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.

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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 ...
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Polyhedra Intersection

Suppose we are given two polyhedra defined as $P_1 = \{x | A_1x \le b_1\}$ and $P_2 = \{x | A_2x \le b_2\}$. How can we show that if $P_1$ and $P_2$ dont not intersect, then there exists vectors $s,t ...
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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 ...
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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 ...
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27 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 ...
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34 views

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

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 ...
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55 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 ...
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48 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 ...
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18 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 ...
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48 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 ...
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1answer
45 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 ...
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27 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) = ...
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33 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 ...
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1answer
21 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 ...
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50 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 ...
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1answer
18 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 ...
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67 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 ...
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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 ...
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29 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 ...
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40 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, ...
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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 ...
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21 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 ...
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37 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 $x^2+y^2+2x+2y-2=0$?
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43 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 ...
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35 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 ...
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26 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?
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30 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 ...
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25 views

Intersect and Trim lines with a polygon

I have defined a Polygon. I want to intersect and trim a list of other Lines with the Edges ...
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49 views

Geodesics intersection on a cylinder

My problem is the following: I have a cylinder, and a couple of geodesic segments on its surface. The segments are defined by the coordinates of their start and end points. I have to obtain the ...
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1answer
68 views

Area of intersection between 4 overlapping circles.

I'm having difficulties finding the are of a section on the 4th circle when 4 circles intersect. The circles have a diameter of 150 mm, and the centers of adjacent circles are 100 mm apart. The shaded ...
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22 views

Are all subbasis subsets of basis?

In topology, each element of basis $\{B_k\}$ can be expressed as finite intersections of elements of subbasis, i.e. $B_k=S_{n_1}\cap ...\cap S_{n_m}$ Does the meaning of "finite intersections" also ...
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68 views

Finding the area of the shaded region on a circle.

So I need help finding the area of the shaded A region. I was going to do pi*(r^2)*(45/360) - (the area of the smaller triangle). I just dont know how to get the angle or the lengths of it. Is there ...
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1answer
15 views

How to find last pt of triangle

How to find last pt of triangle. I got (1,7) and (0.5, 4). The equations are y = 3|2x − 1| + 4 and y = −|x − 4| + 10
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1answer
23 views

Intersection to infinity problem

I have the problem $$\bigcap_{n=1}^{\infty}[-n,3^{-n}]$$ and I had thought the solution was $[-1,0)$ however it turned out to be $[-1,0]$. Why when $3^{-n}$ will never reach $0$?
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60 views

Extending the Intersection of Subspace

For two subspace, one can express the dimension of the sum as $$ \dim(U_1 + U_2) = \dim U_1 + \dim U_2 - \dim (U_1 \cap U_2).$$ However, the obvious extension to three subspacess fails, in the ...
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61 views

Calculating Intersection of Three Spheres Step by Step

How do I calculate the intersection of three spheres step by step? Assume that the spheres are $S_i(c_i, r_i)$ where $i = 1,2,3$, $c_i$ is the center coordinates of $S_i$ and $r_i$ is the radius of ...
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39 views

Two circles intersection

Could you tell what are all the four points in following? Two circles intersect at two points maximum when we want to draw intersecting circles. But there we are solving quadratic equations, what is ...
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60 views

Two circle intersection

Two circles intersect at two points maximum when we want to draw intersecting circles. But there we are solving quadratic equations, what is the argument about the other two missing points?
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Probability for Subsets

I am examining a set S, which is composed of a finite number known of elements. The size of the set is much larger than the number of possible types of elements, so each repeats many times. I am ...
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1answer
34 views

Similarity between $2$ sets

I have two sets $S_1=\{1,2,3,4\}$ and $S_2\{1,2,3,4,5,6,7,8,9\}$. $Intersection (I) = 4$ Number of non-equal elements (N) = $5$ I am trying to find a way to combine the ...
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1answer
31 views

Vectors in the Third Dimension

I am just beginning to learn about three dimensional vectors and I am not really sure how to go about this problem. I set r1=r2 but I'm not quite sure where to go from here. Any help would be ...
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Finding the equations of the lines and tangent to the circle

Find the equations of the lines through $(2,0)$ and tangent to the circle $x^2+y^2=1$. I tried to solve this and I know the right answer but I just can't solve this. The right answer: $\sqrt{3}y=x-2$ ...
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60 views

Intersection between sphere and ellipsoid

I am failing since two days to compute and to plot the intersection of an ellipsoid in parametric notation ...
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1answer
36 views

Two sets of number ranges where one influences the other, how to find the intersection point?

Suppose I have the following number ranges: a = [x = 1, y = 5] b = [x = 9, y = 3] Now say a donkey is travelling between the number range 'a' and a horse is moving between number ranges 'b'. The ...
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19 views

Transversal Intersection

If $X, Z$ are manifolds of complentary dimension in $Y$, where $X$ compact, $Z$ is closed. Then show that in $ X \times Z, I_2(X \times \{0\},\{0\} \times Z) = 1$. Is this obvious because they ...
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line segment intersection

Do these two line segments intersect ? I'm confused because if you extend the below line then they will intersect otherwise not but we can't extend them as they are line segments. Is line segment ...
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103 views

Sphere Plane Intersection Circle Radius?

How would one find the radius of the circle that's the intersection of a sphere and a plane ? It is some how associated with distance from the center of the sphere.. Distance from plane to center of ...
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Find all the intersection points of a vector parabola (in R3) and a sphere

Given that I have a vector in R3 (7t, 10t - 2t^2, 5t) | (These numbers are arbitrary for the sake of the process) A sphere centered at the point ( 15, 25, 10) with a radius of 20 There is a ...
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91 views

Region of integration of intersection between cone and sphere

Let's suppose we have a sphere with radius $R>0$, and half a cone with an opening angle $\alpha \in (0, \pi/4)$. The vertex of the cone is in the surface of the sphere, and the center of the sphere ...
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Detecting ray cross after hit on a convex object

I have a hw question im struggling to solve - Any guidance will be appreciated.