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

learn more… | top users | synonyms

1
vote
1answer
44 views

inscribed circle in $n$-gon

If I'm given a circle with radius $r$ and I want to create a polygon with side $n$ (say $n=5$) which can cover the circle fully, then how to prove that a regular polygon is the solution with minimum ...
1
vote
0answers
114 views

Apollonian gasket

Okay , is there a way to find the radius of the nth circle in a apollonian gasket .. Something like this Its like simple case of apollonian gasket .. I found from descartes' theorem $R_n = ...
-4
votes
1answer
35 views

problem on circles [on hold]

Find the radius of the circle which touches both the coordinate axes, and touches the line x/a + y/b = 1, $a>0,b>0$, and its centre lies in the first quadrant.
0
votes
0answers
26 views

How to scale x- and y- axes equally in Maple?

I have the ellipse $\frac{25}{36}x^2+\frac{5}{36}y^2=1$. Maple draws it as a circle: How can I change the coordinates, to make it look like an actual ellipse?
-1
votes
2answers
24 views

Euler's formula for off-center circle [closed]

A circle with radius $R$ and center at $(a,b)$ is given by the formula $(x-a)^2 +(y-b)^2 = R^2$. A circle with radius $R$ whose center is at the origin is given by Euler's formula: $R e^{i \theta}$. ...
14
votes
6answers
2k views

How is the area of a circle calculated using basic mathematics?

Area of a circle is addition of circumference of layers of a onion. If n is radius of a onion then area is $$ A = 2 \pi \cdot 1 + 2 \pi \cdot 2 + 2\pi \cdot 3 + \ldots + 2 \pi \cdot n $$ which $$ ...
1
vote
1answer
25 views

List all sets of points in a plane that are enclosed by circles with given radius

My problem is: Given N points in a plane and a number R, list/enumerate all subsets of points, where points in each subset are enclosed by a circle with radius of R. Two subsets $S_i$ and $S_j$ should ...
-2
votes
3answers
90 views

Circles in circle

If we are given one big circle and infinite amount of smaller circles with equal radius (of course radius of the smaller is < radius of the big one) and we have to put in the center of the big ...
13
votes
1answer
286 views

How big is my pizza, if I know its slices' sizes?

I bought a box of frozen pizza: eight slices, baked and then frozen, stacked in a box. The packaging assured me that I was holding an 18-inch[-diameter] pizza. That got me thinking: how do I know ...
3
votes
1answer
37 views

Conversion between trig functions and hyperbolic trig functions

Using trig identities we can see that $\sin^2 x + \cos^2 x = \tanh^2 x + \text{sech}^2 x = 1$ , and so the parametric graph $(\cos t, \sin t)$ is similar to $(\text{sech} t, \tanh t)$. The first ...
0
votes
1answer
27 views

Area of intersection of two Annulus

Given two separate annulus with centers $[C_1,C_2]$ and their corresponding radii being $[R_1,r_1]$ and $[R_2,r_2]$ respectively, larger radius being $R$. There are methods to look at whether they are ...
1
vote
1answer
32 views

Find corners of a square in a plane in 3d space

I am given two angles (similar to theta and phi in spherical coordinates) from which I can calculate a normal vector to a plane in 3d space. I am also given the center point of the square and the area ...
1
vote
1answer
31 views

How to evaluate Area of $B:= \{(x,y,z) \in A | z \le 1 \}$ with $A:=\{(x,y,z) \in \mathbb{R}^3 | x^2 + y^2 = z\} = \frac{\pi}{6}(5 \sqrt{5}-1) $?

I have following problem: Let $$A:=\{(x,y,z) \in \mathbb{R}^3 | x^2 + y^2 = z\} \\ B:= \{(x,y,z) \in A | z \le 1 \}. $$ Compute the area $\mu_2(B) $. First, I thought $\mu_2(B) $ would just be the ...
1
vote
1answer
34 views

Two circles intersect in two points and the line through these two points

Consider two circles $C,C'$ in euclidean plane which intersect in exactly two points $Q,R$ and consider the line $QR$ through these points. The claim is that a point point $P$ lies on the line $QR$ ...
1
vote
1answer
35 views

How to find out how big a ball is?

Ok, This is probably a really simple question but. I need to know how I can find out how big a ball is. For example, a tennis ball is 2 1/2 inches big, but how do you find that? Though, for ...
1
vote
2answers
38 views

Is circle the only Jordan curve with this property?

