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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0
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2answers
44 views

Splitting a segment with a ratio

I came across the homework question that I attempted to do. After looking at the answers, and getting it wrong I didn't understand why. I'm specifically lost at why we would get a fraction of 2/5 ...
1
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1answer
48 views

A point P is selected inside an equilateral triangle. If sum of lengths of perpendicular dropped on to sides from P

Problem : A point P is selected inside an equilateral triangle. If sum of lengths of perpendicular dropped on to sides from P is 2014, then $\frac{\mathrm{length\; of \; altitude \; of \; ...
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1answer
50 views

What basis and coordinate system is used in this quadratic Bézier triangle equation? $[x,y,z] = A*s^2 + B*t^2 + C*u^2 + D*2st + E*2tu + F*2su$

I have the following equation for a quadratic Bézier triangle, but I'm having a lot of trouble understanding how to describe it: $[x,y,z] = A*s^2 + B*t^2 + C*u^2 + D*2st + E*2tu + F*2su$ ...
4
votes
1answer
40 views

Family of lines $\sin\alpha x +\sin\beta y +\sin\gamma =0$

Problem : If $\sin(\alpha + \beta)\sin(\alpha -\beta) =\sin\gamma (2\sin\beta +\sin\gamma), 0 < \alpha , \beta ,\gamma <\pi$ then the family of lines $\sin\alpha x +\sin\beta y +\sin\gamma =0$ ...
2
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2answers
39 views

Number of non zero integer values of $k$ for which the points ($k,k^2)$ lies inside the triangle formed by the given three lines

Problem : Number of non zero integer values of $k$ for which the points ($k,k^2)$ lies inside the triangle formed by the lines $11x+6y+14=0$, $9x+y-12=0$, $2x+5y-17=0$ (a) $0$ (b) $2$ (c) $3$ ...
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2answers
20 views

If the circle $x^2+y^2+4x+22y+c=0$ bisects the circmuference of the circle $x^2+y^2-2x+8y-d=0$ the…

Problem : If the circle $x^2+y^2+4x+22y+c=0$ bisects the circmuference of the circle $x^2+y^2-2x+8y-d=0$ then c +d equals (a) 60 (b) 50 (c) 40 (d) 30 Solution : Equation of common chord ...
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1answer
46 views

Find if a rectangle passes through another in cartesian plane

I want to know how to prove or find out if the red big rectangle passes through one of these small rectangles i have the coordinates of the big rectangle (the top left) and i have it's width and ...
2
votes
1answer
155 views

What percentage of rooms would be trapped in the cube?

In the movie Cube the design is based heavily in math. I'm trying to figure out the approximate percentage of rooms that would be trapped. His knowledge of the outer shell's size allows Leaven to ...
3
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0answers
88 views

What distinguishes elliptical coordinates from polar coordinates?

I am trying to identify what characteristic distinguishes elliptical coordinates from polar coordinates. For concreteness, let's write down the expressions. Polar: $$ x=r \cos(t) \\ y=r \sin(t) $$ ...
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1answer
25 views

If the distances from origin of centre of three circles $x^2+y^2+2\lambda_i-c^2=0$ (i=1,2,3) are in G.P…

Problem : If the distances from origin of centre of three circles $x^2+y^2+2\lambda_i-c^2=0$ (i=1,2,3) are in G.P ( Geometric progression). Then lengths of tangents drawn to them from any point on the ...
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2answers
47 views

Position of a point with respect to two reference frames

I working on a project where doing some image processing detect objects using Kinect camera and then move it to a desired location with a help of robotic arm. In this project the sensor gives pixel ...
0
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1answer
43 views

Sending Messages

N animals are sitting on the X axis and want to send messages to each other.One animal can send a message to another one if the distance between them is less or equal to K.P pairs of animals are ...
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0answers
32 views

Getting coordinate vector in linear algebra

I know how to get the coordinate vector of single matrices by just joining them and doing a gauss jordan. But these are a 2x2, I don't know how to go about this, apparently no elimination can take ...
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0answers
23 views

How many kinds of simple coordinates are there in a 2D space?

The question comes form an idea to solve a motion-with-potential problem in 1D space by finding a mathematically equivalent uniform-motion problem in 2D space. ...
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0answers
32 views

How do points change in a curved surface?

In the middle picture it shows a row of sticks at certain points along a flat surface. Now in the outer left picture (never-mind the outer right one), when the surface becomes curved the points ...
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3answers
51 views

If there are $N$ people on the positive $x$-axis and one man can send a message to another one only if the distance between them is $\leq k $.

