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

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3
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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
181 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
212 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
703 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
733 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
251 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
495 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
855 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
197 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
284 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
109 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
883 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
560 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
6answers
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
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
148 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
285 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
333 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 ?
9
votes
7answers
9k 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
134 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
219 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
385 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
276 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
15k 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
346 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
416 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
375 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 $AC$.
4
votes
2answers
355 views

Problem on circles- Plane Geometry

The chord CD of a circle center O is perpendicular to the diameter AB. The chord AE goes through the midpoint of the radius OC. Prove that the chord DE goes through the midpoint BC.
0
votes
1answer
105 views

circle that touch quadrantal internally

I want to know how to construct circle that touch quadrantal(1/4 part of circle) internally. I spend several hours for solving this problem but I have no luck. I attached the picture what I've ...
4
votes
1answer
179 views

Determine if circle is covered by some set of other circles

Suppose you have an existing set of circles $\mathcal{C} = {C_1, .., C_n}$ each with a fixed radius $r$ but varying centre coordinates. Next, you are given a new circle $C_{n+1}$ with the same radius ...
0
votes
1answer
114 views

How do you express how much a curve or part of a circle is “bent”?

Given a certain curve, or part of a circle, how do you express how much it is bent? If I have for example 1/3 of a circle (without seeing the full circle). How do I calculate and express that it is ...
8
votes
2answers
451 views

Coloring a sphere with minimum colors (with constraints)

This is a problem we've been considering in our undergraduate math club, and I thought it would be nice to get further thoughts on the subject. I will start with a two dimensional case and then ...
1
vote
2answers
108 views

Is circle formula same in different XY system?

I want to check an element if it's in a circle in my browser. I know the circle formula from my high school: But I'm not sure if it's same in browser XY system too. Because browsers zero ...
1
vote
1answer
1k views

Area of a square using circle

So I have this square and theres a circle inside of it. The circle of radius $r$ is inscribed in the square. So how do I find the area of the square in terms of $r$? I know that area of a circle is ...
0
votes
1answer
161 views

What is the ratio of the area?

If the segment A'B' is tangent to the incircle of triangle ABC, and that segment AB = segment CM; then, what is the ratio of the area of the triangle ABC to the area of the small triangle A'B’C? ...
0
votes
0answers
250 views

A section of the circle's ring

What is the simplest way to calculate the area of the blue section of the circle's ring shown below using the following datas : a) K is the center of the square ABCD, b) Vertices A and C are on the ...
0
votes
2answers
169 views

Algorithm to randomly place circles at least $D$ distance away from one another

I'm trying to work out how to write an algorithm to randomly place circles of $R$ radius, in a 2d rectangle of arbitrary dimensions, such that each placed circle is at least $D$ distance away from ...
1
vote
0answers
93 views

How to determine the center of a circle with pen and straightedge [duplicate]

Possible Duplicate: Determine the centre of a circle My buddy draws a circle then he erase its center. He quiz me how can find the center with only pen and straightedge (no compass). Do ...
2
votes
3answers
625 views

what formula describes the convex hull of two circles (i.e. two circles connected by tangent lines)?

I'm investigating the following problem. Imagine a circle at the origin with radius r. The circle moves upward with speed s and its radius simultaneously increases by a length of b per time unit. ...
5
votes
1answer
293 views

Is this concept of circle geometry known?

Astonishingly, no mathematician ever could give a "Mr. Foobar invented this" whenever I came up with this construction, although it is very elementary. Given are 3 circles C1,C2,C3 (avoid degenerate ...
4
votes
2answers
357 views

rotating 90 degrees around a circle on a co-ordinate plane

I thought the answer would be square root of 3. It would seem that the x co-ordinate of Q would just be the opposite of the x co-ordinate of P. I'm not sure if the picture is just being ...
2
votes
2answers
430 views

Chord dividing circle , function

Two chords PA and PB divide circle into three parts. The angle PAB is a root of f(x)=0. Find f(x) Clearly , PA and PB divides circle into three parts means it divides it into 3 parts of equal areas ...
1
vote
2answers
3k views

Calculating point around circumference of circle given distance travelled

Its the end of the day and my brain just cant cope anymore. Can anyone help with, what I hope, is a simple question.. Given a point on a circle (x, y coordinates) how can I calculate the coordinates ...
2
votes
1answer
93 views

Finding the location of the end of an arc, knowing the beginning, the arc's length and the radius

I apologise in advance if this is really basic. I have a circle of radius 15, from which i work out an arc, given an angle of arbitrary value (it's for a computer program). Given that i know the point ...
3
votes
2answers
280 views

Circle bitangent angles

Say we have two circles $C_1$ and $C_2$ with radii $r_1$ and $r_2$, respectively. Let their centers be $d$ units apart. There are 4 bitangents, two outer and two inner. Examine the intersection of an ...