The intersection of two or more sets, written $A\cap B$ or $\bigcap_{i\in I} A_i$, is the set of all elements contained in *all* given sets.

learn more… | top users | synonyms

1
vote
0answers
7 views

Construction of concurrent or parallel lines from a parallelogram (proof by vectors)

I have a problem with this probably easy exercise on vectors. Any help would be great. Let ABCD be a parallelogram. The line parallel to AB intersect BC and AD in points Q and S, respectively. The ...
0
votes
0answers
20 views

Find points that defines the intersection of an ellipse with a plane.

I want to test for the intersection of two ellipses $E_1$ and $E_2$ in $\mathbb{R}^3$ represented on a computer. In some sense, this isn't a hard problem: ...
1
vote
1answer
17 views

Measure on intersections of unions

Let $(X,\mathcal{A},μ)$ a measurable space and let $A_1,A_2,...∈\mathcal{A}$, assume that $\sum\limits_{j=1}^{\infty}=\mu (A_j)<\infty$ We have ...
0
votes
0answers
12 views

Measure of intersections [duplicate]

Let $(X,\mathcal{A},μ)$ a measurable space and let $A_1,A_2,...\in \mathcal{A}$, assume that $\sum^{\infty}_{j=1}\mu(A_j)<\infty$ I want to show that ...
2
votes
0answers
62 views

Prove that the two polynomials intersect each other only at a single point

Here are the polynomials: $$D^K_1(\theta)=\sum_{i=\lceil{K/2}\rceil}^K \binom{K}{i}\theta^i(1-\theta)^{K-i}$$ and $$D^K_2(\theta)=\frac{1}{2}\sum_{i=\lceil{K/2}\rceil}^K ...
1
vote
1answer
19 views

Vector Parametrization of a Hyperbolic Paraboloid and a Plane

So I need to find the intersection between a hyperboloid ($z=\frac {y^2}{b^2}-\frac{x^2}{a^2}$) and some related plane ($bx+ay-z=0$). I have tried solving for $z$ and equating the two: ...
1
vote
1answer
17 views

Determine Circle of Intersection of Plane and Sphere

How can the equation of a circle be determined from the equations of a sphere and a plane which intersect to form the circle? At a minimum, how can the radius and center of the circle be determined? ...
2
votes
1answer
29 views

Find the equation of line and finding a point in given example

The outer circle is $x^2+y^2=1$ and the smaller circle is $x^2+(y+1-r)^2=r^2$. The arclength is parameterised anticlockwise with $s=0$ at the bottom as shown. If we know $s_n$ and $s_{n+1}$ can we ...
3
votes
1answer
31 views

Longest chord inside the intersection area of three circles

I am currently working on my masters thesis in computer science and I stumbled onto a geometry problem. My goal is to compute the length of the longest possible chord inside the intersection area of ...
3
votes
1answer
17 views

Intersection problem

I am given an interval $A=(0,1)$ and $B=(1,2)$. How can I show that $A \cap B$ is an empty set? I tried to prove by contradiction by saying an arbitrary element $k\in A\cap B$ so $k \in A$ and $k \in ...
0
votes
1answer
29 views

Finding the limit of sets

I have a problem, where I have difficulties with solving these two exercises. Here is the problem If $C_1$, $C_2$ ... are sets where $C_k \supset C_{k+1}$, where k=1,2,3. Then the limit of $C_k$, ...
2
votes
1answer
40 views

How to compute coordinates of a point that intersects an sphere

Hi all. Is there a way to compute the S(x,y,z), given the following information: A(x,y,z) e = elevation (from the line AS) Az = azimuth (over A). Perpendicular to x axis. Can vary from 0 tp 360. ...
0
votes
1answer
20 views

How to determine a general arithmetic sequence formula for two intersecting trig function

I have equations out of two trigonometric functions. For example $\cos(4\alpha$) = -$\sin(5\alpha)$ $\tan(0.5\alpha$) = 2 $\sin(\alpha)$ How can I determine a general arithmetic sequence formula ...
0
votes
5answers
74 views

How to find the point of intersection with three equations?

Given the following equations with three variables $a, b, c$ $a-5b+4c=-3$ $2a-7b+3c=-2$ $-2a+b+7c=-1$ How can I determine the point (if it exists) at which all three lines intersect?
1
vote
4answers
53 views

The intersection of $3$ set is empty, would the intersection of $4$ sets be empty?

