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

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3
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2answers
93 views

Two questions on clock arithmetic

I have two questions on clock arithmetic, both of which I have solved, but I am looking for neater proofs. Let us suppose we have a circle named $\mathbb{Z}_n$ with $n$ equally spaced points on it ...
1
vote
0answers
101 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 ...
6
votes
1answer
92 views

Area of circles: represent $x$ in terms of $r_1$ and $r_2$

See the image. Area of green and red regions are equal. Can you represent $x=|O_2D|$ in terms of $r_1$ and $r_2$ for $r_1> r_2$ ? Edit: The point $O_1$ does not enter in the region of small ...
1
vote
1answer
558 views

3D Circle/ground intersection

This one stumps me: A circle in 3D space given by its center = $(0.15, 0.5, 1.0)$, its radius $=64$ and an orientation vector that points away from the circle's plane $(0.251, -0.796, 0.551)$ How ...
0
votes
2answers
63 views

Calculate Point based on distance in 2D-Space

I have a Point P in unit circle (on or in it) with a radius of r. How can I calculate a Point Q with a fixed radius of x, which has the same angle like P
2
votes
3answers
85 views

Drawing dynamic circles based on input value

Is there a formula that will allow me to calculate the radius of a circle based on an input value? The input value could be as small as zero or as large as $10^7$, or larger. The circle is ...
2
votes
1answer
536 views

Circle Packing: Unsolved Problem in Geometry?

Graham and Sloane minimize the second moment of the centres of a number discs in order to maximize their compactness. They use computational geometry techniques to find the optimal packings for ...
1
vote
3answers
299 views

Would a circle overlap a parabola's bottom by more than just its vertex?

I mean, out of the condition that a circle actually crosses the parabola. My question is when a circle is "inside" a parabola, would it touch part of the parabola other than just the parabola's vertex ...
2
votes
2answers
187 views

Is the value of $\pi$ in 2d the same in 3d? [closed]

I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!) Given my first question: What is ...
3
votes
3answers
9k views

What is the perimeter of a sector?

I don't understand this. So we have: ...
0
votes
1answer
306 views

Ray Disk intersection

So if I have a ray parameterized as $O + tD$ where $O$ is the origin, $D$ is the direction and $t$ is the parameter variable and a flat circular disk with a center point $P$ in 3D space and a radius ...
1
vote
1answer
99 views

$\pi$ is just a number, or also the circumference of a sub-unit circle?

A unit circle defined in the Cartesian plane has a radius of $1$ and a diameter of $2$. So making a full round is $2 \pi$. Now, $\pi$ is the ratio of the circumference over the diameter, so if I have ...
1
vote
1answer
130 views

Circular motion trig

We have $x_P = -2 + 4 \cos (-\pi t)$ and $y_P = 1 + 4 \sin ( - \pi t)$ with $t$ in seconds. We have to find the coordinates of the intersection with the y-axis. So I use trig and I eventually end up ...
2
votes
0answers
168 views

Ellipse radius interpolation with different radiuses

I am writing a library for graphical LCDs and I want to incorporate a function to draw a circle on the screen. I have already succeeded in drawing simple circles, however, I want to be able to pass a ...
4
votes
4answers
8k views

Relation between chords length and radius of circle

Two chords of a circle, of lengths $2a$ and $2b$ are mutually perpendicular. If the distance of the point at which the chords intersect,from the centre of the circle is $c$($c<$radius of the ...
1
vote
1answer
148 views

Are the area of a circle inscribed in a square and the area of the “spandrels” (the four corners that remain) commensurable?

