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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9
votes
2answers
183 views

Is there any way to find the equation for this situation?

$\mathbb N = \{1,2,3,4\dots\}$ Let us suppose we are starting at a point with coordinates $(0,0)$. Now draw a line from $(0,0)$ to $(1,0)$ and from $(1,0)$ to $(1,2)$. Now by the Pythagorean theorem, ...
0
votes
2answers
223 views

Gram-Schmidt Orthogonalization - does it distort?

I am writing a 3D solar panel positioning programme and have a section of code where I use the Gram-Schmidt Orthogonalization process to go from 3D to 2D for easier calculations. (For reference, here ...
1
vote
1answer
296 views

how to get rotation component of quaternion form using 3d coordinates

I have a series of 3d coordinates distributed in a 3d space according to a root point. I can determine the x, y , z component using reducing the vectors. but I am not clear how to get rotation ...
1
vote
0answers
125 views

Circle-Circle intersection coordinate system

Consider two points in the 2D Euclidean plane, the origin $0$ and $x$. One can define a co-ordinate system such that for any point $y$ in the plane, $y$ is parametrized by its distance from $0$, call ...
1
vote
1answer
83 views

Find $a$ for which figure's area is maximum

Suppose that we have following interval $(-5,2)$,we should find such $a$, which takes all possible values from this interval,creates following inequality systems $$5+a-|2y|\ge 0$$ $$|x|\leq ...
2
votes
2answers
163 views

Are there derivations of equations of non-degenerate real quadric surfaces

Take the ellipsoid for example $$(x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1$$ in the x-y plane you have an ellipse described by $$(x^2/a^2)+(y^2/b^2)=1$$ (suppose z=constant) in the y-z plane you have an ellipse ...
0
votes
1answer
753 views

Find the coordinates of a point on a circle given 2 points and an angle

I have a circle with A as a center, B and C 2 points on the circle. I have the coordinates of A (the center) and B (the point on the circle). How can I find the coordinates of C (another point on the ...
0
votes
1answer
169 views

Z-index of an arbitrary point on a flattened 3-dimensional triangle

I have a triangle in a 3-dimensional coordinate system that I want to draw to a screen. I'm able to flatten the triangle to 2 dimensions and determine whether an arbitrary point on the screen falls ...
2
votes
0answers
365 views

Gradient when changing coordinate system

A change of variables from $\vec{r_1}$, $\vec{r_2}$ to $\vec{r}$, $\vec{R}$ is given by: $$ \vec{r} = \vec{r_1}-\vec{r_2}\text{ , }\vec{R}=c_1 \vec{r_1} + c_2 \vec{r_2} $$ I'm supposed to find ...
1
vote
4answers
156 views

How to determine the position of neighbor points?

I have two points (red points represented on the image below), they form a line that is described by a specific formula (y = mx + n), I need to determine the coordinates of 4 other points (blue ...
0
votes
2answers
162 views

How to place rectangle so it envelopes two circles, one circle in the very right end of the rectangle and one in the other end.

How can i place a rectangle so it envelopes two circles, one circle in the very right end of the rectangle and one in the other end. Say i have two circles with the xy coordinates and a radius: ...
2
votes
2answers
2k views

How to get upper-left, upper-right, lower-left and lower-right corners XY coordinates from a rectangle shape.

How can i get the get upper-left, upper-right, lower-left and lower-right corners XY coordinates from a rectangle shape when i have the following data available to me? ...
1
vote
3answers
156 views

How do I calculate a change of coordinates given two lines as new axis?

Suppose we have an old coordinate system using the variables $x$ and $y$. We are given two equations for lines to form the axis for new coordinates. e.g. The line $z=0$ is given by the equation $y = ...
2
votes
1answer
946 views

invariance of cross product under coordinates rotation

Question goes as If $\vec A$ and $\vec B$ are invariant under rotation, the prove that $ \vec A \times \vec B $ is also invariant. However solution of on the other page is not given. Says ...
1
vote
1answer
371 views

divide triangle into ratio 1:2

I have a problem related to triangles. Please give me some hint to progress. Suppose we have the following coordinates $A(-2,3)$,$B(1,-1)$,$C(-1,-1)$. From point $A$, draw a line which divides ...
0
votes
1answer
128 views

Find the number of common normals to both these curves.

Find the number of common normals to the curves $ x^2 + (y-1)^2 =1 $ and $y^2=4x$. My take : I formed a cubic in $m$ i.e. slope, so there'll be 3 normals. Please help.
2
votes
1answer
200 views

How to find the eccentricity of this conic?

