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

learn more… | top users | synonyms

1
vote
2answers
43 views

How to know if two points are diagonally aligned?

If I have two points at different X/Y coordinates, I know that: They are vertically aligned if both are at the same X coordinate; They are horizontally aligned if both are at the same Y coordinate. ...
1
vote
1answer
95 views

Manifolds, coordinate systems, books

Which books, say Lee's Introduction to Smooth Manifolds or Munkres' Analysis on Manifolds explains how the theory of a differentiable manifolds can be used to solve a problem that is expressed in a ...
3
votes
2answers
118 views

Scalar product invariance

The question is somehow silly, but I can't seem to find a way out right now. Consider the vector $v\in\mathbb R^2$, expressed in Cartesian coordinates as $(1,1)$ and in polar coordinates as $(\sqrt ...
0
votes
0answers
37 views

Mapping cartesian coordinates to circular coordinates

I have some "rectangular" x,y coordinates which I like to convert to "circular" coordinates. Notice I'm not sure if I'm using the correct terms here, so bear with me - I drew an example to show how ...
1
vote
0answers
20 views

Parabolic Coordinates and the Normal Derivative

I would like some help with the following problem. Thanks for any help in advance. Determine the largest region Ω’ in R^2 spanned by (u,v) such that the transformation T that defines parabolic ...
1
vote
0answers
63 views

Mapping A point from one 3D Coordinate System to Another 3D coordinate System with Euler Angles between the two systems given

Suppose I have a point in the green coordinate system, and I wish to describe it in reference to the orange coordinate system. I know the roll, pitch, and yaw of the green system with respect to the ...
1
vote
0answers
53 views

distance in n-dimensional space

According to answer of this question : Distance between 2 points in 3D space (in spherical polar coordinates) The distance between 2 points in 3 dimensional space is : $$ ...
1
vote
1answer
18 views

Coordinate transformation (or conversion) into yards

Following is a soccer field with its dimensions. There is a similar field, but I am capturing coordinates via mouse-movement. So, what (115,75) shows here, is ...
0
votes
1answer
35 views

Square labeled with same number.

Recently I met this combinatorics problem: "Let all points with integer coordinates in a plane be labeled with one of the numbers $1,2,3,...,n$. Prove that there is a rectangle whose vertices are ...
0
votes
1answer
48 views

How to rotate an orientation (Euler angles)

If I have an orientation defined by Euler angles and I want to simulate a rotation of the coordinate system about the origin (doesn't matter to me how the rotation is specified), how would I get the ...
0
votes
0answers
31 views

How to express standard deviations and correlations of 6 points as one measure of uncertainty?

Algorithm that I use, uses a weight matrix P of size n x n to compute $XPY^T$ where $X$ and $Y$ are 3 x n matrices - representing X,Y,Z coordinates for n points. This means that points are weighted ...
0
votes
1answer
37 views

coordinates of 3rd point (vertex) of a right triangle knowing lengths and direction

In a last post I wanted to know the 3rd point of vertex, actually I have some similar problem .... I think I have all data.. for example...: 3 vertex cordinates in order to have the direction(gray ...
0
votes
0answers
27 views

Making Homogenous Parabola Equation

Find the locus of the mid-points of the chords of the parabola $y^2=4ax$ which subtend a right angle at the vertex of the parabola. Now we say $y^2=\frac{4ax(yk-2ax)}{k^2-2ah}$ coefficient of ...
4
votes
1answer
70 views

How to get coordinates of a point after an image is rotated? (with images)

I have a problem that involves a rotating image and finding a previously known point. Firstly, there is a sequence with the rotation. We start with an empty image. A line is drawn vertically, ...
0
votes
0answers
13 views

linear functional basis and affine map

Suppose that the domain under consideration is the right triangle with coordinates (0,0), (1,0), and (0,1). At each vertex, let $\sigma_k(x,y)$ be such that $\sigma_k(x_k,y_k) = 1$ and ...
0
votes
1answer
22 views

How do I find the symmetrical point B given the centre of symmetry C and another point A?