And how would you demonstrate that most simply? See the beginning of my blog post for a little more: http://seekecho.blogspot.fr/2013/02/different-ilks.html
2
votes
3answers
532 views

Geometry - Equilateral triangle covered with five circles

I have to cover an equilateral triangle (whose sides are 1m long) with 5 identical circles: what's the minimum radius of the circles?
3
votes
3answers
189 views

Marking the prime points on a circle

If you travel around a circle and mark all the points on the circle where the distance you travelled is a prime number, where you would go through many rotations*, do you end up marking the entire ...
1
vote
1answer
68 views

Homeomorphism on Identification Space

Let $\sim$ be and equivalence relation on the unit line $X=[0,1]$ defined by $x\sim y$ if either $x=y$ or $\textbf{both}$ $x$ and $y$ $\in$ {${0,\frac{1}{2},1}$}. Construct a homeomorphism ...
0
votes
1answer
139 views

How to find a point on the tangent line whos length is 1?

im trying to figure out a formula to find the point(x,y) on a tangent line whos length is between 0 and 1 while it rotates around the unit circle uniformly, so the point would either be right on the ...
2
votes
1answer
71 views

Approximate radius of a group of n packed circles

I am looking for a formula to estimate the radius of a circle which would hold n number of circles with some radius r. I understand this is part of the packing problem which does not have a definite ...
2
votes
2answers
67 views

Could someone please explain the theory behind finding if a given point is inside a circle on a grid?

Let us say I have a grid of 1000 x 1000, and on that grid is drawn a circle, the circle could be anywhere. If I then pick a random point from the grid with an x and y co-ordinate I can work out if ...
2
votes
1answer
423 views

Center of circle that has two points on its circumference and a known tangent

I've found a related question, which helped me get started on this. I can get it to work for the example on the question, but I'm running into an issue when the tangent is not y = 0. Other question ...
1
vote
1answer
464 views

2D triangulation

I understood what it is from the following link: http://electronics.howstuffworks.com/gadgets/travel/gps1.htm But I want to know : In a 2D plane, if we know the (x, y) positions of three “guard” ...
1
vote
1answer
136 views

Two sticks between two concentric circles

Let's start with two concentric circles of radii $r<R$. Then we put two sticks inside the outer circle while avoiding the inner circle, say $AB$ and $CD$. Then we compare the length of inner ...
0
votes
3answers
4k views

Calculating circle radius from two points and arc length

For a simulation I want to convert between different kind of set point profiles with one being set points based on steering angles and one being based on circle radius. I have 2 way points the ...
4
votes
2answers
375 views

Math Puzzle: Area of Concentric Rings

The problem below appeared on the latest round of Google Code Jam: Maria has been hired by the Ghastly Chemicals Junkies (GCJ) company to help them manufacture bullseyes. A bullseye consists of a ...
3
votes
2answers
234 views

Given a latitude how many miles is the corresponding longitude?

OK so lines of longitude (the distance/circumference around the earth horizontally) differ based on what latitude you are at (0 at north and south poles up to ~25k at the equator.) So given a ...
0
votes
1answer
281 views

Bounds of double integral given a circle and a line

Calculate the double integral of the area between the function $$x^2+y^2=25$$ and the line $$y=-x+5$$ in the first quadrant. Now, I am unsure how to choose the bounds for y, I understand that the ...
1
vote
1answer
114 views

Calculate points(x, y) within an arc

I am trying to draw lines from the center of a circle to points (x, y) in the circumference. To calculate this the angle is used. I need to render points in between two angles. E.g. Angle 0 to angle ...
1
vote
1answer
100 views

Calculating circle properties.

How can I incrementally calculate the angle from angle 0 and the point (x, y) in a circumference path if I have the center of the circle coordinates and the radius of the circle. I have 127 segments ...
1
vote
1answer
144 views

Similarity of triangles in a circle

The problem: c is a circle with a diameter AB. t is the tangent at the point B. Now C and D are two points on t and at different sides of B. I draw the line segments AC and AD, the point where AC ...
0
votes
2answers
139 views

Distance from the midpoint of a radius to another point on the same radius

Here is a picture of the problem. Note that $M$ is the midpoint of $OB$. How do I figure out what $MH$ is?
2
votes
1answer
196 views

One circle, two lines Apollonius' problem

I've been trying to solve special case of Apollonius' problem, where instead of 3 circles i have 1 circle and 2 lines. Acording to: ...
2
votes
4answers
6k views

Finding the equation of a circle and a tangent line to the circle given two end points

