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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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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acreage/areas of intersections

Hi I'm looking for the acreages/areas E and F between the following graph f(A) and the rectangle B. A, B, C and the are known values. E and F are unknown.
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24 views

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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63 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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11 views

Detecting ray cross after hit on a convex object

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

Determine the closest point along a circle's $(x_1, y_1)$ radius from any point $(x_2, y_2)$, inside or outside the radius of the circle.

I have a circle centered at point $(x_1, y_1)$ and another point at $(x_2, y_2)$. This point, $(x_2, y_2)$ may or may not be within the radius ($r$) of the circle. I wanted to create a line going from ...
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17 views

Intersect Ray (Line) vs Quadratic Bezier Triangle

I'm trying to find the intersection between a line segment and a quadratic bezier triangle for my OpenCL real time raytracer. The main recomendations I've seen are to try subdivision, or tensor ...
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13 views

Detect Regions Described By Lines in Rectangular Coordinates

Need some help from the superior math minds here. This problem is part of a software project. Essentially, I have a Cartesian grid. The user can create lines by plotting points (every 2 points ...
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30 views

Points in intersection

Given a matrix[nrows][ncols], and suppose it represents a terrain, like: (0,0) (1,0) (2,0).. (0,1)..... or a cartesian plan... and I have 2 points, both choosen by the user... How can I know which ...
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36 views

Intersection of two subspaces in 4D

I would like to know if there is some way to imagine the case when a 3D subspace intersects with a 2D plane in a 4D space. For example, let's have a 3D space in 4D $$A = \left(\begin{array}{c}1 & ...
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Minimum number of vertex moves to un-intersect a polygon with itself

In my game, I have n points that form a self-intersecting polygon. The points can be moved by dragging them. How can I form a non-intersecting polygon this way, in ...
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30 views

Is there a relation for when a circle intersects more than half the perimeter/circumference of another circle?

Is there some nice formula or algoritm for determining when a circle "hides"/intersects more than half of the perimeter of another circle, in a circle-circle interaction. Example image: Two example ...
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37 views

Crossing Circles

On a plane, you are only allowed to draw circles. After drawing 1 circle, can you ALWAYS draw another so that the new circle crosses all existing circles at 2 points? Why?
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39 views

The intersection of $u_{A} : A \longrightarrow A + B$ and $u_{B} : B \longrightarrow A+B$ is zero.

I am trying to show that the intersection of $u_{A}:A \longrightarrow A+B$ and $u_{B}:B \longrightarrow A+B$ is the zero map. Here, the $u_{A}$ and $u_{B}$ are the embedding maps into the coproduct of ...
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4answers
34 views

Metric Space Properties

I am revising my notes on metric spaces and one of the Theorems is stated but the proof has been ommitted and was looking for some help as I don't know where to start. Let $(X,d)$ be a metric space, ...
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15 views

Finding intersections points of pairs of polar curves?

Find all intersections of the curves $r=3^{(1/3)}\cos(\theta) , r=\sin(\theta)$ What I have done so far is to just put them equal to each other like this: $3^{(1/3)}\cos(\theta)=\sin(\theta)$, but ...
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2answers
51 views

Angle of intersection lines

I have got $3$ points say $(x_1,y_1)$, $(x_2,y_2)$ and the point of intersection $(x,y)$. I need to know the angle of convex angle of intersection of points. I need to whether the angle of ...
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66 views

Working algorithm for testing two rectangles for overlapping in Earth GPS coordinates plain

Here is a seemingly simple, but actually quite tricky problem: I am trying to figure out the correct algorithm to test intersection/overlapping of two rectangles, which are plotted on the Earth's ...
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42 views

psittacism: Fundamental Theory of Time

This question is in reference to the programming question found here. What method of approach should I be thinking of if I have a list of lectures A, B, and C, and discussions D, E, and F, that are ...
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1answer
52 views

intersection of finite intervals in $\mathbb{R}$

I'm studying some properties of Real Numbers. I have a claim that graphically seems true, but I don't know how to prove it. Let $p_i,r_i$ for $i=1,\ldots,n$ be real numbers such that ...
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2answers
34 views

