Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.
6
votes
1answer
57 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
24 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 ...
1
vote
0answers
17 views
Normalizing the Second Moment of $n$ Discs
Consider $n$ non-overlapping discs of diameter $d$ positioned (centred) at $P_1,\dots,P_n$ ($||P_i - P_j||\geq d, i\neq j$).
Graham and Sloane use the second moment as a measure of compactness for ...
-1
votes
0answers
22 views
set of all equi distant strings from a string is a circle or a polygon? [closed]
the fundamental particle of the universe the string quoted in string theory, do the set of these strings which are equi distant from a string do form a circle or a polygon?
0
votes
2answers
21 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
33 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 ...
1
vote
1answer
163 views
Surface Area Problem with Specific Formulas
I noticed this question in a Math Problem-Set book.
These were the only formulas allowed:
$1. Area(quadrant) = \frac{1}{4}\pi r^2$
$2. Area(square) = (side)^2$$3.Area(semicircle) = \frac{1}{2} \pi ...
1
vote
1answer
35 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
votes
0answers
39 views
Distance on the surface of a sphere
Given a sphere which radius is r.
There are two red points on the sphere. Given the location of the two points in spherical coordinate system.
If the surface distance between a point and a red point ...
1
vote
3answers
48 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 ...
1
vote
2answers
106 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
1answer
50 views
2
votes
3answers
69 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?
0
votes
1answer
12 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
74 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
20 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
4answers
43 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 ...
0
votes
0answers
25 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 ...
2
votes
2answers
45 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 ...
1
vote
1answer
31 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
40 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
40 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
64 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
27 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
1answer
51 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 ...
3
votes
1answer
199 views
Relationship between two centers of circles in a Venn diagram
Let $S$ be a circle of 1 unit area. No part of circles $A$ and $B$ are outside the circle $S$.
Let $n(S)=1$, $n(A)$, and $n(B)$ be the area of circle $S$, $A$, and $B$, respectively.
For the given ...
1
vote
1answer
52 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 ...
1
vote
1answer
17 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” ...
0
votes
2answers
121 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
79 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
43 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
0answers
27 views
Incorrect Points in Circumference
I am trying to calculate points in a circumference and I do not get expected values.
I am calculating it like this:
...
1
vote
2answers
639 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 ...
0
votes
1answer
23 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 ...
0
votes
1answer
22 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 ...
2
votes
1answer
48 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:
...
1
vote
1answer
35 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
37 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
58 views
Circle problem. Finding the length of a segment in the circle.
Here is a picture of the problem. Note that $M$ is the midpoint of $OB$. How do I figure out what $MH$ is?
Original image here
2
votes
2answers
398 views
Calculate radius of variable circles surrounding big circle.
I got a circle, which I know all the details about him. (Radius [100], Diameter [200], Circumference [628.32], Area [31415.93]...)
I would like to surround this circle, with smaller circles. I know ...
1
vote
3answers
3k views
Determine coordinate of intersection between a line and a circle
I'm putting together a simple script in processing to visualise layout possibilities within the fluid environment of a web page.
I need some help calculating a point on a circle:
The circle is as ...
2
votes
4answers
125 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:
...
48
votes
4answers
4k views
Why is a circle in a plane surrounded by 6 other circles
When you draw a circle in a plane you can perfectly surround it with 6 other circles of the same radius. This works for any radius. What's the significance of 6? Why not some other number?
I'm ...
2
votes
1answer
36 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 ...
-3
votes
0answers
27 views
Mensuration: Squares and Circles
RSTV is a square inscribed in a circle with centre O and radius R.What is the total of the shaded region?
1
vote
3answers
81 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:
...
0
votes
1answer
210 views
Calculating the coordinates of a point on a circles circumference from the radius, an origin and the arc between the points
We have a circle with the known radius $r$ and the circumference $2\pi r$, and we know a point $P_1$ somewhere on it's circumference. Now, we want to get the coordinates $[x_{P_2},y_{P_2}]$ of the ...
1
vote
1answer
62 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
33 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
28 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 $90^{\circ}-\frac{1}{2}A$, ...
