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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33 views
Measuring distances on any coordinate system
I was reading the book The ABC of Relativity from Betrand Russell, and at some point, the author mentions a method for measuring the distance between 2 points on any coordinate system. He says that ...
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0answers
11 views
Estimate for a rigid transform given a set of noisy measurements
I have a set of rigid transforms $\in \mathbb{R}^{4x4}$, where each transform is an approximation to some unknown, "correct" transform. I'm looking for an algorithm to estimate the correct transform ...
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2answers
81 views
Plotting in the Complex Plane
I just wonder how do you plot a function on the complex plane? For example,$$f(z)=\left|\dfrac{1}{z}\right|$$
What is the difference plotting this function in the complex plane or real plane?
Thank ...
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0answers
14 views
Comprehending change of (Galilean) basis
Everybody knows the Galilean transform
$\left[\begin{array}{cc}t' \\x' \\\end{array} \right]
= \left[\begin{array}{cc}1 & 0 \\v & 1\\\end{array} \right]
\left[\begin{array}{cc}t \\ x ...
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0answers
20 views
Transformation into cartesian coordinates
I need some help with specific transformations and rotations.
But first, I need to describe context.
Imagine two points in space situated at $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ respectively. In
a ...
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1answer
28 views
Find position on surface of a lens
If I have a lens with coordinates UV on the lens surface where U, V are [-1, 1] and I want to find the real-world (x,y,z) coordinates of the UV point, how would I do that if I have the following ...
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1answer
22 views
How do I compute the Laplacian of a function in terms of a given (general) coordinate transformation?
Consider a coordinate transformation $\boldsymbol{x} = \boldsymbol{x}(\boldsymbol{\xi})$ (with Jacobian $\partial \boldsymbol{x}/\partial \boldsymbol{\xi})$, the scalar function $f(\boldsymbol{x}) = ...
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1answer
23 views
Vector direction
I have a vector in the 2nd Coordinate of the Cartesian plane. I want to know that how can I find out the direction of the vector that whether it is towards the ...
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39 views
Calculate the distance between the points (1, 2, …, n) and (2, 3, … n, 1)
I know that the operation to find the distance between two vectors is:
$$\sqrt{(b_1-a_1)^2+(b_2-a_2)^2+...+(b_n-a_n)^2}$$
So:
The distance between $(7, 5, 3, 1)$ and $(1, 3, 5, 7)$ is:
...
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0answers
17 views
Movement in Cartesian system with sinus / cosinus
I use this little snippet to have movement in my little game in writing to learn. It works, but I don't understand why. Could somebody explain this to me? Or point me in the direction of a site where ...
1
vote
1answer
60 views
Coordinate transform
Can anyone see what transformation $$r\to f(r)$$ transforms $$\exp(2\phi(r))(dr^2+r^2d\theta^2)$$ to
$$df^2+\sinh^2(f)d\theta^2$$?
I there a systematic way to attack such a problem -- rather than just ...
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2answers
54 views
If the diagonals of a trapezoid are congruent, then the trapezoid is isosceles.
Thanks in advance to anyone who can help me out on this. I'm currently a junior in high school taking and doing well my school's honors pre-calc class, but of all of the math I've ever learned, proofs ...
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0answers
26 views
Difficulty understanding the definition of the Barycentric coordinate system
Specifically, the definition at http://en.wikipedia.org/wiki/Barycentric_coordinates_%28mathematics%29#Definition
Let $x_1, \dots , x_n$ be the vertices of a simplex in a vector space $A$. If, for ...
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1answer
25 views
Given coordinates of $C$ and $\overline{AC} = \overline{BC}$, find $A$ and $B$.
If $C$ has coordinates $(\sqrt 7, \sqrt3)$ and $\overline{AC} = \overline{BC}$, what are the rational coordinates of $A$ and $B$?
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1answer
37 views
Can one use Pick's theorm to prove that area size 5 covers at least 6 grid points?
According to Pick's Theorem, the size of an area $A$ can be calculated by the sum of
the interior lattice points located in the polygon $i$ and the number of lattice points on the boundary placed on ...
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0answers
24 views
Invariance of inner product wrt coordinate transformation
Given two vector fields $A=\{A^1,A^2,A^3\}$ and $B=\{B^1,B^2,B^3\}$ I have to transfer them to spherical coordinates and compute the inner product and show that it is invariant. I already have ...
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1answer
44 views
What is the name of two points that share one coordinate?
Is there an adjective to characterize two points in $\mathbb R^2$ that have the same value for one of the coordinates?
