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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1answer
32 views

Formula to convert Cartesian coordinates to spherical coordinates? [on hold]

I have this formula: x, y, z = cos(vertical)*sin(horizontal), sin(vertical), cos(vertical)*cos(horizontal) Which maps a spherical coordinates (horizontal and ...
1
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1answer
49 views

The ant is moving through the coordinate system, Started at $(0,0)$ to $(4,4)$. What is the probability that the ant will find food at $(3,2)$?

The path to the $(3,2)$ is $3+2 \choose 3$ or $3+2 \choose 2$. Total path is $4+4 \choose 4$ And the probability is : $ \frac{3+2 \choose 3}{4+4 \choose 4}$ = $ \frac{5 \choose 3}{8 \choose 4}$ = ...
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1answer
15 views

Given the end-vertices of two line segments, how do you calculate the point at which they intersect?

Given only the vertices of each line segment, and it's assumed they intersect, how do I calculate the point at which they intersect (in two and additionally three dimensions)?
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3answers
21 views

Finding a coordinate over a right angle in a triangle where the other two coordinates are known

a B ------- C \ | \ | \ | c \ | b \ | \ | \| A Alright, this is a triangle I have, and ...
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0answers
40 views

Three line segments made by intersection in harmonic progression [on hold]

I'm learning coordinate geometry in high school and have this question as a doubt. The equations of three lines are $7x + y = 16$ , $5x - y - 8 = 0$ and $x - 5y + 8 = 0$. A variable line through ...
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1answer
23 views

How to transform the quadratic form of an ellipse to a circle

Consider the ellipse $x^TPx\le a$. I would like to transform (the quadratic form of) this ellipse into a circle $y^T\begin{pmatrix}1&0\\0&1\end{pmatrix}y\le b$ via a coordinate transform ...
3
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0answers
25 views

Get the largest rectangle in a quadrilateral

So I have coordinates for a few shapes with 4 sides of varying angles. I need to find the largest rectangle in them, even if the rectangle is rotated. Is there an algorithm for this? In the example ...
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1answer
44 views

Finding all intersecting circles of one circle.

I have one circle $C_0(x_0,y_0,R_0)$ in a plane (which moves around here and there). There are many other circles on the same plane $C_1(x_1,y_1,R_1),C_2(x_2,y_2,R_2).....,C_n(x_n,y_n,R_n)$ where ...
6
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1answer
62 views

Is this GRE math problem wrong?

I'm working out of the Manhattan GRE test prep book and I've come across a question that I can't figure out why they chose the answer they did. "Perpendicular lines m and n intersect at point (a,b), ...
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3answers
163 views

Average of points on an xy plane

I was at a family reunion yesterday which required a bit of travel. Most of that part of the family lives near one another, so I am the outlier. I can't reasonably expect them to have the next reunion ...
4
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1answer
44 views

Determining the angle of a photograph containing known parallel objects/lines.

I have a photograph of a house and a window taken at an angle. I'm trying to determine the angle at which the photograph was taken. The house has wooden siding that can be safely assumed to be ...
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0answers
14 views

Spherical coordinate system remain the same if the origin is changed and each point make the same translation?

Now I have a spherical coordinate system whose origin is located at (a,b,c)[cartesian], and I have another point whose location is (r, theta, tho) in this spherical system, and P's cartesian ...
0
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1answer
11 views

Write the co-ordinates of E such that the parallelogram ABCE is a rhombus.

I'm unsure how to do this and it's always in my exams. (The original shape was a triangle and E was originally not a point) A:(1,0) B:(0,8) C(7,4) Gradient of AC:2/3 AC equation:2x - 3y - 2 = 0 ...
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2answers
16 views

Finding coordinates of points $P, Q$ given $A, P, Q$ are collinear. [closed]

In the $x,y$-plane, point $P$ lies on the line $y=2x-5$ and point $Q$ lies in the line $y=12-x$. A point $A(1,2)$ is such that $A, P, Q$ are collinear and $AQ=3AP$. Find th coordinates of $P$ and $Q$. ...
0
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1answer
36 views

intersect area of two polygons in cartesian plan [closed]

is possible to calculate the overlapping polygons area of two polygons in cartesian plan coordinate: polygon 1: $(1,1) - (2,2) - (3,3) - (4,2)$ polygon 2: $(1,0) - (2,3) - (3,2) - (4,1)$ ...
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0answers
5 views

How to match the time for given points in two different 3D Cartesian coordinate system?