Given the endpoints $(11, 23)$ and $(6, 13)$ of a circle, find the equation of the circle and the equation of a line tangent to the circle. First, I found the center using the midpoint formula: ...
2
votes
1answer
511 views

Point on circumference a given distance from another point

I am writing a game and need to figure out some math. If I have a circle with the equation $r^2 = (x-d)^2+(y-e)^2$, where $r$, $d$, and $e$ are constants, and a point $A(a,b)$, how do I find the ...
1
vote
3answers
2k views

Center of Mass of a Circle

How would one find the center of mass of a circle? The center of mass of a rod is given by: $$\frac{1}{M}\int^{L}_{0}\rho x dx$$ So, for a sphere, it would be an area integral, such as: ...
1
vote
1answer
106 views

Calculating mean velocity of an orbiting body as it moves towards a point.

I'm making a game, in the game planets orbit a central point in circular orbits, they move directly towards their targets and the vector is simply added to their orbital path. Whilst not realistic it ...
1
vote
2answers
760 views

How to calculate angles required to lay out flat pieces in a circle

I want to construct a wheel made of flat pieces of wood, something like this picture: I am unsure how to calculate the difference in angle between each of the flat pieces of wood that make up the ...
0
votes
1answer
44 views

Bisectors of angles of circle

Bisectors of angles $A$, $B$ and $C$ of a triangle $ABC$ intersect its circumcircle at $D$, $E$ and $F$ respectively. Prove that the angles of the triangle $DEF$ are $90^{\circ}-\frac{1}{2}A$, ...
1
vote
1answer
645 views

How to determine if two points lie in a particular section of circle.

I'll take assistance from the figure below. O is the center of the circle, and A,B,C are the points on the circle, and are known. i.e. the x,y coordinates of these three points are known. I want to ...
2
votes
1answer
172 views

How do we know $\pi$ is a constant? [duplicate]

How did the ancient Greeks discover that the ratio of a circle's circumference to its diameter is constant? It does not seem so intuitive. Thanks!
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2answers
250 views

Diameter of a circle with 3 coordinates

The question is: A circle has the points $A=(6,-1)$ $B=(10,-3)$ and $C=(-2,-9)$ on its circumference. A diameter of the circle is drawn which is parallel to BC. How far apart are the two parallel ...
0
votes
1answer
311 views

Find a formula for a vector field with given properties

This is the exercise: Give a formula $$F = M(x, y) i+N(x, y)j$$ for the vector fIeld in the plane that has the properties that $$F = 0$$ at $(0,0)$ and that at any other point $(a,b)$, $F$ is tangent ...
1
vote
1answer
650 views

when we have circle in hyperbolic plane,what is the center and radius of this circle in Euclidean plane?

Let C be the hyperbolic circle with center Xi, where x>0 and radius r>0. Find the center and radius of this Euclidean circle.
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1answer
77 views

What is the maximum number of circles in proximity to a given point.

The title maybe a bit obscure so I'll try my best to explain the problem here. Below is the Picture that I'll take help from. Say I have a circle A of Radius R ...
0
votes
1answer
117 views

What is the official proof (if there is any) for the area of a circle of radius 'r'?

What is the official proof (if there is any) for the area of a circle of radius 'r' ? I remember in my school days they simply told that area of a circle of radius 'r' is $\pi*r^{2}$. The teacher ...
1
vote
1answer
452 views

Math - 11th Grade Geometry - Locus

I have a test tomorrow and this might be a question on it. I do not know the answer and I have no idea how I would draw it out if I had to. The question is... Describe the locus of the centers of all ...
3
votes
2answers
301 views

Euclidean Geometry Area Problem

Let $\Gamma $ be the circumcircle of triangle $ABC$. Let $A_0$ be the center of the circle lying outside of $\triangle ABC$ and which is tangent to the segment $BC$ and to rays $\overrightarrow{AB}$ ...
1
vote
1answer
99 views

Form a Circle with Circles

I need to form a perfect circle out of circles. Given N number of circles each with radius R, how can I find the distance away from the center?