in Gumma Prefecture. The base of an isosceles triangle sits on a diameter of the large circle. This diameter also bisects the circle on the left, which is inscribed so that ...
1
vote
2answers
720 views

Finding the intersection points of two circles - where one circle has a diff x and y coord than the other

Following this link: http://mathworld.wolfram.com/Circle-CircleIntersection.html I now understand how to calculate the offset of the radical line from circle_a (a) However: ...
0
votes
1answer
243 views

How to calculate the coordinates of the middle point of a given arc?

Does anybody know how to solve this problem? I am trying to calculate the green sides of this triangle: I know / have : the arc length, the arch base, the radius, and the h (distance from the red ...
3
votes
1answer
466 views

How can we prove the locus is a circle?

Given two fixed points A and B, find the locus of the point P, satisfying PA=2PB. Of course we can use Cartesian geometry to find the equation of the curve. Let the midpoint of A and B be the ...
8
votes
1answer
803 views

Diffeomorphism group of the unit circle

I am given to understand that the group of diffeomorphisms of the unit circle, $\operatorname{Diff}(\mathbb{S}^1)$, has two connected components, $\operatorname{Diff}^+(\mathbb{S}^1)$ and ...
2
votes
2answers
4k views

Find the differential equation of all circles of radius a

Can someone please post a detailed step-by-step procedure. Given the circle with a radius a, what is the differential equation of the circle.
4
votes
1answer
191 views

A circle cut into smaller pieces can become a smaller circle?

While I was on a plane, a Math professor once told me that it was possible to divide a circle in multiple smaller pieces in such a way that, when those smaller pieces are assembled in another way, ...
5
votes
1answer
280 views

Extension of real analytic map on the unit circle

Given a real-analytic map $f : \mathbb{S}^1 \rightarrow \mathbb{S}^1$, where $$\mathbb{S}^1 = \{z \in \mathbb{C} : |z| = 1\},$$ does it admit a complex-analytic extension $\tilde{f} : U \rightarrow ...
1
vote
1answer
108 views

Function to Generate Two Circles For a Color Gradient

I am working on a project creating a gauge package in software, but I am posting here because it is more of a mathematical question. In short, I need a function to create a color gradient to fill in ...
1
vote
2answers
869 views

Check if point on circle is in between two other points (Java)

I am struggling with the following question. I'd like to check if a point on a circle is between two other points to check if the point is in the boundary. It is easy to calculate when the boundary ...
1
vote
2answers
546 views

How to calculate a specific area inside a circle?

I want to calculate the area displayed in yellow in the following picture: The red square has an area of 1. For any given square, I'm looking for the simplest ...
14
votes
5answers
11k views

A circle with infinite radius is a line

I am curious about the following diagram: The image implies a circle of infinite radius is a line. Intuitively, I understand this, but I was wondering whether this problem could be stated and ...
0
votes
2answers
1k views

Angle of reflection off of a circle?

I've made simple 2D games in the past using mostly just squares. If an object collided with another object (all squares/rectangles) it would just change the slope to the opposite based on what side ...
3
votes
2answers
86 views

every point on boundary of region of convergence is singular

I am given the following function: $$f(z)=1+z^2+z^4+z^8+z^{16}+ \cdots$$ and shall show that it is holomorphic in the unit disc, that $f\to\infty$ as $z\to e^{2i\pi/2^n}$, and that every point on ...
2
votes
1answer
147 views

Intersections of 2 circles

Let me ask a similar question to the one I did yesterday. I got answers which said that the following problem had no general solution for x and y. $\sqrt{(n_1-x)^2+(n_2-y)^2}=n_3$ ...
3
votes
4answers
2k views

Is an ellipse a circle transformed by a simple formula?

Does any ellipse $E$ have a circle $C$ such that you can obtain $E$ by transforming $C$ by a simple formula $F$? In details , both $E$ and $C$ have the same center and the axes of $E$ are the XY axes. ...
0
votes
2answers
1k views

Find, inside a large circle, the maximum number of small circles placed 60 degrees to each other and

... starts with a small circle in the center of the large circle. The above picture shows a program I wrote to actually draw the circles out. But you can see that this method does not yield maximum ...
1
vote
2answers
277 views

how to get the width of a segment of a circle, given its area?

On a circle, 2 parallel chords delimit a segment of which we know the area : A. We also know the distance to the center of the circle of 1 chord : d1. How to find d2, the distance of the other chord ...
5
votes
1answer
310 views

Area of a circle taken as equal to that of a square

I just picked up this book Intro to foundations and fundamental concepts of math (Howard Eves/Carroll Newsom) Practice problem: In the Rhind papyrus area pf a circle is taken as equal to that of a ...
12
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4answers
1k views

How to equally divide a circle with parallel lines?

How can I "draw" $n$ parallel lines in such a way that they will divide a circle (disc) in $n+1$ equal areas ?
9
votes
7answers
7k views

a circle graph is not a function?

I'm a little confused by the rule: If you draw a vertical line that intersects the graph at more than 1 point then it is not a function. Because then a circle like $y^2 + x^2 = 1$ is not a function? ...
1
vote
2answers
128 views

Angles And Their Measurements

I have an intuitive understanding of what degrees and radians are and what arc length, subtending, area of the sector and the derivation of the formula $$s = r \cdot \theta.$$ However due to lack of ...
5
votes
2answers
216 views

Center and radius of circle question

For a circle that has the equation $(x-a)^2 + (y-b)^2 = r^2$ , I know it has center $(a,b)$ and radius $r$. But what happens if the equation is $x^2 + (y-b)^2 = r^2$ ? With $b$ not equal to $0$ and ...
2
votes
1answer
378 views

Concentric circles(IMO 1988/Problem 1)

Let us consider 2 concentric circle radii R and r (R > r) with centre O.We fix P on the small circle and consider the variable chord PA of the small circle. Points B and C lie on the large circle; ...
0
votes
2answers
255 views

Finding centre and radius of circle

Let $a,c \in \mathbb R$ with $a \neq 0$, and let $b \in \mathbb C$. Define $$S=\{z\in \mathbb C: az\bar{z}+b\bar{z}+\bar{b}z+c=0\}.$$ a. Show that $S$ is a circle, if $|b|^2 > ac$. ...
11
votes
5answers
14k views

Parametric Equation of a Circle in 3D Space?

So, my dilemma here is... I have an axis. This axis is given to me in the format of the slope of the axis in the x,y and z axes. I need to come up with a parametric equation of a circle. This circle ...
1
vote
2answers
327 views

How can I find an upper bound for the radius of an arc, given arc length and chord length?

This is similar to this question, except I am finding the radius now using the Bisection method and then Newton's method for finding a zero. This is a computer science for a Numerical Methods course. ...
2
votes
2answers
391 views

Calculating point on circle after time

I have a question that seems very similar to calculating-point-around-circumference-of-circle-given-distance-travelled and calculating-point-on-a-circle-given-an-offset, but I don't believe they are ...
1
vote
1answer
373 views

A plane Geometry Problem

The triangle $ABC$ has $CA=CB$, circumcenter $O$ and incenter $I$. The point $D$ on $BC$ is such that $DO$ is perpendicular $BI$. Show that $DI$ is parallel to $AC$.