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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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 a similarity transformation on this coordinate system that turns the cone ...
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1answer
12 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
24 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 ...
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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 ...
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0answers
39 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 ...
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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 ...
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2answers
27 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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0answers
11 views

Could I transport “sine function” from left hand-side to right hand-side?? [closed]

I'm new to sine function. So if the below expressions are definitely wrong, please forgive my ignorance.. [enter image description here][1] *L : the length of the chord *a : the angle of the chord ...
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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 ...
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0answers
24 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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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°?
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0answers
42 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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0answers
9 views

Area of triangle in argand plane [closed]

If $A(z_1), B(z_2), C(z_3)$ are vertices of a triangle in the argand plane. What is the area of the triangle ABC? Proof needed without taking $z_3$ as origin.
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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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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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1answer
35 views
+50

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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0answers
36 views

Wolf moves through line spiral [closed]

Ok, so i have next exercise: There's a wolf who lives in the plane forest, which is located on the Cartesian coordinate system. When going on the hunt, the wolf starts at point (0, 0) and goes ...
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3answers
74 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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0answers
32 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 ...
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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
49 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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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 ...
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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 ...
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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 $0xy$ ...
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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
28 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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0answers
23 views

Coordinate Geometry, Circle Sector Area

Wondering if someone might be able to help out on this. I need to calculate the area of a sector and then eventually the area of a segment using co-ordinate geometry and then create a computer to ...
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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 ...
3
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1answer
33 views

Find the area of the square using co-ordinates

Given a square $ABCD$ such that the vertex $A$ is on the $x$-axis and the vertex $B$ is on the $y$-axis. The coordinates of vertex $C$ are $(u,v)$. Find the area of square in terms of $u$ and $v$ ...
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0answers
20 views

Change of coordinates using the wedge product?

I while back (over a year ago) I was told about wedge products (or something very similar) and how they can be used to change e.g. the curl in Cartesian coordinates to in spherical coordinates. ...
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0answers
25 views

Surface Areas of an element in elliptic cylindrical co-ordinates

I'm trying to find the surface areas of an elliptic cylindrical segment. I know how to find the Area of faces in a cylindrical system. If we consider the figure below. Then, the surface area of the ...
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1answer
22 views

Defining a region in $\mathbb{R}^2$

I was trying to do this exercise but my answer doesn't match with the solution and I'm wondering why: Consider the coordinates transformation defined by $x=2u+v$ and $y=u^2-v$. Being $T$ the ...
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0answers
10 views

Transformation of 3D vectors to other planes in 3D

Suppose I have a set of points A, B, C, D, E, F... defined by the 3D vectors AB, AC, AD, AE, AF, AG etc. I can describe the geometry of these by defining them in an arbitrary plane e.g. z = 0 ...
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1answer
29 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: ...
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1answer
26 views

Convert ODE to polar coordinates.

$$k \frac{d}{dx}[A(x)\frac{dT(x)}{dx}] - hP(x)[T(x) - T] = 0 $$ What I had in mind was: $$x = rcosϴ, r = \frac{x}{cosϴ} , \frac{dr}{dx} = \frac{1}{cosϴ} $$ $$\frac{dA(x)}{dx} = ...
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1answer
34 views

isomorphism from one vector space to another one

This is from my textbook I don't quite understand what isomorphism means. Greek word "isomorphism" means same structure, but how can we say $P_3$ has the same structure as $R^4$?
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1answer
25 views

Unit base vectors in a new coordinate system

Let's assume we have a function $f:\Omega =R^2 \rightarrow R $ $f(x,y)=x+2xy+x^2y$. Obviously our unit base vectors on $\Omega$ are $e_x=\hat{i}$ and $e_y=\hat{j}$. Now we want to change the ...
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2answers
34 views

How to determine standard equation of a conic from the general second degree equation?

From a given general equation of second degree i can determine the conic by following rules: Given equation: $ax^2+by^2+2hxy+2gx+2fy+c=0$ then if, $abc+2fgh-af^2-bg^2-ch^2$ is not equal to zero ...
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1answer
11 views

Reaching a point B in Cartesian coordinate via Euler angles knows its initial point A Euler angles and B Euler angles

I have a point A: Known it's Cartesian coordinates (X,Y) and its Euler angle Aka head rotation (R,P) respectively Roll (rotation around X axis) , Pitch (rotaion around Y axis). (I'm not using Yaw ...
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1answer
27 views

How to understand rotation around a point VS rotation of axes?

I am puzzled about linear transformation and coordinate transformation, any help will be appreciated. From wiki rotation matrix, we know rotates points in the xy-Cartesian plane counter-clockwise ...
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1answer
22 views

Aligning 2 Coordinate Systems

I have a camera and a table and I want to align the camera to co-exist in the same coordinate system as the table. Here is an image of the setting. What type of mathematical transformations I need to ...
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4answers
29 views

Check if a given coordinate lies in path of a ray (coordinate geometry)

As shown in the image I have two known coordinate pair A and B and few other known coordinate pairs (RED blob) on the graph. I need to know if any of the other given coordinates fall in line of the ...
0
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1answer
34 views

Why are scale factors not always unity?

A scale factor in curvilinear coordinates is defined as $$h_v \equiv \left|\frac{\partial\vec{r}}{\partial v}\right|$$ where $\vec{r}=(x,y,z)^T$ is a position vector. The partial differential can be ...
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0answers
25 views

How to use slopes (3 points are given) to prove that they form a right triangle?

Question: Use slopes to show that $A(-3, -1)$, $B(3, 3)$ and $C(-9, 8)$ are vertices of a right triangle. My try at the problem: I know that we can find the slopes of $AB$, $BC$ and $CA$ and then ...
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0answers
18 views

Height function of a hypersurface

I was reading an article by do Carmo and Warner, which says: "By the height function for an oriented hypersurface at a point $p$ we shall mean the function defined on a neighborhood of the origin in ...
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1answer
20 views

Get vertex points of transformed rectangle knowing bounding box and transform matrices

(I'm not a mathematician so talk down to me). I have a rectangle that has been transformed by a series of matrix transforms. I can recover the transform matrices and get the x,y coordinates of each ...