Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.
0
votes
2answers
99 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
47 views
0
votes
1answer
11 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
72 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 ...
0
votes
0answers
17 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
4answers
39 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
29 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
65 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?
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
62 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
26 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
44 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
49 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
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” ...
1
vote
1answer
49 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
2answers
117 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
74 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
41 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:
...
0
votes
1answer
22 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 ...
1
vote
1answer
34 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
35 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
55 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
1answer
44 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
109 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
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
25 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
80 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
59 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
32 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 $90^{\circ}-\frac{1}{2}A$, ...
0
votes
1answer
33 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
107 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!
1
vote
2answers
37 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
27 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
53 views
when we have circle in hyperbolic plane,what is the center and radius of this circle in Eucliden plane?
Let C be the hyperbolic circle with center Xi, where x>0 and redius r>0. Find the center and radius of this Eucliden circle.
1
vote
1answer
30 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
66 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
98 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
85 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
47 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?
4
votes
2answers
68 views
Circumference parametrization
Let $C=\{(x,y)\in \Bbb R^2: (x-x_0)^2+(y-y_0)^2=r^2\}$ and let $\varphi :[0,2\pi]\to \mathbb{R}^2$, $\theta \mapsto (x_o+r\cos \theta, y_0+r\sin \theta)$, with $r>0$.
I'm trying to prove that ...
0
votes
2answers
52 views
Question on inverse trig functions and quadrants? Please Help!
Alright, I was doing a question in a book, and it said:
$\displaystyle \cos(2x - \frac{\pi}{6}) = \frac{\sqrt{3}}{2}$
I proceeded and got: $\displaystyle 2x - \frac{\pi}{6} = \frac{\sqrt{3}}{2}.$
I ...
1
vote
1answer
74 views
What is the relative behaviour when a center circle surrounded by 6 circles is (recursively) replaced by 6 circles
Start with a given "inner" circle of arbitrary radius (blue) centered at C. Surround it by 6 circles of equal radius. This concerns to known issues of circle packing and is a frequently treated ...
0
votes
0answers
38 views
Given 2 outer points of a perfect circle, find the centerpoint
Alright, I hope this makes some sense.
I am using a software that can create arcs.
This arc is defined by:
Begin point
End point
Center of "circle"
The center is supposed to be the center of the ...
0
votes
2answers
36 views
Finding the intersctions of two given curves
Given
$$
\begin{align}
r &= -2\sin(\theta) &&(i)\\
r &= 6\cos(\theta) &&(ii)
\end{align}
$$
I'm trying to find their intersections.
I know $(i)$ is a circle with radius $1$ ...
0
votes
1answer
35 views
Problem of sketching a circle
I've to solve a problem in which I've been given this equation: $x^2$ + $y^2$ $=$ $4$ and I've to sketch a circle which is the locus of the equation. Here $'2'$ is the radius $r$ of the circle. 2 ...