Intersection of two lines in parametric form [closed]

This is a problem from an exam I had, neither me nor my friend manage to solve it. Consider the following two parametric lines in $R^3$: $ l_1: x = -3t + 4, y = 6t - 4, z = -6t + 9 $ $l_2: x = -2s ...
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27 views

Conic equation from cone/plane intersection

In an orthonormal cartesian frame $(O; \vec{x}, \vec{y}, \vec{z})$ consider: an infinite plane $P$ defined by: a point $p = (p_x, p_y, pz)$ an normal vector $\vec{n} = (n_x, n_y, n_z)$ a cone $C$ ...
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1answer
31 views

Convergence of a sequence in two different $L_p$ spaces

If I have a sequence $\{f_n\}_{n\in \mathbb{N}} \subset L_p\cap L_q$ that is Cauchy under both norms, I am wondering if $f_n \to f$ in $L_p$ implies that $f_n\to f$ in $L_q$. I have been working on ...
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20 views

Probability of objects position

So I have an interesting problem. I've got two objects, their area and position for their centre of mass in Cartesian coordinates. Their position is given as a bivariate normal distribution and I've ...
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1answer
50 views

Calculate possible intersection point of two lines

I'd like to know the $I$ coordinates $[x, y]$. $I$ is the possible intersection point of line $|AB|$ with $|XY|$ and $|X'Y'|$. Values that are known: Angle $AIX$ and $AIX'$ Coordinates of points ...
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79 views

How to find the curve of intersection of a ellipsoid and a plane?

Let $C$ be the curve of intersection of the ellipsoid $x^2+2y^2+3z^2=39$ and the plane $3x+y-7z=0$. Find the parametric equations for the tangent line to $C$ at $(5,-1,2)$. I don't know how to find ...
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33 views

Solving quartic equations

I am solving quartic equations by finding the intersections of two quadratics. The given quartic function is of the form $x^4 + px^2 + qx + r = 0$. I know one of the quadratic functions to be $y=x^2$. ...
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41 views

Venn diagram, is C = (A ∩ B ∩ C)?

I just saw a Venn diagram that has: A = All integer numbers between 1 and 100 that is dividable by 2. B = All integer numbers between 1 and 100 that is dividable by 3. C = All integer numbers between ...
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2answers
58 views

Line of intersection/quadric surfaces

Let $C$ be the curve of intersection of the cylinder $\frac{x^2}{25}$ + $\frac{y^2}{9}$ = $1$ with the plane $3z = 4y$. Let $L$ be the line tangent to $C$ at the point $(0,-3,-4)$. What is the ...
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39 views

Plane intersection

The planes $5x + 3y + 2z = 0$ and $ 2x + 8y - 5z = 0$ intersect. Find the equation of the intersecting line. I get the parametric equation: $x = t$ y = $\frac{29}{34}t$ z = $\frac{-121}{170}t$ ...
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52 views

Find points of intersection with cone on a plane at a given angles

The provided variables are the cone angle(cA) of a cone that starts at the origin along the Z axis, the vertical angle (vA) of the direction the cone is facing, and a horizontal angle (hA) along with ...
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59 views

Find the basis for the intersection of two subspaces in infinite-dimensional vector spaces

For an infinite-dimensional vector space U, and two subspaces W and V, we assume at least one of the two subspaces (W and V) is also infinite-dimensional. How can I find the basis for the ...
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2answers
39 views

Finding the self-intersection of a cruve

I need to find the self-intersection of the curve $$ C_1:x=t^2-5t+4, y=4\sin({\pi t\over 2}), 0 \le t \le 6 $$ I figured I would try to solve these equations on my TI-nspire: ...
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1answer
22 views

Expected intersection of two card draws of unequal length

here is my specific question: If two people draw independently without replacement, different numbers of cards from different (complete) decks. How do I figure out the expected number of matches or ...
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3answers
39 views

Determine, if there is one, the point of intersection between the line given by the equation:

The equation for the line is \begin{equation} \frac{x-5}{2} = 1 - y = \frac{z - 15}{4} \end{equation} The equation for the plane is \begin{equation} \left(\begin{array}{c} x \\ ...
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39 views