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31 views
Polar coordinates on a set T
This exercise show that f is a gradient on the set $$T= \mathbb{R}^2-\{(x,y)| y=0, x \leq 0 \}$$
consisting of all points in the xy-plane except those on the nonpositive x-axsis.
If $(x,y) \in T$, ...
1
vote
1answer
76 views
Coordinate Transformation on Local coordinate system
I am having a point $P(x,y,z)$ in $3D$ with respect to global coordinate system. I want to create an another Local Coordinate System by picking three points $N1, N2, N3$ in 3D. Now I want to know the ...
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votes
2answers
54 views
Don't understand how to use jacobian for transformation of coordinates
Hello. I fail to understand why the Jacobian matrix is used to transform Cartesian coordinates to polar coordinates.
If I'm not misunderstanding, it is assumed that the matrix ...
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vote
2answers
87 views
Finding the locus of the midpoint of chord that subtends a right angle at $(\alpha,\beta)$
There is a circle $x^2+y^2=a^2$. On any line that cuts the circle in two distinct points(it is a secant), the points of intersection with circle are taken and at those two points I draw the tangents ...
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1answer
28 views
Creating bounds of a shape
I have a list of coordinates, I need to find the bounds of the points as in a shape where all the points fit into, this shape can be any type of 2D shape (I only have (x, y) no z), as in lets say I ...
3
votes
1answer
50 views
maximising the angle $\theta$
OK, suppose I have two points in cartesian coordinate system, say $P(x_1,y_1)$ and $Q(x_2,y_2)$. I have a line as well, that is, for simplicity
$$y=mx$$
Assuming that
$$y_1\neq mx_1,y_2\neq mx_2$$
I ...
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votes
1answer
64 views
Find coordinates of n points uniformly distributed in a rectangle
I have a rectangle R of width W and height H.
I have N points inside this rectangle.
I need to find an algorithm to position my points in the rectangle in the most uniform way possible (no overlaps, ...
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0answers
25 views
Is it possible to define a coordinate system $(u,v,w)$ that its $u=cnst$ surfaces are in an arbitrary form?
Is it possible to define a coordinate system $(u,v,w)$ that its $u=cnst$ surfaces are in an arbitrary form (for example a high order superquadratic)?
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1answer
61 views
When to use cylindrical coordinate and when to use spherical coordinate?
so i was told that any kind of 3 space Cartesian coordinate volume question can be solve using rectangular coordinate, cylindrical coordinate and spherical coordinate. Here is the thing, by using one ...
2
votes
1answer
43 views
Number of integer solutions of $xy - 6 (x+y)=0$
What are the number of integer solutions of $xy - 6 (x+y)=0$ with $x\leq y$ is ?
Equation $xy - 6 (x+y)=0$ can also be written as $1/x + 1/y = 1/6$
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0answers
43 views
Which complex number cannot be written in polar form?
I'm really confused by this question. Is there such a number?
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vote
1answer
14 views
Maximal region in the cylindrical space
I would like to determine a maximal region in $(r, \theta, z)$- space which maps injectively into $(x,y,z)$-space
Thank you
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votes
2answers
53 views
derivatives transformation
I'm currently doing a calculation for the connection coefficients using the standard space-time coordinates, namely x[0],x[1],x[2],x[3]. The setup is a spherically symmetric problem.
In my ...
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1answer
37 views
Euclidean space problem
In three-dimensional space, is it true that if you take line $a$ of a plane and line $b$ of the plane perpendicular to the first one, then the angle between line $a$ and $b$ (at which they intersect) ...
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1answer
113 views
How to find equation of parabola when we only know the equation of latus rectum and coordinates of vertex?
Suppose the equation of latus rectum is x=4 and the vertex is (2,3). I am confused wouldn't there be many parabola with this same vertex and latus rectum.If not how to find the equation?
The answer ...
4
votes
2answers
68 views
Coordinates of parallel triangle with a distance of 'd' between the parallel edges?
I have a triangle with Co-ordinates $\{(x_1,y_1),(x_2,y_2),(x_3,y_3)\}$. I need to find co-ordinates of a triangle,whose edges are exactly $\alpha$ distance from previous triangle. Below is the figure ...