I have two machine to record a men's motion (what we actually record are the 3D coordinates of the men's 14 different body parts). machine 1 record the coordinates 100 times per second, and machine 2 ...
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0answers
29 views

The gradient in $n$-dimensional spherical coordinates

I am in the middle of a computation where I need to work with the formula of the gradient in spherical coordinates in $\Bbb R ^n$ (no preferred convention for the angles). I could patiently and ...
0
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0answers
16 views

Formula for a involute

Given the graph of the function in Cartesian coordinates, $f(x)$, what is $g(x)$ such that $g(f(x))$ is the involute of $f(x)$? In polar?
1
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1answer
15 views

Co-ordinate analysis

Coordinates $ (\alpha, \beta, R) $ with $ -1 \ge \alpha,\space \beta \le1,\space R \lt 1 $ are related to Cartesian co-ordinates $ (x, y, z) $ via $ x= R \alpha, \space y= r \beta $ and $ \space ...
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2answers
37 views

Please help me solve this problem on Coordinate Geometry

Problem: A rod of length 2 units moves so that its ends are on the positive X-axis and on the line $x+y=0$ which lies in the second quadrant. Find the locus of the midpoint of the rod. I've ...
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1answer
16 views

Graph the area of the surface in Spherical Coordinate System

I would like to know how to graph a surface area in spherical given the value of the area. It is because I would to calculate the surface area and I dont know how to visualize which side of the sphere ...
2
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1answer
53 views

conversion of laplacian from cartesian to spherical coordinates

In cartesian coordinates, the Laplacian is $$\nabla^2 = \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}\qquad(1)$$ If it's converted to spherical ...
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1answer
12 views

Converting a point from Rectangular to Cylindrical Coordinate Systems

I am solving this problem and I am stuck on converting a point from rectangular to cylindrical coordinates. The answer is from $B(0,5,0)$ to $B\left(5,\frac\pi 2,0\right)$. The problem is when I ...
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2answers
38 views

Calculating distance between 2 points - confused about radians

Let me start by saying math is NOT my strong point - by a long shot. I was asked to write a program calculating which locations from a given list (the co-ordinates given in degrees) are within 100km ...
0
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1answer
24 views

The shape of the hyperbolic curves coordinates

Any one has an idea about hyperbolic coordinates ? and how to imagine it ? Indeed I am trying to find the shape of the coordinate curves far away from origin ! and what is the shape of them at $u=0 ...
2
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1answer
21 views

Conversion of spherical coordinates to cartesian

For the flow $A = \frac{c}{r}$ with $r=\sqrt{x^2+y^2+z^2}$ I wanted to calculate the velocity field with $\nabla A$ As a result I get $(-\frac{c}{r^2},0,0)$. So far so good. When I tried converting it ...
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0answers
29 views

Cartesian transformation

I am led to believe a Cartesian Transformation is what I need, but I am not sure. Here is my problem. I have two coordinate systems one Global x,y,z another local i,j,k that exists inside of x,y,z I ...
4
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1answer
35 views

Square inside a Polar coordinate system

I have a square lying on a polar coordinate. Is there any general relationship between radius and angle, which may be derived along the side of square. More generally put, given the coordinates of the ...
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0answers
24 views

How To know if points are going up or down?

Lets assume that we are in $d$-dimensional coordinate system and we have convex body of some shape. We have a point on that border of that body and we want to know by its $k$ points surrounding it ...
5
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1answer
71 views

Evaluate integral with gaussian curvature

I thought evaluating it in the following way: $$\begin{align} \int_0^{2\pi}\int_0^{\pi}K(x,y)\sqrt{\det(g_{ij})} \, dy\,dx &= \int_0^{2\pi}\int_0^\pi \sqrt{\det L_{ij}}\cdot \sqrt{{\frac{\det ...
2
votes
1answer
58 views

Pair of tangents to a hyperbola

How do I find the joint equation of the pair of tangents drawn to the hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ from an external point $(x_1, y_1)$. My book says that the answer is $SS_1 = ...
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0answers
22 views

Divergence free part of laplacian operator in cylindrical coord. (Curl Curl operator)

I want to derive $\nabla \times \nabla \times \mathbf{V}$ in cylindrical coordinates. My variables are $(u,v,w)$ in $(z,r, \theta)$ (axissymetric, radial and azimuthal directions). I computed first ...
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4answers
51 views

