Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.

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0answers
16 views

Converting coordinates

I am having huge trouble converting between cartesian to polar and to spherical. I need these methods for my limits of integration in most cases but using the formulas never seem to work, I just ...
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2answers
22 views

parametric polar equation of a circle

I discovered that Mac's Grapher has a parametric polar mode, i.e. where $r$ and $\theta$ can be specified in terms of a parameter, usually $t$. I am attempting to convert the generic equation for a ...
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1answer
25 views

Cone under similarity transformation

Suppose we have a cone passing through the origin of $xyz$ coordinate system. Now, the question is that whether we can find an invertible transformation on this coordinate system that turns the cone ...
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0answers
10 views

Linear equation scale transform

I have a linear equation in the general form: Ax + By = C in the standard coordination (Cartesian Coordinate System). I would like to scale this linear's coordination to a custom ratio (for example x ...
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1answer
26 views

Triple integral $\int_{0}^{2\pi} \int_{0}^{2\cos(\theta)} \int_{0}^{\sqrt{2r\cos(\theta)}} r \ dzdrd\theta$ to find volume of a solid

On evaluating the volume between $$x^2+y^2 = 2x\\z^2=2x$$ I set up the triple integral $$\int_{0}^{2\pi} \int_{0}^{2\cos(\theta)} \int_{0}^{\sqrt{2r\cos(\theta)}} r \ dzdrd\theta$$ for which ...
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0answers
17 views

Using GPS coordinates in trillateration

for a project we need to find a certain position. The info we have : 3 surrounding positions and the distance between those positions and the point we are looking for. We've got a setup like this ...
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0answers
370 views
+50

Change in neumann boundary conditions through coordinate transformation of elliptic PDE, weak formulation

The standard weak formulation of the Neumann problem for the Poisson equation is to find $u \in H^1 ( \Omega)$ such that for every $v \in H^1 ( \Omega)$: $$ \int_{\Omega} \nabla u \nabla v d x = ...
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0answers
17 views

coordinate transformation of operators

I recently came across a youtube video (https://www.youtube.com/watch?v=6O6iZug6e6Y) on transformation electromagnetism (yes this is physics) and some of the math equations that was postulated did not ...
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1answer
19 views

Find coordinates of point C in a equilateral triangle [closed]

How to find the coordinates of point C in a equilateral triangle, where $A=(-2,2)$ and $B=(6,2)$. http://i.stack.imgur.com/TXjjG.png Thanks in advance
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1answer
16 views

How to find coordinates of $D$

How can I find the coordinates $D$ if I have the other coordinates of a parallelogram $A(-3/-2)$, $B(4/1)$, $C(6/5)$, $D(?/?)$. Thanks in advance
1
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1answer
15 views

how to find the pivot/axis and angle that move one coordinates space to another?

I am writing a plugin for a 3d modeler, and I am stuck. For my plugin, I need to get the axis and the angle used for rotating a 3d object. But I only get the coordinates (~ 3dmatrices) of the objects ...
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1answer
25 views

Can point in 3D space be represented as vector?

If yes, then such vector is just displacement from origin in coordinate system? Also, I have another(optional) question, how to name variable that represnts particular point using vector? Position or ...
2
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1answer
597 views

Triangle and parametric coordinates

I'm studying on a book where it says: "A triangle is the set of points where for some point po, where u and v range over the parametric coordinates (we are talking about barycentric coordinates ...
2
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0answers
39 views

Faster Alternative than Calculating Euclidian Distance to determine which Coordinate has Max Distance from a fixed coordinate (eg (0,0))

I am developing a program that needs me to determine which coordinate in a $2$-D figure has maximum distance from a fixed coordinate. Let me demonstrate: $3$ points: $(1,3), (2,2), (5,0) $; Fixed ...
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0answers
10 views

determine lat/lng coordinate by adding distance in one direction from another coordinate

How can I calculate the coordinate of a latitude/longitude point that is X feet in one direction (North, South, East, or West). For example, how do I get the point 1000ft North of 45,-100? 500ft East ...
13
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4answers
6k views

Simple proof of integration in polar coordinates?