The question is how to determine a function which would decide if a pair of persons can communicate with each other, where communication is possible only if the distance between two individuals are ...
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2answers
44 views

Converting from set of Cartesian equations to Polar Equation

Is it possible to convert the set of Cartesian equations: $$x(t) = (20-30)*\cos(2t)+45*\cos(2t*(20-30)/20))$$ $$y(t) = (20-30)*\sin(2t)+45*\sin(2t*(20-30)/20))$$ where $$t \in [0,2\pi)$$ Into a ...
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2answers
40 views

Partial differentiation in transformed coordinates

Following lecture notes from MIT it says that, given some variable $A = A(x, y, z(x, y, r, t), t)$ where $r$ is a transformed vertical coordinate $\left. \frac{\partial A}{\partial x} \right|_r = ...
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3answers
2k views

Minimum moves to reach destination [closed]

Given that a person is standing at $(0,0)$ and initially look in direction of $X$-axis. Now he can walk only at right angle to previous move. Like if he has to go to $(3,3)$ then $6$ moves are ...
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2answers
43 views

Locating a point on a circle

I am having trouble getting the $(x,y)$ of a certain point on the circle. Please look at the image: The circles are the identical, the radius is $1000 \text{ units}$, $S$ is the center with ...
0
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1answer
38 views

cylindrical and rectangular coordinates

Hi! I am currently working on some online homework and I don't understand what I am doing wrong when solving this problem. I know that the first and third coordinates are correct, but I seem to be ...
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0answers
17 views

Vocabulary of line coordinates

We can represent a line in 2 and 3 dimensions using 2 and 4 parameters respectively. For example, in 2 dimensions, we can represent a line using the angle $\theta$ of the normal and orthogonal offset ...
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1answer
43 views

Estimate Rotation and Translation from two sets of points in different coordinate systems

I got one set of 3d $(x,y,z)$ points $( \# \geq3 )$ located in two diffent coordinatesystems. Is it possible to estimate the rotation and translation between these systems? Something like $$ ...
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0answers
45 views

Dividing an infinite plane into regions

I am currently working on a computer program for computing layout of graph-based diagrams. Their content is placed in an "infinite" 2D plane with cartesian coordinates in the center of the diagram. ...
0
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1answer
29 views

How many lines are larger lines made of in a dotted grid?

In a dotted 2d grid, lines can be drawn between the dots. But every dot that the line touches breaks the line up into smaller lines. I want to be able to work out how many lines this bigger line is ...
1
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1answer
59 views

Equation of pair of reflected straight lines given the equation of pair of incident straight lines

If $ax^2 + 2bxy + by^2 = 0$ represents a pair of lines, then find the combined equation of lines that can be obtained by reflecting these lines about the x-axis. I know that this can be done by ...
0
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1answer
26 views

How does the transformation $u=x+y$, $v=x/y$ transform the first quadrant?

How is the region $(x,y) \in [0,\infty] \times [0,\infty]$ transformed under the change of coordinates given by $$u=x+y$$ $$v=x/y$$ Would appreciate any hints on how to find the image of such ...
0
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1answer
64 views

What are the coordinates of a point on a rigid body after a rotation in 3D Euclidean space, given the initial coordinates and a center of rotation

Main question Let ($x_p$, $y_p$, $z_p$) be the initial coordinates of a point $P$ on a rigid body in a right-handed 3D Euclidean space. Let ($x_r$, $y_r$, $z_r$) be the coordinates of a center of ...
0
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3answers
65 views

Alternatives to polar coordinates for mapping point onto one dimensional coordinate

I can map a point (x,y) to polar coordinates (angle,length). However, let's say in this (angle, length) pair, "length" doesn't actually interest me, so I can map (x,y) to a one dimensional ...
2
votes
1answer
90 views

Example of a Problem Made Easier with Skew Coordinates

Skew or oblique coordinate systems are coordinate systems where the angle between the axes is not 90 degrees. The second answer to this question has formulas to convert between these systems with an ...
0
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1answer
81 views

Convert $r^2\cos(2\theta)=9$ to Cartesian

I need to convert $r^2\cos(2\theta)=9$ to Cartesian coordinates. How should I do it? What I did: $$r^{2}\cos2\theta=r^{2}2\cos^{2}\theta-1=9\Rightarrow r^{2}\cos^{2}\theta=5\Rightarrow x^{2}=5$$ Did ...
2
votes
1answer
53 views

From any arbitrary point $P$ on $y =\cos x$ tangents $PA$ and $PB$ are drawn to a circle which passes through

From any arbitrary point $P$ on $y =\cos x$ tangents $PA$ and $PB$ are drawn to a circle which passes through the points $(1,0)$ and $(3,0)$ and touches the circle $x^2+y^2-2x-8=0$ and have its ...
1
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1answer
37 views

Consider a series of n concentric circles $c_1,c_2 \cdots c_n$ with radii $r_1,r_2.\cdots r_n$ satisfying $r_1>r.$.