I have a point $A (-2k; 3)$ and a point $B$ that is symmetrical to the point A given the centre of symmetry $C (-1; 0)$. I tried applying the following formula, where $x_o$ and $y_0$ are the ...
-3
votes
1answer
75 views

Need Help in Coordinate Geometry (Straight Lines) [closed]

A line $L$  is drawn from the point $P\equiv(4,3)$  to meet the parallel lines $L_1: 3x + 4y + 15 =0$  and $L_2 = 3x + 4y + 5 =0$ at points $A$  and $B$ respectively. From $A$, a line perpendicular ...
0
votes
2answers
38 views

Calculate new(x,y) for a line

Suppose if tanks has to rotate its main gun by $30^\circ$ to hit the target, what will be its new $(x,y)$ coordinate or a formula to calculate it as shown in image? If bullet is fired from the main ...
0
votes
0answers
35 views

Cylindrical coordinates - Orthonormal system

Using cylindrical coordinates and the orthonormal system of vectors $\overrightarrow{e}_r, \overrightarrow{e}_{\theta}, \overrightarrow{e}_z$ describe each of the $\overrightarrow{e}_r$, ...
0
votes
3answers
61 views

The geometric meaning of certain mappings written in cylindrical or spherical coordinates

What is the geometric meaning of the following mappings, that are written in cylindrical coordinates? The mappings are: $$(r, \theta, z) \rightarrow(r, \theta , -z) \\ (r, \theta , z) \rightarrow (r, ...
0
votes
3answers
32 views

Cylindrical - Spherical coordinates

We are given a point in cylindrical coordinates $(r, \theta , z)$ and we want to write it into spherical coordinates $(\rho , \theta , \phi)$. To do that do we have to write them first into ...
1
vote
1answer
24 views

Cylindrical coordinates - Surfaces

I found the following: Cylindrical coordinates $(\rho , \theta , z)$. This system consists of the following coordinate surfaces: Cylinders with common $z-$axis: $\rho=\sqrt{x^2+y^2}=\text{ ...
1
vote
0answers
39 views

Show that the point satisfies the conditions

A round membrane in space, is over the space $x^2+y^2 \leq a^2$. The maximum coordinate $z$ of a point of the membrane is $b$. We suppose that $(x, y, z)$ is a point of the inclined membrane. ...
0
votes
0answers
58 views

Volume between a paraboloid and a parabolic cylinder

Find the volume of the region bounded by the paraboloid x=y^2 + z^2 and the parabolic cylinder x=2-y^2. I set up the integral as the integral of theta from 0 to 2pi, integral of (2/(sin^2theta + ...
0
votes
1answer
25 views

Multiplication order of rotation matrices

I have three 3D coordinate frames: O, A and B, as shown below. I want to know the rotation matrix RAB between A and B, that is the rotation that is required, with respect to the frame A, to move ...
0
votes
1answer
66 views

Transformations between two coordinate systems on a rigid body

I have two coordinate frames, A and B, which are rigidly attached to each other on a body. This body then translates and rotates, such that A starts at A1, and moves to A2, and B starts at B1, and ...
0
votes
2answers
36 views

Rotation matrix between right- and left-handed systems, with an additional rotation

I have two coordinate frames, A and B. I want to create the rotation matrix RAB which takes you from A to B. A is a right-handed system, and B is a left-handed system. Furthermore, after moving from a ...
6
votes
3answers
88 views

Why is $\partial_z\partial_{\bar z}=\frac14\left(\partial_r^2+\frac1r\partial_r+\frac1{r^2}\partial_{\theta}^2\right)$?

I have to show the identity I wrote in the title: it should be $\partial_z\partial_{\bar z}=\frac14\left(\partial_r^2+\frac1r\partial_r+\frac1{r^2}\partial_{\theta}^2\right)$ but some computation ...
0
votes
0answers
39 views

Integrals For AMC 10B #25?

Could an answer be found to this AMC 10B #25, using integration? A rectangular box measures abc, where a, b, and c are integers and 1<=a<=b<=c. The volume and the surface area of the box are ...
0
votes
0answers
23 views

Multiplication order for coordinate frame transformations

Suppose I have three coordinate frames: $A$, $B$ and $C$. If $T_{AB}$ is the transformation from $A$ to $B$, then which of the following is correct? $T_{AC} = T_{AB} \cdot T_{BC}$ $T_{AC} = T_{BC} ...
15
votes
1answer
621 views

Abscissa, Ordinate and ?? for z-axis?

Like x-axis is abscissa, y-axis is ordinate what is z-axis called? It is one of basic doubts from my childhood.
0
votes
0answers
24 views

Moving die on cartesian plane so as to minimize sum of facing face

I have a problem that I have been working on for which I cannot find a solution. Problem: Assume you are on a cartesian plane, and you want to move a die to a specific point. You can move the die ...
0
votes
0answers
33 views

Tangent undefined for polar curves ($r^2=a^2sin(s\theta)$)?

I am considering the function $r^2=a^2\sin(2\theta)$ and am trying to find tangents perpendicular to the initial line, so $\frac{dx}{d\theta}=0.$ However, when I take the derivative by implicit ...
0
votes
0answers
58 views

Tangents perpendicular to the initial line for cardioid? Polar coordinates…

For the polar curve $r=a(1+cos\theta)$, I am trying to find the equations of the tangents perpendicular to the initial line by setting $\frac{dx}{d\theta}$ equal to zero. I am able to factorise a sine ...
0
votes
1answer
36 views

How can I prove non-geometrically that there is a bijective correspondence between polar and cartesian representations of coordinates?