Points on 3d line

Say we have $2$ points on a 3d line, point $A(x,y,z)$ and point $B(x,y,z)$. If we want to get the coordinates of a third point, beyond point $B$ but a certain distance from point $A$, how would we do ...
1
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1answer
23 views

new plane equation after transformation of coordinates

I have a plane equation $ax + by + cz + d = 0$ w.r.t to a particular coordinate frame. this coordinate frame w.r.t to the world coordinate frame is $$\begin{vmatrix} r_1 & r_2 & r_3 & ...
1
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1answer
20 views

Finding the equation for the tangent plane to earth given latitude and longtiude

I'm creating a program where I need to calculate the equation of the plane tangent to the earth at a given latitude and longitude. I used Projecting an Arbitrary Latitude and Longitude onto a Tangent ...
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0answers
4 views

Transformation from unknown orientation representation to DCM

I'm working with some really strange software which has some sort of custom orientation representation, and I'm trying to get it into a standardized format (direction cosine matrix). However, that's ...
0
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3answers
22 views

How to move the position of a curve $x,y$ coordinates?

I have some silly problem. I want to know how to move the curve in $x,y$ coordinates which I have some curve. For example, $f(x) = x^2$ and this is originally start at $(0,0)$. But I want to this ...
0
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1answer
11 views

Angle of Elevation in Earth Coordinate Systems

Does a calculated angle of elevation differ between earth centered earth fixed (ECEF) coordinates and geodetic coordinates? I've computed an angle of elevation from one object to another in 3D space ...
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0answers
20 views

How can I obtain a unit vector of a shifted spherical system?

I hope that I can explain myself clear enough, Assuming I have a sphere that has been moved down in the $Z$-axis. I know that r unit vector when the sphere is not shifted can be expressed as: ...
0
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0answers
7 views

How can I obtain a unit vector of a shifted spherical system?

I hope that I can explain myself clear enough, Assuming i have a sphere that has been moved down in the Z-axis. I know that the radial unit vector when the sphere is not shifted can be expressed as: ...
2
votes
3answers
230 views

Parametric coordinates of parabola?

Can $(a(\sin(t))^2 , 2a \sin(t))$ be the parametric coordinates of the parabola $y^2 = 4ax$ ? I found that these coordinates satisfy the equation of the parabola but my friend says that although ...
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0answers
36 views

Coordinate Systems Transformation(Rectangular to Cylindrical)

I am new to this subject: Cartesian, Cylindrical and Spherical coordinate system. Coordinate System Transformation I have this example problem that I cant get the right answer. Transform to ...
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3answers
49 views

Do these points make a straight line?

I'm trying to prepare for my calculus 3 class coming up this fall and doing some practice problems. I'm having a hard time visualizing some of these 3D coordinates. $D(0,-5,5)$ $E(1,-2,4)$ ...
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0answers
15 views

Finding the 3D coordinates of an object with cameras

I'm working on a project where I need to find the coordinates of an object. I used this paper for now http://dsc.ijs.si/files/papers/S101%20Mrovlje.pdf . It describes how with two cameras facing the ...
1
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1answer
34 views

Interpolating Random Points

I have a list of (x,y) co-ordinates that need to be interpolated. The co-ordinates are not necessarily part of a function. Therefore, polynomial interpolation will not work. Is there a way to use some ...
0
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0answers
13 views

lat/lon spherical coordinates to equidistant spherical coordinates

How to transform spherical data expressed in latitude/longitude pairs (parallels/meridians) in a new set of pair expressed just in parallels pairs? In other words, I need to transform data expressed ...
0
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0answers
47 views

Converting longitude and latitude to altitude and azimuth

I am interested in a problem where a camera is mounted on the Earth that has a mechanism for altitude and azimuth adjustments. The longitude, latitude and altitude of the camera are known, and the ...
0
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1answer
33 views

Cross product in spherical coordinate

Hello I have a question: Is the formula for the cross product the same in spherical coordinates as in cartesian coordinates? I have found conflicting answers on the internet.
0
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1answer
25 views

Coordinates of regular octagon

There are coordinates of two vertices in a regular octagon $$\{A_0,A_1,...,A_7\}$$ with Cartesian coordinates $A_0 = (2,-4)$, $A_2 = (0,0)$. The task is to find coordinates of all other vertices. ...
2
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1answer
49 views

Conversion between coordinate systems

I am trying to convert between two coordinate systems and think I've come up with the answer but would like to make sure my assumptions are correct and to help with some of the math. The problem is ...