# Tagged Questions

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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### Why must a function be independent of coordinates?

What is the motivation for why a function should be independent of coordinates? In the case of a general manifold I kind of get why, since one (usually) defines a function $f$ as a map from the ...
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### Problem including three circles which touch each other externally

The circles $C_{1},C_{2},C_{3}$ with radii $1,2,3$ respectively,touch each other externally. The centres of $C_{1}$ and $C_{2}$ lie on the x-axis ,while $C_{3}$ touches them from the top. Find the ...
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### determine all (x,y) of the line Normal to an Ellipse

Hi everyone I have a question that requires me to determine the (x,y) coordinates of all points that intersects the x-axis on this ellipse when the normal line has a slope of -4, and I'm curious to ...
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### Given the base of a triangle and the ratio of the lengths of the other two unequal sides , prove that the vertex lies on a fixed circle .

Can someone please explain to me how to approach this question ? I don't want the solutio
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### Find the minimum of sum

Let $A(1, 1)$ and $B(3, 2)$ be two points. Find point $M(x, 0)$ so that the sum $AM + MB$ is minimum. After that, find the minimum of the sum. In order for the sum to be minimum, I concluded that $x$ ...
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### Why Circle is traced counterclockwise and ellipse is traced clock wise?

In the Lecture 32: Polar Coordinates,professor traces the circle counterclockwise, but traces the ellipse clockwise. "Which was this one here. And first we noted that this does parameterize, as we ...
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### Laplace Equation on Prolate Spheroidal Coordinates

I'm currently trying to solve Laplace's equation outside of a prolate spheroid. The scalar field has to vanish far from the spheroid. Because of the geometry I thought it might be convenient to use ...
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### 'Tetrahedral' coordinates in space (generalization of hexagonal coordinates)

The Cartesian coordinates are the most widely used in Euclidean space of any dimension. However, there is another set of coordinate systems which can in some way be considered optimal. Imagine ...
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### Translating co-ordinate from one rectangle to another rectangle

I am trying to translate a co-ordinate from one rectangle to another. In realty, the second rectangle is the first rectangle "scaled-up". I am using the following method: ...
I am an engineer not a mathematician. So, please accept my apology if this is a very simple problem for this site. Given a coordinate $A(x_{1A},x_{2A},...,x_{nA})$ and a value d in n-dimension space. ...