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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2answers
410 views

How to verify a conversion to spherical coordinates?

Is it possible to verify if a conversion of an integral in Cartesian coordinates to spherical coordinates was done correctly other than revising it looking for mistakes? I mean, is there some kind of ...
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0answers
158 views

Change of coordinates in 3D

It's been a while since my last geometry class and I need some help in solving a very simple problem I have. I need to implement a zoom function in 3D in a piece of software I am writing. My system ...
2
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1answer
203 views

Proper change of coordinates

It's a really easy one for you guys. I'm performing a simple cylindrical change of variable from Cartesian coordinates, but I want to write it out properly and I'm stuck with the differential ...
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0answers
50 views

graph of moving object

let us consider following three picture grouped as in one picture suppose that we have following problem: during the $1$ hour,biker was moving around station $A$ and during this $1$,he did not ...
4
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0answers
44 views

Solving a system of equations

I'm trying to prove the existence of a solution to the system of equations $$c_i = \gamma x_i + (1-\gamma) \frac{x_i^2}{\sum_{j=1}^\infty x_j}$$ for $i\in\{1,2,....\}$ where $\sum c_i=1$. I am also ...
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2answers
20 views

How can I get the $(x,y)$ of a sub-line, which has 0.45 length of the original line, between two points?

Given two points $(x_1, y_1)$ and $(x_2, y_2)$, they forms a straight line. The target is to find a point $(x_t,y_t)$ between these two points, and the length from $(x_1, y_1)$ to $(x_t,y_t)$ is 0.45 ...
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0answers
30 views

How to figure out if a point is inside the bounds of a rotated rectangle [duplicate]

I'm trying to figure out an approach (or a formula) to determine if a point (x,y) is inside the bounds of a rotated rectangle. For this test we can assume that the rectangle is centered on the ...
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1answer
313 views

Transform between cartesian coordinate system and abstract coordinate system

I am trying to find a transformation that takes me between Cartesian coordinates and a pseudo-coordinate-system I have developed which is described as follows: Please first see the diagram below. ...
2
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1answer
165 views

Find meeting coordinates of two points

First of all, sorry for my English, because I am from Russia. The task is: We are given two points (see image) - $(x_1, y_1)$ and $(x_2, y_2)$. Point $(x_2, y_2)$ is moving and has a speed of ...
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3answers
2k views

project a point in 3D on a given plane

A point in a 3D space is given as $ P(x,y,z) $. I want to find the position of this point projected parallel to the normal on a plane Q defined by $3$ non-collinear points $ Q1(x1,y1,z1), ...
2
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1answer
84 views

find parameter for maximize area

suppose that we have Cartesian coordinate system.and suppose that we have three point which depend on parameter $t$,where t belongs to $(0,1)$;points are $A(cos(3-t),sin(3-t))$ $B(cos(t),sin(t))$ ...
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1answer
301 views

Homothetic transformation

Suppose that, we have a homothetic transformation in a rectangular coordinate system, with center origin $(0,0)$ and $k$. This homothetic sends point $A(2,3)$ to point $B(2x-1,x)$. My aim is to find ...
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4answers
75 views

A vector should more be thought an identity of an entity in space rathar than magnitude + direction?

Can I say that vector is more like a "unique identity" of an entity in space rather than calling it an entity with magnitude and direction ? For example a line. A vector $(10,10,0)$ is the identity ...
2
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3answers
257 views

How to check if three coordinates form a line

Assume I have three coordinates from a world map in Longitude + Latitude. Is there a way to determine these three coordinates form a straight line? What if I was using a system with bounds that ...
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2answers
270 views

Expansion of velocity in polar coordinates using kinetic equations

Why does total energy $$E=\dfrac{1}{2}\mu\mathbf{v}^2+U(r)$$ expand to $$E=\dfrac{1}{2}\mu(\dot{r}^{2}+r^2\dot{\phi}^2)+U(r)?$$ It's some form of the kinetic equations in polar coordinates. I know ...
4
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0answers
238 views

Orthogonal Coordinate Systems Intuition

I'd really love it if you could give some intuition on how to derive the $x$, $y$ & $z$ coordinates from all/any of the orthogonal coordinate systems in this list, how you think about, say, ...
1
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1answer
229 views

Convert spherical coordinates to Cartesian coordinates for a vector

So let's say I have a normalized vector $N$ given in cartesian coordinates and I have another normalized vector $V$, defined in spherical coordinates relative to the vector $N$. So $\theta_V$ is the ...
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1answer
38 views

Conversion of $F(x) = {1 \choose 0} (2t^2 - 3t + 1) + {3 \choose 1} (4t - 4t^2) + {1 \choose 2} (2t^2 - t)$

I have a textbook with a calculation step that is pretty unclear to me: $$F(x) = {1 \choose 0} (2t^2 - 3t + 1) + {3 \choose 1} (4t - 4t^2) + {1 \choose 2} (2t^2 - t)$$ $$= {-8 \choose 0} t^2 + ...
0
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0answers
80 views

Spherical object with n vertices and no coordinate singularities

I'm programming a tool where I want to track the directions of a unit vector. I want to store the position to which the vector is pointing on a unit ball. Each time the vector points to a position $x$ ...
0
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1answer
90 views

which algebraic curves admit (nice?) geometric characterizations?