How to find the eccentricity of this conic? 4(2y-x-3)² - 9(2x+y-1)²=80 My approach : I rearranged the terms and by comparing it with general equation of 2nd degree, I found that its a hyperbola. ...
1
vote
1answer
674 views

unit vector transformation in rotation of coordinate system

The transformation of coordinate from $(x, y, z)$ to $(x', y', z')$ is given by $$ x' = a_{11}x + a_{12}y + a_{13}z\\ y' = a_{21}x + a_{22}y + a_{23}z\\ z' = a_{31}x + a_{32}y + a_{33}z$$ If $(\hat i ...
1
vote
5answers
7k views

Find out the differential equation of the following families of curves.

Find out the differential equation of the following two families of curves : Straight lines having slope and $x$-intercept equal in magnitude. Straight lines at a fixed distance $p$ from the origin. ...
0
votes
1answer
309 views

Produce function of curve, given some coordinates

I tried asking something similar to this before, but I guess I didn't explain it very well. Hopefully this will be more clear. I need to get an equation which describes a curve with certain points. ...
2
votes
1answer
130 views

determinant of matrix of transformation from Cartesian to orthogonal curvilinear

Let $(x_1, x_2)$ and $(y_1, y_1)$ be two orthogonal coordinate system with unit vectos $(\hat i_1, \hat i_2)$ and $(\hat e_1, \hat e_2)$ respectively defined by the $x_1 = x_1(y_1,y_2)$ and $x_2 = ...
2
votes
1answer
77 views

gradient in polar coordinate by changing gradient in Cartesian coordinate

I'm tried to do following and I can't see what went wrong. $$\begin{bmatrix} \hat r\\ \hat \theta \end{bmatrix} = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta ...
1
vote
1answer
217 views

Gradient in curvilinear coordinates

The gradient is usually written as the product of the unit vectors times the derivative with respect to that coordinate. In Einstein summation convention: $\hat e_i \partial_i$ I've seen it written ...
4
votes
3answers
328 views

On a two dimensional grid is there a formula I can use to spiral coordinates in an outward pattern?

I don't know exactly how to describe it, but in a programmatic way I want to spiral outward from coordinates 0,0 to infinity (for practical purposes, though really I only need to go to about ...
1
vote
4answers
3k views

how to change polar coordinate into cartesian coordinate using transformation matrix

I would like to change $(3,4,12)$ in $xyz$ coordinate to spherical coordinate using the following relation It is from the this link. I do not understand the significance of this matrix (if not for ...
3
votes
1answer
3k views

building transformation matrix from spherical to cartesian coordinate system

How to arrive at the following from given $ x = r\sin \theta \cos \phi, y = r\sin \theta \sin \phi, z=r\cos\theta $ $$ \begin{bmatrix} A_x\\ A_y\\ A_z \end{bmatrix} = \begin{bmatrix} \sin ...
0
votes
2answers
421 views

convert values from one coordinate system (x,y) to another coordinate system (x', y')

Following is a graph that contains both coordinate systems (x,y) and (x',y'). x, y, x', and y' are all axes ...
1
vote
1answer
8k views

Transformation of unit vectors from cartesian coordinate to cylindrical coordinate

Let $ (\hat i, \hat j, \hat k) $ be unit vectors in Cartesian coordinate and $ (\hat e_\rho, \hat e_\theta, \hat e_z)$ be on spherical coordinate. Using the relation, $$ \hat e_\rho = ...
14
votes
2answers
200 views

Was there some prior idea that inspired both Fermat & Descartes to invent coordinates?

It seems incredible to me that both Descartes & Fermat could have both simultaneously discovered such a novel & significant idea, without there being some single prior idea that they both ...
2
votes
2answers
262 views

Triangle related coordinate geometry question

Given triangle $\triangle ABC$ , with $AB=AC$ and 2 times(length of inradius) which is equal to the length of exradius of excirle opposite vertex $A$. Setup the coordinate system in the plane ...
0
votes
2answers
53 views

Is there a simple way of arriving at this solution?

Suppose we are given the matrix $$\begin{pmatrix}x'\\y'\end{pmatrix}=\begin{pmatrix}\cos(\omega t)& -\sin(\omega t)\\\sin(\omega t)& \cos(\omega ...
5
votes
2answers
125 views

Why does it always take n numbers to characterize a point in n-dimensional space (or does it)?