When I was thinking about one problem that has to do with Jordan curves the problem which I am going to describe now, arose in my mind. And here it goes. It is known that for every $n\geq3$ the ...
3
votes
2answers
61 views

Centroid of a Triangle on a inscribed circle

$AB$ is the hypotenuse of the right $\Delta ABC$ and $AB = 1$. Given that the centroid of the triangle $G$ lies on the incircle of $\Delta ABC$, what is the perimeter of the triangle?
1
vote
0answers
54 views

Calculating the Area of a Circle Occupied by a Rectangle

This is a question regarding how to calculate the area of a circle occupied by a rectangle when that rectangle is larger than the circle (see this link for a example image ...
0
votes
6answers
52 views

How to find center of a circle given 2 points on the circle

I need a Formula for this: we have two points on the circle. How can we find the center of circle? For example $A(4.2,5.2)$, $B(5.2,6.3)$.
5
votes
4answers
31 views

get length of line connecting sector of a circle

What's the formula for getting the length of a line (in this case the red one) connecting starting point and end point of an arc, given the circle's radius R and angle A?
0
votes
4answers
48 views

Interpolation between 2 points on the perimeter of a circle?

I'm trying to produce movement on a unit circle from one point to another in equal increments, but I'm having trouble doing this without the use of angles (which isn't an option). Given 2 points on a ...
0
votes
3answers
33 views

Find the equations of the lines that pass through the point $(1,3)$ and are tangent to the circle $x^{2}+y^{2}=2$

Since the line passes through $(1,3)$ I substituted: $3=m+b$ so $m=3-b$ and $y=(3-b)x+b$. But if I then plug the line equation into the circle equation and take the discriminant, I end up with terms ...
1
vote
3answers
23 views

Find the values of b for which the line $y=3x+b$ intersects the circle $x^{2}+y^{2}=4$

I'm not sure how to tackle this question. First thought was to sketch both the line and the circle together, but it doesn't make it much clearer how to find b. Solving for both equations for y and ...
-4
votes
0answers
38 views

Why do the triangles in the unit circle after 90 degrees look like this?

e.g. any triangle in the unit circle has one side (the hypotenuse) which is always positive? why is it positive? I edited this picture http://mathforum.org/mathimages/imgUpload/Trig_refangle.jpg to ...
0
votes
0answers
13 views

Relations, functions and transformation (circles)

Circular ripples are formed when a water drop hits the surface of a pond. If one is represented by the equation $x^2 +y^2=4$ and then $3$ seconds later by $x^2+y^2=190$, where the length of ...
1
vote
2answers
40 views

How to calculate length of common chord of two intersecting circles?

Two circles having radii $7$cm & $19$ cm are separated by a distance of $22$ cm between their centers. If they are intersecting each other at two points $P$ & $Q$ then what will be the ...
0
votes
2answers
28 views

Evaluate $\int_C z^2 e^{1/z} \cosh(1/z)\,dz$, where $C$ is any simple-closed curve, oriented counterclockwise, and containing 0 in its interior.

Evaluate $\int_C z^2 e^{1/z} \cosh(1/z)\,dz$, where $C$ is any simple-closed curve, oriented counterclockwise, and containing 0 in its interior. my works I'm stuck in next step
2
votes
3answers
135 views

How do mathematicians invented and introduced $\pi$ term in the case of circle?

This is basic question. Since childhood I am mugging the mathematical formulae areas of square, rectangle and circle etc. Now,it is possible for me to understand formula of area of square I.e. ...
3
votes
2answers
43 views

Meaning of the expression “orientation preserving” homeomorphism

The only time that I've heard the term "orientation-preserving map" was in Linear Algebra, but today I read the term orientation-preserving homeomorphism of the circle in the following context: If a ...
1
vote
1answer
69 views

Intersection of a convex polygon and a moving circle

I have a straight line which intersects a convex polygon in 2D plane. There exists a circle with constant radius. The center of circle is moving on this line. So at first the polygon and circle don't ...
0
votes
1answer
61 views

How to find the radius of small inscribed circle?

There are three circles of radii $5 cm$, $9cm$ & $11 cm$ touching each other externally. What will be the radius of the largest circle inscribed in the region bounded by three circles? Thus ...
0
votes
2answers
74 views

Algorithm to find a line segment is passing through a circle or not?

I have a line segment between two points P1 (X1,Y1) and P2 (X2,Y2). And I have a circle at point Q(Xq , Yq) with radius R . Can I have an equation in which I can put these values and the result shows ...
5
votes
3answers
84 views

Compass-and-Straightedge Construction

I stumbled upon this question in math class, and I got stuck. The Question: You're are given a circle, and two points. How do you construct a circle that goes through the two points and is tangent to ...
1
vote
1answer
29 views

How do I convert these conics to standard form?