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vote
1answer
41 views
Solve $x_0 = a\cos(x) + b\cos(x+y-\pi) + c\cos(x+y+z-2\pi)$ and $y_0 = a\sin(x) + b\sin(x+y-\pi) + c\sin(x+y+z-2\pi)$
It has been a while since last time I have tried to solve a trigonometric problem
$x_0 = a\cos(x) + b\cos(x+y-\pi) + c\cos(x+y+z-2\pi)$
$y_0 = a\sin(x) + b\sin(x+y-\pi) + c\sin(x+y+z-2\pi)$
Is it ...
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votes
1answer
41 views
Triangle $z$-index interpolation between the vertices
I got a $2$D triangle, each vertex has a $2$D coordinate with a $z$-index value (NOT a $z$ coordinate!). The $z$-index value indicates whether a vertex lays on, in front of, or behind your screen ...
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2answers
30 views
computing the $y_{cm}$
Suppose I have a half disc and the coordinates axes at the centre of base of the disc. For the given system, I have surface mass density $S$ as $$S=S_0 sin\theta$$($S_0$ being positive constant). I ...
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2answers
50 views
Find the tangent to a function
Find the tangent to this
$\displaystyle y={1 \over x+3}$
it's crossing the point $(-2,1)$
I have drawn the lines but I can't calculate it
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votes
1answer
51 views
How to handle two-center bipolar coordinates?
In my problem, I want to integrate a 2D function $f(x,y)$ which explicitly depends on the vector $ \vec{r}_1=\vec{r}-\vec{R}_1 $ and $\vec{r}_2=\vec{r}-\vec{R}_2$, where $\vec{R}_1=(a,0)$ and ...
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0answers
11 views
Converting DD to DMS and vice versa
I want to know how to convert DD(Decimal degrees) to DMS(degrees, minutes, seconds). I am creating a script that will convert DMS to DD. Please use 37.391933,-122.043667 decimal degree as an example ...
4
votes
1answer
94 views
Every conic in $\Bbb{P}^2$ equivalent to $XZ - Y^2$ - what is meant by hint here?
I am looking at Miles Reid's UAG book. There he claims that every projective conic is projectively equivalent to $XZ = Y^2$. He asks to show that $Q$ a non-degenerate quadratic form is such that ...
1
vote
1answer
28 views
Co-Ordinate Geometry : Please find the mistake
http://i.imgur.com/H59VgOK.png
I think there is some mistake in my diagram or the work. Please check the link .
The above formula is of Distance Formula(in the link). that is $$\sqrt{(x_2 - x_1)^2 ...
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0answers
23 views
Equation to calculate intersected cells in a grid, given a selection rectangle
I am looking for an equation which will calculate which cells (returned either as a pure index or as a row/col) are intersected by a selection rectangle when provided with the box coordinates of each ...
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0answers
53 views
How to solve a distance problem inside of a picture?
sorry for my bad english. I have the following problem:
In the picture you can see 4 different positions. Every position is known to me (longitude, latitude with screen-x and screen-y).
Now i want ...
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1answer
51 views
Find a locus of points to satisfy these conditions?
So, we have to straight lines:
$$3x-4y+5=0$$
$$2x+3y-4=0$$
You have to find a locus of points from which all perpendiculars to the two lines given are in a 2:3 ratio.
3
votes
2answers
48 views
Quick question regarding coordinate geometry
Note: My exam is in about 1 hour and i just realized that i have a unsolved paper, this is one of the questions that i wasn't able to answer from it. I would highly appreciate it if a full explanation ...
3
votes
3answers
60 views
Two questions for coordinate geometry
Note: I am burning through dozens of questions from sample papers and these i couldnt understand, these are not homework and i would appreciate it if the full answer could be provided.
The first ...
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0answers
26 views
Magnetometer electronics engineering " having values X,Y,Z How to calculate angle from north in 3d
Having values X,Y,Z Mathematics of How to calculate angle from north in 3d?
Thank's in advance
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0answers
21 views
Linear 2D transform in the sense of geometric figures?
Consider tranformation which turns one aligned rectangle to another:
This tranformation can be written in matrix form in the following way
where
...
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29 views
How to apply transformations to line equation?
I use line equation of style $y=a*x +b$ , I want to apply transformations (rotation, translation in $x$ and $y$) on the line without changing the form by only changing the $a$ and $b$, I know for ...
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1answer
109 views
triple integral - ecliptic coordinate
I need to find the $V$ by triple integral.
the limits from up is (1) - ecliptic cone.
and from dwon - (2) - elepsoide.
$$(1) \ \ \ \ z=-\sqrt{3x^2+5y^2}$$
$$(2) \ \ \ \ {3 \over 10}x^2+5y^2+{z^2 ...