I don't know if this is obvious and a dumb question or not, but, here we go. To characterize a point in 2-d space we can use standard $x,y$ coordinates or we can use polar coordinates. There are ...
2
votes
1answer
146 views

How to get new orientation on a sphere?

This is my first question here, hopefully it fits. Imagine all people on the northern hemisphere are looking North to the Pole. Now I want them to look towards a new location given by latitude, ...
3
votes
2answers
904 views

How to find a 2D basis within a 3D plane - direct matrix method?

I have a plane equation in 3D, in the form $Ax+By+Cz+D=0$ (or equivalently, $\textbf{x}\cdot\textbf{n} = \textbf{a}\cdot\textbf{n}$), where $\textbf{n}=\left[A\:B\:C\right]^T$ is the plane normal, and ...
3
votes
1answer
429 views

Coordinate transformation

I have some problems with a geometrical calculation. I want to know the coordinates of the point $P_2$ in my coordinate system $A \ (x,y,z)$ as shown in the following figure. Point $P_1$ (in $A \ ...
2
votes
1answer
752 views

Finding points relating to the edge of a circle in an x,y coordinate system

My question is a bit hard for me to express, so please bear with me. I never got far in trig, and haven't done much on the subject in years; trying to get back into it as it's a pretty major part of ...
0
votes
1answer
213 views

Coordinates on diamond

I got a couple of diamond put side by side like on the image below The only coordinates I know on the image are the top corners (green text). I need to know which diamond does a dot belong. ...
9
votes
4answers
4k 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 ...
1
vote
1answer
172 views

Curves and first fundamental form

Would I be right to think that if I have a coordinate system $(x,y)$ so that the lines/curves where one coordinate is fixed, so something like $x=a$ and $y=b$, always intersect at the same angle, then ...
2
votes
1answer
76 views

Changing coordinates in a grid

I'm a developer very bad in math, and I got a problem that I'm not able to solve. I got a grid each cell got a position X and Y like shown in the picture below Actually I got the red coordinates, ...
1
vote
0answers
200 views

2D Cartesian Matrix / coordinate transformation.

I has initially asked this question in the programming site but did not get an answer that worked. This is my first question on this site so please bear with me. Consider a page with three distinct ...
1
vote
0answers
170 views

Relative spherical coordinates of 2 points.

I have 2 points in space, defined by their spherical coordinates. I'd like to know the spherical coordinates of the second point in a reference system centered on the first point (I know the unit ...
2
votes
2answers
15k views

How to find the equation of a graph with given coordinates? [duplicate]

Possible Duplicate: Writing a function $f$ when $x$ and $f(x)$ are known If I am given 9 co-ordinates of a random graph say for e.g ...
0
votes
1answer
170 views

Calculating Travel Direction of two coordinates

Maths isn't my strong point and i've been stuck here for hours trying to figure out how do to this (it's probably gona be very easy to do now as well) but it's driving me crazy so i'm going to ask for ...
0
votes
1answer
219 views

Help needed with volume integral in Cylinder coordinates

Problem (more here and the problem XIV.6:6 here on page 976) Integrate $\int_A z dx dy dz$ in cylinder-coordinates when $$A=\{(x,y,z)\in\mathbb R^3 | x^2+y^2 \leq z \leq ...
1
vote
1answer
84 views

Coordinates translation in space

First of all sorry if the title is somewhat opaque, the problem I am trying to solve is already hard to explain properly in my first language. So, let's consider we have a plane, rectangle target in ...
0
votes
1answer
38 views

Counting ways on the coordinate system

What is the number of ways in which you can reach a point (2,2) from the origin, taking unit steps at a time , in not more than 7 steps?
0
votes
1answer
436 views

Evenly distributed normal distribution on surface of a unit sphere

Hello I am using Mathematica code to to generate NPoints of randomly generated points normally distributed around one point on the surface of a sphere using Return[Table[ ...
1
vote
1answer
283 views

What do the parameters skewX and skewY mean in the transform specified by Flash's motion XML?

Flash has the ability to export animations into a format they call motion XML. Its specification is here I am trying to write a python renderer for these animations using pyglet. I understand ...
2
votes
1answer
635 views

Given an arbitrary number of points, how do you find an equidistant center?

Given an arbitrary set of points on a Cartesian coordinate plane, is there a generalized formula to find the closest point that is equidistant from all the given points? My first guess was finding ...