There are two conics I need to convert from general form to standard form but I am not sure if I am going about it right. They are $9x^2 + 5y^2 + 18x - 36 = 0$ and $2x^2 - 8x + y + 6 = 0$ The ...
0
votes
1answer
23 views

How do I plot sagitta versus arc length.

I'm working on a curvature sensor, but I'm finding it hard to find the equation for my h (sagitta) as a function of my arc length. In particular, I want to solve $\epsilon=\frac{Arc Length - Chord ...
0
votes
1answer
84 views

Area of Circle Overlapped by Rectangle

I'm trying to determine 'how much' (as a percentage) a 2D rectangle fills a 2D circle. Actual Application: I was comparing the accuracy of some computer game weapons by calculating the max possible ...
0
votes
1answer
30 views

Recurrent points and rotation number

I need to show that if $f:S^{1} \rightarrow S^{1}$ is a preserving-order diffeomorphism and $f$ has irrational rotation number, then $f$ has at least one recurrent point. How can I prove that? ...
0
votes
1answer
30 views

How to calculate new coordinates on a circle's circumference when an angle is given?

I am working on digital maps and I have a circle plotted. I have the circle's centre in lat, long and the circle's radius in meters. Now I have a point on the north end (0 deg) of this circle's ...
1
vote
0answers
41 views

Existence of a recurrent point [duplicate]

I need to show that if $f:S^{1} \rightarrow S^{1}$ is a preserving-order diffeomorphism and $f$ has irrational rotation number, then $f$ has at least one recurrent point. How can I prove that? ...
1
vote
2answers
47 views

Finding a length in a circle

A circle centred at $O$ has radius $1$ and contains a point $A$ on the circumference. Segment $AB$ is tangent to the circle at $A$ and angle $\measuredangle AOB=\theta$. If point $C$ lies on $OA$ ...
0
votes
0answers
17 views

Finding constant angular acceleration

Hello and thanks for reading my post! The question I'm working on states: Find the constant angular acceleration of an object moving along a circle if starting from rest it makes 3600 revolutions ...
0
votes
4answers
37 views

Circles and right angles

The following is a standard fact about circles: THEOREM: Let $p$ and $q$ be two antipodal points on a circle in $\mathbb{R}^2$ and let $r$ be another point on the circle such that $r \neq p,q$. ...
0
votes
1answer
57 views

Show that A is an open subset of M

If $m\in\mathbb{N}$, $M=\{0,1\}^{\mathbb{N}}$ and $A \subseteq M$ is an open set of sequence where the number 1 appears at least $m$ times. Show that $A$ is an open subset of $M$. I wanted to show ...
1
vote
0answers
33 views

Equation for the points touching a circle.

In the plane $\mathbb R^2$, a point $P$, a point $M$ and the radius $r$ are given. Suppose, that $|\overrightarrow {PM}|>r$ Then, there exist two tangents from $P$ to the circle with mid point ...
2
votes
1answer
45 views

Finding the point of intersection of two tangents to a circle

19. A circle $C$, of radius $r$, passes through the points $A (a, 0)$, $A_{1} (-a, 0)$ and $B (0, b)$, where $a$ and $b$ are positive and are not equal; a circle $C_{1}$, of radius $r_{1}$, passes ...
2
votes
1answer
34 views

Interior Angle Embedded in a Triangle Embedded in a Circle

With only knowing the angles of $B$, $C$, and $D$ (shown above), is it possible to find the interior angle $A$? And if so, how?
3
votes
3answers
47 views

The equation of a tangent to a circle at a given point

18. Show that the equation of the tangent $PT$ at the point $P \left(\frac{1}{5}, \frac{3}{5}\right)$ on the circle $$x^{2} + y^{2} + 8x + 10y - 8 = 0$$ is $3x + 4y - 3 = 0$. Find ...
2
votes
2answers
33 views

Proving a differential equation is a circle

So, I have solved the differential equation, to find the general solution of: $$\frac{y^2}{2} = 2x - \frac{x^2}{2} + c$$ I am told that is passes through the point $(4,2)$. Using this information, ...
3
votes
2answers
48 views

How to find the equation of diameter of a circle that passes through the origin?

So this was a question that I was solving that got me stuck. Its as follows: Q. Find equation of diameter of the circle $x^2 + y^2 - 6x + 2y = 0$ which passes through the origin. Now I have tried the ...
0
votes
3answers
48 views

Proof concerning circles

How do I prove that the diameter of a circle subtends a right angle at a circumference? Thank you in advance! I haven't got the slightest idea.