In every example I saw of integration in polar coordinates the Jacobian determinant is used, not that I have a problem with the Jacobian, but I wondered if there's a simpler way to show this which ...
4
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0answers
43 views

Flea on the coordinate system

We drop a flea on a point of the coordinate system(with integer coordinates). Due to the dimensions of the flea we can not see it. The flea jumps away every second by one unit (always in the same ...
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2answers
25 views

Volume of paraboloid $z = x^2+y^2$ with heigth $h$

I am asked to find the Volume of paraboloid $z = x^2+y^2$ with heigth $h$. How would be the best way to approach that problem (cartesian/cylindrical)? My reasoning using cylindrical coordinates ...
0
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0answers
18 views

Evaluate the integral $f(x,y,z) = x$ within $x^2+4y^2+9z^2 \leq 1$ and $x \geq 0$ and also $y \geq 0$

I am asked to evaluate the integral $f(x,y,z) = x$ within $x^2+4y^2+9z^2 \leq 1$ and $x \geq 0$ and also $y \geq 0$ using a change of variables. Should I proceed with spherical coordinates? If so, is ...
0
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0answers
26 views

Using cylindrical coordinates evaluate $\int_{0}^{2} dx \int_{0}^{\sqrt{2x-x^2}} dy \int_{0}^{a} z \sqrt{x^2+y^2} dz$

I am asked to solve the following problem: Using cylindrical coordinates evaluate $\int_{0}^{2} dx \int_{0}^{\sqrt{2x-x^2}} dy \int_{0}^{a} z \sqrt{x^2+y^2} dz$ Before doing that long ...
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2answers
34 views

Evaluating the integral of $f(x,y,z) = \frac{y}{\sqrt{z}}$ on $y \geq 0$ and $0 \leq z \leq x^2$ and $(x-2)^2+y^2 \leq 4$

I am asked to evaluate the integral of $f(x,y,z) = \frac{y}{\sqrt{z}}$ on $$ y \geq 0\\ 0 \leq z \leq x^2\\ (x-2)^2+y^2 \leq 4 $$ What I have so far (and it seems a little off) is $$ ...
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1answer
54 views

Find limits of integration for the interior region of sphere with center $(a,0,0)$ and radius $a$ using spherical coordinates

I am asked to find limits of integration for the interior region of sphere with center $(a,0,0)$ and radius $a$ using spherical coordinates. How can one do that? I know that one may use $$ x = r ...
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2answers
1k views

What is the number of integer coordinates on a line segment?

What is the number of integer coordinates(end points included) on a line segment with integer end coordinates $(x_1,y_1)$ and $(x_2,y_2)$? Integer coordinate means that both abscissa and ordinate are ...
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1answer
1k views

Extrinsic and intrinsic Euler angles to rotation matrix and back

currently I'm working on the visualization of coordinate systems in space to understand rotation matrices better. Until now I thought everything would be ok, but there is a thing that does not get ...
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3answers
54 views

Converting into rectangular form

I have 2 related questions: First: Let $z_1 = 2+2i$ and $z_2 = 2-2i$. Find $z_1z_2 $ in rectangular form. I have no idea... I'm also clueless about this question: Change the following to ...
8
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3answers
76 views

There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$

There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$. A point $P$ satisfies following condition: The straight line passing through $P$ and dividing the area of square $Q$ in ...
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1answer
29 views

What's the name of the two diagonals in a 2D plot? [duplicate]

In a 2D plot (with x and y), what's the correct name of the diagonal lines, i.e. the line at 45° and that at 135°?
3
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1answer
342 views

Vector Algebra Coordinate Transformation

Let us look at two coordinate systems $K$ and $K'$ with axes, respectively, $(x_1,x_2,x_3)$ and $(x_1',x_2',x_3')$ and unit vectors ($\vec{e_1},\vec{e_2},\vec{e_3}$) and ...
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0answers
34 views

Project (lat,lng) GPS point to a line segment (road segment) [closed]

Is there a way to project a point A to a B,C line segment and find a point D ? The points ...
1
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1answer
28 views

Co-ordinate transformation of metric

In a past exam paper that I am using to prepare for my upcoming finals, I have encountered the following question (paraphrased): Given the metric: $$\mathrm{d}s^{2} = ...
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0answers
43 views

There is a square that vertices are (0,0) (0,2) (2,0) (2,2) [duplicate]

A point P satisfies following condition : The straight line passing through P and dividing the area of the square by 1:3 does not exist. Can we know the locus of P and the area of the locus ? I ...
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2answers
18 views

Find limits of integration for region under sphere $x^2+y^2+z^2=a^2$ inside cone $x^2+y^2=z^2$ and above $0xy$

I am asked to find the limits of integration for region under sphere $x^2+y^2+z^2=a^2$ inside cone $x^2+y^2=z^2$ and above $0xy$. Should I use spherical coordinates or cylindrical coordinates? Is it ...
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0answers
19 views

Good way to plot coordinate system in computer?