We have a function $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ as $f(x,y) = (\sqrt{x^2 + y^2}$, $\tan^{-1}\left(\frac{y}{x}\right))$ which takes a Cartesian pair $(x,y)$ to its polar form, and a ...
0
votes
1answer
23 views

Minimum points to choose from a set such that midpoint is also in the set

Consider the set $S =\{ (x, y)$ : $x$ and $y $ are integers $\}$. The midpoint of a pair of points $ P_1$ = ($ x_1 $, $y_1 $) and $P_2 $= ($x_2$ , $y_2$ ) is $ ( \frac{x_1 + x_2}{2}, ...
0
votes
0answers
17 views

Confused by Parameterizations and Coordinate Conversions

So I have a few questions regarding parameterizations and coordinate conversion. Ever since dealing with parametric equations last semester I have felt like I have never truly understood ...
0
votes
0answers
91 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
votes
0answers
19 views

Polar coordinates for vector difference in $\mathbb{R}^2$

I have a function $F(\boldsymbol X)=\tilde F(x,y)$ of $x$ and $y$ in the plane, and I can transform it in a function of $r$ and $\theta$, say $f=f(r,\theta)$, through the change of coordinate $$x=r ...
0
votes
1answer
49 views

Using Barycentric coordinates to check whether a point lies within a Degenerate triangle

http://www.blackpawn.com/texts/pointinpoly/ I used this site to learn how to determine whether a point lies within a triangle. However, the site does not say whether or not this method can handle ...
0
votes
0answers
44 views

Coordinate Systems on the Complex Plane: Rectangular, Polar, Exponential, … Imaginary?

In the complex plane there is a nice relationship between rectangular, polar, and exponential coordinates: $$(x+iy) = r(\cos\theta + i~\sin\theta) = re^{i\theta} $$ $$where~~x ,y ,\theta, r \in ...
0
votes
0answers
24 views

Cylindrical coordinates: Paradox?

Let's say the vector field $\vec A_1 = \begin{pmatrix} r\\ 0 \\ z\end{pmatrix}$ in cylindrical coordinates is given and I want to calculate $\vec A_1 \cdot \vec e_r$, where $\vec e_r = \begin{pmatrix} ...
0
votes
0answers
19 views

Transforming a vector field in cylindrical coordinates - simple

I want to transform $\vec F = \alpha \vec r$ in cylindrical coordinates, i.e. $x=\rho \cos(\phi), y=\rho \sin(\phi), z=z$ Now since $\vec r = \begin{pmatrix} x \\ y \\ z\end{pmatrix}$ I receive $ ...
0
votes
0answers
23 views

How to formulate a coordinate transformation

Thank you in advance for taking the time to consider this. I'm trying to figure out how to formulate a coordinate transformation problem (at least that is what I think it is). Background: I have an ...
0
votes
0answers
17 views

Transform to cylindrical coordinate system

I tried so many approaches , at least give me a hint on how to find The unit vectors $$ \vec{V} = y\vec{i} + x\vec{j} + \frac{x^2}{\sqrt[2]{x^2+y^2})} \vec{k}\ $$
0
votes
0answers
22 views

Syncronize positions of 2 rectangles with different origin point while rotation

Suppose we have 2 rectangles in Cartesian coordinate system with (0,0) at the top left corner of the screen. Both of rectangles (a and ...
0
votes
0answers
159 views

Can someone help me convert definitions of hip movement in Cartesian coordinates into spherical coordinates?

I am a biomechanist. I am having a problem converting an idea in Cartesian coordinates $(x,y,z)$ to spherical coordinates $(r,\theta,\phi)$. I wondered if someone could help me. I can physically ...
0
votes
0answers
18 views

Polar-Cartesian Plot Interconversion

The Question How can we interconvert any general graph of polar or cartesian function so they give the same plot in the other coordinate system. Note: I do not mean to ask about interconverting a ...
0
votes
1answer
20 views

What symmetry statement can be made about the points $(a, b)$ and $(b, a)$?

The question is: if $a$ and $b$ are any two numbers, what symmetry statement can be made about the points $(a, b)$ and $(b, a)$? I'm not sure whether this is a symmetry statements and whether it is ...
0
votes
4answers
48 views

Find a point on the line through $A=(2,3)$ and $B=(-5,-4)$ that is twice as far from $A$ as from $B$

Find a point on the line through $A=(2,3)$ and $B=(-5,-4)$ that is twice as far from $A$ as from $B$. Please indicate the actual position of the point.