Find intersection of 2 parameterized planes

I have two parameterized planes, for example, {u, 0, v} and {u-1, v-1, 1}. And I have to find the parametric equation of the line that intersects both planes. By setting both planes equal to each ...
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Open Nested Interval Question [duplicate]

Find a family $\{ I_n \}$ of open nested intervals such that no two $I_n$ are equal and the intersection is equal to $\left[-2,2\right]$.
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1answer
47 views

Family of Closed/Open Nested Intervals

Find a family $\{I_n\}$ of closed nested intervals, such that no two $I_n$'s are equal and their intersection is $[-2,2]$. An answer for the same question except for dealing with open nested ...
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1answer
60 views

Avoiding collision with a plane

I am developing the software to control a common fly's flight in Opensim simulator, although I am facing some troubles determining when the fly must maneuver to avoid hitting a wall. Questions How ...
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1answer
48 views

Find the intersection of two planes.

Find the intersection of the planes $x+(y-1)+z=0$ and $-x+(y+1)-z=0$. These two planes are 3-dimensional and I am confused on how to solve it.
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125 views

Computing “radius” of the Intersection of a Circle and an Ellipse

I've been stuck on the following problem for awhile now. Does anyone have any ideas as to how to get a solution? Suppose $r > 0$ is a real number. The circle $x^2 + (y + 4)^2 = r^2$ has radius ...
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1answer
24 views

Showing for $f,g:\mathbb{R}\rightarrow\mathbb{R}$ that for $M>0, |f(x)|\le M|g(x)|$ for $x>x_0$

Showing for $f,g:\mathbb{R}\rightarrow\mathbb{R}$ that for $M>0, |f(x)|\le M|g(x)|$ for $x>x_0$. This is a repost of a question that is probably too long to ever get an answer (I feel compelled ...
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Odly phrased big-oh question, have I done what is required? (because it's not really big-oh, it's more graph sketching)

I've encountered these before, but never phrased or defined as follows, I'd like to know if I've done whatever the question wants to draw attention to (if it didn't want to draw attention to ...
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40 views

Simple question about dimensions of finite vector spaces

I have a very basic question. if I have a vector space $V$ of dimension $n$, and two vector subspaces $W,W' \subseteq V$, and I know that $W \cap W' = 0$, and I know that $V\subseteq W+W'$, does it ...
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2answers
55 views

Calculating intersection between a linear function and a cosine function

I'm trying to calculate the intersection between the two following functions: $y = kx + m$, $y = A \cos(B(x+C)) + D$. To find the intersection I start by assuming that both of the ...
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28 views

Area of intersection between square and annulus

The annulus' larger radius is $1$, smaller radius is $r>0$, and center is $(0,0)$. The square's sides are parallel with the axes, the lower left corner's coordinates are $(a,b)$, and the upper ...
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1answer
60 views

Assume that $P( A\mid B) < P( A)$ & $P( B\mid C) < P( B)$ . Is it true that $P(A\mid C)<P(A)$?

If $P( A\mid B) < P( A)$ & $P( B\mid C) < P( B)$ , then is it true that $P(A\mid C)< P(A)$, where $P( A\mid B)$ is the conditional property of $A$ given $B$? I tried the following: ...
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140 views

Probability- significant difference between $(A' \cap B) $ & $(A' \cup B)$ or $(A \cap B')$ & $(A \cup B')$?

Venn Diagrams in general! I've honestly been struggling with these kinds of questions for HOURS, I still don't get it. I went on the internet, researched to find an answer but only stumbled upon a ...
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85 views

What is the Area formed when a line is traced between two 3D curves?

This question is quite related to intersection of cylinders, Hyperbolic paraboloid and modelling. I am welding a trunnion to a pipe (both are hollow cylinders in different geometry). They intersect ...
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1answer
66 views

Smallest value for P(A)=P(B)=P(C) s.t. P(A and B and C) always exceeds 0.95

What is the smallest value for P(A)=P(B)=P(C) s.t. P(A and B and C) always exceeds 0.95? I have made some attempts: P(A and B and C)=P(A)P(B|A)P(C|A and B)>0.95. But how should the conditinal ...