I want to plot a coordinate system rotation in my paper, I want to know what would be a good way to make the plot? The plot would look like:
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1answer
50 views

Coordinate charts vs. coordinates on manifolds

I just realised that I'm confused what coordinates really means in the context of manifolds. For example, say $M=S^2$. Then we can define smooth charts as follows: Let the open sets be $U = S^2$ ...
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2answers
811 views

Inverse rotation euler angles

I have three angles representing a rotation (Pitch, roll and yaw). I need the inverse rotation (working on coordinate system transforms). What I do now is transforming these angle to a rotation matrix ...
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2answers
455 views

New x coordinate of a rotated line

I need help finding the equation to find $x$ I work in GIS and I'm working on a script that uses the new x coordinate of a rotated line. I havent work with trigonometry in a long long time so I ...
5
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3answers
138 views

Finding equation of chord of hyperbola.

Equation of chord of hyperbola joining points $(a\sec\phi,b\tan\phi)$ and $(a\sec\phi_1,b\tan\phi_1) $ $$y-b\tan\phi=\frac{b\tan\phi-b\tan\phi_1}{a\sec\phi-asec \phi_1}(x-a\sec\phi) $$ This reduces ...
0
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1answer
19 views

Evaluate $f(x,y,z) = z^3$ on the region defined by $z \geq 0 \ x^2+y^2 \leq 1 \ x^2+y^2+z^2 \leq 2$

I am asked to solve the following problem: Changing the variables, evaluate the integral of the function $f(x,y,z) = z^3$ on the region defined by $z \geq 0 \quad x^2+y^2 \leq 1 \quad ...
2
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1answer
32 views

Evaluate the volume of the solid defined by $x^2+y^2+z^2 \leq 9$ and $x^2+y^2 \leq 3y$

I am asked to solve the following problem: Evaluate the volume of the solid defined by $x^2+y^2+z^2 \leq 9$ and $x^2+y^2 \leq 3y$. I thought about using spherical coordinates: $$ 0 \leq \rho ...
0
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1answer
15 views

What is the intuitive meaning of the partial derivate in coordinate transforms?

We learned that when changing coordinate system from $u^i$ to $u'^i$, a contravariant vector transforms like this (using the Einstein-convencion): $v'^i = \frac{\partial x'^i}{\partial x^j}v^j$, And ...
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0answers
8 views

Why describe basis multipliers as barycentric coordinates?

So a disclaimer up front: I'm from a EECS background as opposed to pure math, so if possible keep that in mind for your answers. I've been reading a paper on 2D-3D triangulation and came across the ...
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1answer
18 views

Formula to move N units along a slope in cartesian system, based upon an angle, which will calculate final point as an x,y location in grid

I need a formula which will calculate my final x,y location in a cartesian coorindate system. First, let me set this up. An Easy Example To Explain What I'm Looking For Start at point 20, 20 in a ...
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2answers
24 views

Set up the triple integral for region between cylinders $x^2 + y^2 = 9 \quad x^2 + y^2 = 16 \quad z = 4+x^2$ and $0xy$ plane

I ran into a problem that I am not sure about the correct answer. The question is: Set up the triple integral for region between $x^2 + y^2 = 9 \quad x^2 + y^2 = 16 \quad z = 4+x^2$ and $0xy$ ...
0
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1answer
32 views

How do you check if a coordinate $(x,y)$ is inside or on the perimeter of a cross

$1.$ How do you check if a $(x,y)$ coordinate is inside a cross? $2.$ How do you check if a $(x,y)$ coordinate is on the perimeter of a cross? The cross is like a medical sign. The cross will have ...
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0answers
29 views

Visualizing Nash Equilibria of a 4 dimensional matrix

Are there any good ways to visualize Nash equilibria of a 4-d matrix? I have created an game theory model which consists of of four players (P1; P2; P3; P4) who can all choose between a set of 27 ...
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2answers
23 views

The expression for reflection of a ray line $ax+by+c=0$ reflected by a mirror whose normal is given by $a'x+b'y+c'=0$.

Using vectors I tried obtain the expression for reflection of a ray line $ax+by+c=0$ reflected by a mirror whose normal is given by $a'x+b'y+c'=0$. The point of intersection is ...
1
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1answer
267 views

Parametric integration negative area?

I know there is a question very similar to mine already here Why does using an integral to calculate an area sometimes return a negative value when using a parametric equation? , but I am still a bit ...
0
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1answer
31 views

Quaternion to Euler angles conversion

I have written the following MATLAB code for transforming Quaternion to Euler angles based on the mathematical formula from wikipedia: ...
0
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1answer
53 views

Why aren't area of triangle not same when calculated by different methods in this case

I came across a question today. Two mutually perpendicular straight lines through the origin forms an isosceles triangle with the line $2x + y = 5$. Then the area of the triangle is ? I know ...
0
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0answers
12 views

Change directly between spherical coordinate systems, without intermediate Cartesian coordinate system.

Is there a practical way to change from one spherical coordinate system to another spherical coordinate system without changing to an intermediate Cartesian coordinate system? The Stack ...