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
21 views

Help solving a problem on plotting a graph

The question is to plot two points lying on y-axis which are equal distance from the origin.What is the exact meaning of the question and how do I solve it?Please help.
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1answer
110 views

Valid Points in a Hexagon within a 3d Grid

We are working on a projection system that takes 3 dimensions and spits out hexagons. When we looked through the values, it seems that for each movement of any one of the three axes x, y and z, it ...
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1answer
80 views

Determining the value of the product of the base vectors: [closed]

The question and answer is, $\displaystyle\,\mathbf{a}_x \cdot \mathbf{a}_\phi = -\sin \phi = - \frac{y}{\sqrt{x^2 + y^2}}\;$ according to the book. It has something to do with polar and cylindrical ...
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0answers
13 views

Queries on 3d Points

I have an array of 3d points. Each point has an x,y and z coordinate. The maximum size of the array can be 777777. I have Q queries each providing me with four numbers A, B, C, D. for each query I ...
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0answers
11 views

Taking derivative in scaled coordinates

I scaled my coordinates like: $x-x_0=(t_0-t)^{1/2}*m$ $u(x,t)=(t_0-t)^{-1/2}*U(m)$ $u$ was a function of $x$ and $t$ $u(x,t)$. So how can I find $u_t$ and $U_m$ "the derivation" with respect to new ...
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0answers
46 views

Filter by maximum distance from latitude and longitude

I have three variables: latitude, longitude and distance. I want to calculate the latitude ...
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0answers
42 views

Prove that area of a triangle is invariant under the translation of axes.

Let the original co ordinates of the triangle be $A(x_1, y_1), B(x_2, y_2), C(x_3, y_3)$. The origin is $O(0,0)$ Let us shift the origin to the points $O'(h,k)$. My book says that the new co ...
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0answers
12 views

Help with cartesianand spherical coordinates

The problem in question: Convert the cartesian coordinate to a spherical coordinate $$(x,y,z)=(0,\sqrt{3},1)$$ I know the formulas for converting the coordinate, but for finding $\theta$ I need to ...
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1answer
23 views

Doubt on zero dimensional space

Consider the case of two lines that do not intersect at any point on the 2-D plane. Is it correct to say that the intersection of the two lines belongs to the zero dimensional space or is my question ...
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0answers
19 views

Three orthogonal surfaces given by a coordinate system.

Given the following coordinate system: $q_1=\frac{x^2-y^2}{2}$ $q_2=xy$ $q_3=z$ What kind of surfaces are given by $q_1$ constant, $q_2$ constant, and $q_3$ constant respectively? I am pretty ...
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0answers
8 views

Coordinate change for a real hypersurface

Let $\Omega\subseteq\Bbb C^n$ be a domain, $0_{\Bbb C^n}\in\Omega$, $r\in\mathcal{C}^2(\Omega,\Bbb R)$, $r(0)=0$. Call $M$ the real hypersurface described by $r=0$ around $0\in\Omega$. By implicit ...
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1answer
55 views

Formula to convert Cartesian coordinates to spherical coordinates? [closed]

I have this formula: x, y, z = cos(vertical)*sin(horizontal), sin(vertical), cos(vertical)*cos(horizontal) Which maps a spherical coordinates (horizontal and ...
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1answer
67 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
26 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
55 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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1answer
50 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 ...
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0answers
37 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
50 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
101 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
204 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 ...
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1answer
48 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
23 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 ...
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1answer
13 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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1answer
41 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
11 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
27 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?
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1answer
16 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
103 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
34 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
163 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
16 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
64 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 ...
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1answer
27 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
31 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 ...
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1answer
48 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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1answer
81 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
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1answer
120 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
40 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
73 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 ...
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1answer
33 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 & ...
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1answer
67 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
11 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 ...
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3answers
28 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 ...
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1answer
20 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
28 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: ...
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0answers
23 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
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3answers
259 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
157 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
61 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. $D(0,-5,5)$ $E(1,-2,4)$ ...