Caveat lector: this a super soft question. In an effort to help my students, across many different courses, better appreciate and put to work the distinction between geometric objects & ...
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1answer
55 views

Calculate the value of x, y and z coordinates

System of the equations: Equation 1: $$-360 = -6x + x^2 - 40y + y^2 - 20z + z^2$$ Equation 2: $$-600 = -40x + x^2 - 30y + y^2 - 100z + z^2$$ Equation 3: $$59.85 = -10x + x^2 - 4y + y^2 - 10z + ...
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1answer
319 views

Spherical coordinates of a unit vector around a normal $N$

So if I have a unit normal for a surface $N(x,y,z)$ and an incident unit vector $V(x,y,z)$ to that surface, how would I represent the vector V in spherical coordinates relative to the normal?
2
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2answers
104 views

Perpendicular distance question?

I've been having trouble with the following question: "The point $P(x,y)$ is equidistant from the lines $2x+y-3=0$ and $x-2y+1=0$, which intersect at $A$. Use the distance formula to show that ...
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4answers
79 views

A question on geometry?

I wanted to know, given quadrilateral ABCD such that $AB^2+CD^2=BC^2+AD^2$ , prove that $AC⊥BD$ . Help. Thanks.
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2answers
97 views

How many coordinates are unreachable?

I wanted to know, if a man was to go from $(0,0)$ to $(46,46)$ moving only straight and up with the following constraints:- If he walks right, he will walk atleast $4$ consecutive coordinates. If ...
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1answer
129 views

Repositioning and resizing when i change the size of my frame

Moderator's Note: This question is cross-posted on gamedev.SE. I am trying to write a game. When someone resizes the window of my game, I need all the graphics i have drawn on the screen to ...
2
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2answers
55 views

Change of Coordinate Matrix question.

I have this question and the wording is very confusing, I dont understand how to answer it. Any help will be greatly appreciated. I have tried answering it and I just dont know where to begin. ...
1
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1answer
338 views

Linear Transformation of a straight line

Let $L_{1}: x-y-2=0$ be a straight line in the x-y coordinate system. Find a coordinate system $(x_{1},y_{1})$ having its origin at $(0,0)$ and relative to which $L_{1}$ has equation $y_{1}= ...
3
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2answers
114 views

Inertial Frames of Refereence

I am told that in Newtonian mechanics, no coordinate system is "superior" to any other. Also, all inertial frames are in a state of constant, rectilinear motion with respect to one another. So am I ...
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4answers
634 views

Is there any good reason why a protractor starts from right to left, unlike a scale, which starts from left to right?

While studying through the number system, i notice that positive side is from 0 to +ve infinity. The direction is left to right. However, this is opposite in case of angles. The sort of curved number ...
2
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1answer
38 views

Can this logic about locating a point uniquely without using “-” be challenged?

I was just exploring a possibility of locating point without using "-" ( negative ) sign. ( Actually negative sign confuses me a lot when understanding the basics of coordinate geometry ) So, here ...
1
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1answer
300 views

merging the equations of the line

I have two equations for plotting the line. How can I merge them to get a single equation? $$\begin{align}y&=7.515x^3 - 10.229x^2 +5.05x, \,\, x \leq 0.5\\ y&=0.185x + 0.815, \,\, ...
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0answers
49 views

Can all 2-surfaces be “coordinated” using 2 numbers

Consider a 2-dimensional surface embedded in 3 dimensional euclidean space. ex: A plane, a sphere, a hyperboloid of 2 sheets (or 1 sheet), the graph of sin(x + y), 2 parallel planes etc... If we ...
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1answer
119 views

plot a point which is in form of lat and long in a pixel map

I need to plot a point which is in form of lat and long this point is equivalent to a screen coordinate on pixels on my map. I want to make a relation in these two point so if you want to plot a ...
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1answer
55 views

Can't figure out this transformation matrix

So basically I want to write a transformation matrix to take me out of one coordinate system and into another. The transformation has to be as follows: 1) The positive z axis normalized as ...
1
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2answers
3k views

Is it possible to find function that contains every given point?

Let say we have a arbitrary number of given points and there is at least one function, for which every point lies on its graph. Is it possible to find that function using only X and Y coordinates of ...
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0answers
168 views

family of circles in bipolar coordinate system

I don't get the idea how the equation for this family of curve is $\displaystyle y^2 + (x - a \coth v)^2 = \frac{a^2}{\sinh ^2v}$ from this article on Wikipedia. Suppose, the equation is ...
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1answer
25 views

getting line-line intersection if the axis intersections are given

A,B,C and D points are given, how can I calculate the E point? I know this method, but I would like to know if there is any other solution exists, that does not need the equalation of both lines. ...
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1answer
298 views

New x coordinate of a rotated line

I need help finding the equation to find $x$ I work in GIS and I'm working on a script that uses the new x coordinate of a rotated line. I havent work with trigonometry in a long long time so I ...
0
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1answer
79 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 ...
3
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1answer
190 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 ...
9
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2answers
4k 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?
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1answer
39 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
78 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
33 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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1answer
240 views

Calculate the distance between the points $(1, 2, \dots, n)$ and $(2, 3, \dots, n, 1)$

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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1answer
98 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
3k 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
82 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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2answers
2k views

Linear equations; how to write an equation from given coordinates?

A straight line goes through the points $( 0, 1 )$, $( 2, 7 )$ and $( 4, 13 )$ and I need to write the equation of this straight line. How do you write equations? I know you have it's usually $y = x ...