Let me clarify some more. Let's say we have four sets $A,B,C,$ and $D$. If the intersection of any three sets is empty, by default is the intersection of all four sets empty?
2
votes
0answers
41 views

Find circles that completely cover a polygon minimizing the amount of space covered outside the polygon

I have an arbitrary polygon that I need to roughly represent using circles. Any point inside the polygon must lie inside a circle. There will be points outside the polygon that will fall under a ...
1
vote
1answer
12 views

calculate the coordinates of the intersection between a bisector and a sector

I have a sector and would like a formula that gives the intersection between the bisector and the arc. here's a graph of the situation: the point B is the center of a circle of radius AB and the BD ...
0
votes
0answers
42 views

Probability of infinite intersections

While I was studying Probability and random processes I came across the following question. Say I have $A_1,A_2, \ldots, A_n$ events such that $A_i$ is in $E$ but not equal to $E$. What is: ...
0
votes
1answer
29 views

length of secant line.

I'm looking for way to find the length of a secant line intersecting another line through the center of a circle with a known radius. The intersection point is on the circle and the angle between 2 ...
2
votes
2answers
40 views

Circle Line segment intersection

I have a circle with radius r and center $(c_x, c_y)$. I have a line segment $(x_1, y_1)$ and $(x_2, y_2)$ given $(x_2, y_2)$ is always a point inside the circle. I am trying to find the ...
0
votes
1answer
40 views

Union of Intersections [closed]

What is the general formula for finding the union of intersections? For example , Consider the sets $A , B , C $ I need to find $$((A \cap B)\cup(A \cap C)\cup(B \cap C))$$ Please extend this as a ...
2
votes
1answer
40 views

Projective and affine conic classification

I have a doubt on the classification of non-degenerate conics (parabola, ellipse, hyperbola) in projective geometry (my textbook is "Multiple View Geometry in Computer Vision", which, as the title ...
1
vote
1answer
36 views

Outer interval of circle intersection

Is there a consistent way to calculate the outer interval $\left(~\mbox{element of}\ \left[0, 2\pi\right]~\right)$ of a circle created by an intersection ?. I calculated the intersection points and ...
1
vote
2answers
40 views

calculate circle segment area: determine distance

I have a problem calculating the area of a circle segment. I know how to separate this into smaller tasks (triangle and remaining circle segment) that are basically easily solvable, but one distance ...
1
vote
0answers
10 views

Testing hypothesis about window non-overlap

I have a large number (~1.5 million) of protein sequences, each of them of different lengths.There are 6 schematic examples in the attached image. Within each of these sequences, there are >= 0 ...
1
vote
0answers
37 views

Intersection between 2 lines (3D). This doesn't have a solution does it?

so I was looking through an old exam and this question was given: The teachers answer was the point (9, -9, 21) I tried solving this myself, I got x = x, y = y, but I could not find a point where ...
1
vote
0answers
56 views

intersection of a line and plane on a 3-sphere

Suppose I have two 4D points, $\mathbf{a}=(a_1,a_2,a_3,a_4)$ and $\mathbf{b}=(b_1,b_2,b_3,b_4)$, that both lie on a unit 3-sphere (i.e. unit distance from origin). In addition, I have a 2-D plane that ...
1
vote
1answer
49 views

Determining intersecting points between square and circle

I unfortunately have spent too much time trying to solve this question, and have turned to you for help. The corner of my square has intersected some circle, and I need to move it out. I only know one ...
1
vote
2answers
60 views

Geometry : find the points of tangency between two lines and two circles [closed]

I have a programming problem. I need to find the intersection points between two lines tangent to two circles and the circles! I have the circles' radiuses and centers. So I need points ...
0
votes
2answers
58 views

May a monoid have two disjoint submonoids?

I'm asking this question inspired by the similar question about group and its subgroups. I tried to modify the proof presented there to work for monoids but I failed. I'm also not able to find any ...
0
votes
1answer
86 views

Check if point lies on a line segment

I know there are shorter solutions that use dot product, but I don't know what the logic behind doing so involves so I came up with something that I understand myself (i will research the dot product ...
0
votes
2answers
74 views

Parametric equation for intersection of curve

Here's the three part question: A) Find parametric equations for curve which is the intersection of the cylinder $x^2 + z^2 = 1$ and the plane y = -x. B) Show that the curve lies on the surface $x^2 ...
2
votes
3answers
58 views

Euclidean “straight line” calculation

Please see image first.. I have as input the following (I presume these are in effect Euclidean coordinates): The angle and the length of the red line. The angle and the length of the green ...
0
votes
1answer
65 views

