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

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4
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0answers
382 views

Pinwheel- perimeter of semicircular region

Above, we have a larger circle of $r=16$ with 8 equally spaced semicircles of radius=8. Each semicircle has one end on the larger circle's center and the other on the circumference of the larger ...
7
votes
4answers
315 views

Does the graph of $\cos x$ intersect the unit circle other than the point (0,1)?

It would seem the unit circle is nicely tucked under the graph of $\cos x$, touching only at (0,1), but is that what's truly going on here?
2
votes
1answer
170 views

Similar Right Triangles and Incircles [duplicate]

Possible Duplicate: Triangle and Incircle In a setup of right triangles ABC, BDA, and BDC not unlike this diagram (click on the link, and ignore the written side measures and subtext in ...
1
vote
4answers
593 views

Finding the equation of a circle

$A=(3,1)$ and $B=(-1,-1)$ are points on a circle of center $(k, -3k)$ find the value of $k$ I begin by assinging the values $\ g = -k $ and $\ f=3k $. I then substitute $(3, 1)$ and $ g= -k, f= ...
0
votes
1answer
98 views

Finding a point which is constrained to 3 other points.

Is there an easy way to find the 4th point given 3 fixed points and a different minimum length between the 4th point and each of the 3 points? Similar to this question, but with non-fixed minimum ...
0
votes
3answers
4k views

Circle and Line segment intersection

I have a line segment (begin $(x_1,y_1)$, end $(x_2,y_2)$, with $D=5$, let’s say) and a circle (radius $R$, center $(x_3,y_3)$) How can I check that if my line segment intersects my circle? picture ...
1
vote
2answers
220 views

Closest point to a unit circle from a point inside it

I'm working on a code at the moment that calculates the closest point to a circle from a point inside it. Let's say we have the point ($x_0, x_1$) to calculate the closest point to the unit circle it ...
0
votes
1answer
335 views

Determine larger arc from smaller arc

Given two angles (the starts and end of an arc), e.g. 90 degrees to 180 degrees, I need to output the starting and ending degrees of a small arc, and a large arc. In this case the small arc is simply ...
3
votes
2answers
502 views

Formula for the area of a segment of a circle… What am I doing wrong!?

Alright, I'm trying to study for a big test and I know that the area of a segment of a circle will be on it. Problem is, I can't seem to get the formula for it to work. I've gone over it countless ...
2
votes
1answer
209 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
votes
1answer
129 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
votes
3answers
496 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
112 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
95 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
964 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
75 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
votes
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
211 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 ...
3
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
5k 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
63k 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
207 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
305 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
3k 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 ...
6
votes
1answer
192 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
130 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
182 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
216 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.
9
votes
2answers
734 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 ...
2
votes
2answers
761 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
257 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
550 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 ...
9
votes
1answer
907 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
5k 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
206 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
288 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
110 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
916 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
582 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 ...
15
votes
6answers
12k 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
88 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
151 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
293 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
354 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
votes
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 ?