How to determine if two ellipse have at least one intersection point

All of the question are in sequence and related. 1.Given 2 ellipse with the position x1,y1, x2,y2 and the radius a1,b1, a2,b2, construct an equation to determine if both of them has at least one ...
0
votes
1answer
40 views

Binomial distribution or probability intersection

I flip a biased coin, p = 0.5 for getting heads. What is the probability of getting heads 8 times ? Firstly I used probability intersection $$ P(A \cap B \cap C \cap D \cap E \cap F \cap G \cap H) = ...
1
vote
2answers
45 views

internal rectangle area intersected by a circle

I need to compute the internal rectangle area intersected by a circle like (the blue area) on these 3 examples: I know every vertex (x,y) coordinate and then their distance from circle center but ...
2
votes
1answer
43 views

Finding Unions and intersections given two probabilities.

I am currently trying to find the unions and probabilities given: A = .2 and B = .6. P($A\cap B$) = .12 And am looking to find ...
0
votes
2answers
75 views

Find normal to ellipse through arbitrary points

I want to find the normal to ellipse through an arbitrary point. There is an array of points located arround a given ellipse (but not on ellipse curve). What I want to find is the normal of each of ...
1
vote
1answer
36 views

Countable intersections in sigma-rings

A problem in Friedmans Analysis is to show that a $\sigma$-ring is closed under countable intersections. Let the $\mathcal{R}$ be the $\sigma$-ring. I tried to solve it as follows: Since $A - B \in ...
0
votes
1answer
74 views

Find intersections of two ellipses who share one fixed point

Given two ellipses $e_1$ and $e_2$ with $$ e_1 = \{x: \lVert{x - F_1}\rVert + \lVert{x - F_2}\rVert = R \} $$ $$ e_2 = \{ x : \lVert{x - F_1}\rVert + \lVert{x - F_3}\rVert = R \} $$ where $F_1$ is ...
0
votes
1answer
21 views

How can i know that vector x is passing b/w vectors a, b, c, d?

I have been given 4 vectors a, b, c, d, and another vector x. How can i know that vector x is passing b/w vectors a, b, c, d? If the vectors were in R^2 then i will check only for 2 vectors. but they ...
1
vote
2answers
45 views

Parabola and line proof

Given are three non-zero numbers $a, b, c \in \mathbb{R}$. The parabola with equation $y=ax^2+bx+c$ lies above the line with equation $y=cx$. Prove that the parabola with equation $y=cx^2-bx+a$ lies ...
3
votes
1answer
47 views

Points of intersection between circle and parabola

Find the points of intersection between circle and a parable: circle: $x^2 + y^2 - 2x + 4y - 11 = 0$ parable: $y = (-x^2+ 2x + 1 - 2\sqrt{3})$ I don't understand how to solve this, I really tried, ...
1
vote
2answers
62 views

Does anyone know of any open source software for drawing/calculating the area of intersection of different shapes?

I would like to be able to draw any number of different shapes and determine the area of their intersections. I'm looking for free, open source software. I thought about trying to code something up ...
0
votes
0answers
44 views

Area covered by multiple (possibly intersecting) circles on surface of sphere

I have a number of circles of same radius on surface of sphere (Google Maps API). I'm trying to calculate the total area covered by these possibly intersecting circles. My current solution is ...
0
votes
1answer
49 views

Finding the points of intersection of the circles [closed]

How can you find the points of intersection of the circles $x^2+y^2-2x-2y-2=0$ and $x^2+y^2+2x+2y-2=0$?
0
votes
2answers
47 views

Closest Point on a Sphere to Another Point

Given a sphere $S(c,r)$, $c$ being the center point $(x,y,z)$ and $r$ being the radius, there is a point $p(x', y', z')$ which is either inside or outside $S$. I want to find the point $q$ such that ...
1
vote
1answer
36 views

Disjoint conic sections?

is there any simple way to figure out whether two conic sections (e.g. two ellipses or an ellipse and a hyperbola) are disjoint or intersect each other? The conic sections are expected to be known ...
0
votes
1answer
28 views

Intersection of planes

A line perpendicular to the plane $ 3x-5y+4z-11=0 $ passes through the origin. At what point does this normal intersects the plane?
0
votes
1answer
34 views

Calculate if a Circle intersects a Arc

Have a Cartesian Plane cartesian plane And a Arc with the measures: point = 200, 200 radius = 50 start angle = 0 end angle = 180 And a Circle with the ...