Consider a series of n concentric circles $c_1,c_2 \cdots c_n$ with radii $r_1,r_2.\cdots r_n$ satisfying $r_1>r_2>r_3 \cdots r_n$ and $r_1=10$ The circles are such that the chord of contact of ...
1
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1answer
20 views

Longitude and Coordinates

Let $X=(x_1,x_2,x_3)$ and $Y=(y_1,y_2,y_3)$ be two points on the unit sphere $S^2=\{(x_1,x_2,x_3)\,|\,x_1^2+x_2^2+x_3^2=1\}$. Is there a "nice" necessary and sufficient condition on the coordinates ...
0
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2answers
86 views

Collision detection between two accelerating spheres with no initial velocity?

We have two non-touching spheres of radii r1 & r2 are lying in space at rest. Both of them are then given accelerations a1 & a2 respectively at time t=0. Find whether they will ever come in ...
5
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1answer
166 views

Using paraboloidal coordinates

I have the 3-dimensional paraboloidal coordinates $$s_{\pm}=\sqrt{x^2+y^2+z^2}\pm z$$ $$\phi=ArcTan(y/x)$$ with the inverse transformation $$x=\sqrt{s_+ \cdot s_-}\cdot cos(\phi)$$ $$y=\sqrt{s_+ ...
1
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0answers
49 views

Locus of point moving with circle

Consider the circle of radius $1$ unit with its centre at the point $(0,1)$. From the initial position, the circle is rolled along the positive $x$- axis without slipping. Find the locus of the point ...
1
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1answer
75 views

Pi for non mathematician

I've been long gone from math (shamefully) and have trouble using some quite familiar concepts... Consider the following picture in which I render two circles with radius 32 (...
0
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1answer
22 views

2-dim. pendulum: Which coordinates?

I have a rather elementary question: I have a 2-dim pendulum and I do not know how I can descrive the coordinates. In the 1-dim case one coordinates is enough_ the angle. But I do not know how it is ...
1
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2answers
46 views

how to calculate the coordinates center of a squar [closed]

I need to calculate the center of square cells each cell has 4 (x,y) coordinates. Can one help me to Know how can I calculate the coordinates of the center of each cell?
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2answers
201 views

Global and local coordinates on a manifold, and their relations to curvature

I would be pleased to have some information about coordinates in differential geometry. A) First I would like to check whether or not the definitions I use are correct. (Mainly for the sake of ...
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0answers
37 views

Mapping between two unknown 3D coordinate systems from common motion

Coordinate systems A and B are rigidly linked in an unknown way. The platform then moves and the motion vectors [RA|TA] and [RB|TB] are calculated in each coordinate system. They are parallel but not ...
0
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1answer
63 views

Dot product in Curvilinear Coordinate Systems

I came across the dot product in polar, cylindrical, and spherical coordinates, today. After checking they were equivalent to the Cartesian versions, I started wondering how one would figure them out ...
0
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1answer
26 views

Find the nature of the curve

Given: $x=t^2+t+1, y=t^2-t+1$ Find the nature of the curve. My approach: I was trying to relate $x$ and $y$. However I haven't been able to. Please suggest some methods to solve such kind of ...
0
votes
1answer
41 views

Coordinates of specific points on a triangle, given the triangles coordinates

I'm working on a programing project. For that project I have a triangle with points $A,B,C$, where $A(a_1,a_2,a_3);B(b_1,b_2,b_3);C(c_1,c_2,c_3)$. Given the coordinates of the points $A,B$ and $C$, I ...
0
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2answers
67 views

Better way to denote position on a sphere's surface

TL;DR: Read the bold text. If you have a rectangular plane, you can use two coordinates (X, Y) to define any position on the plane. If you have a sphere, you can still use polar coordinates to denote ...
2
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2answers
87 views

What is a coordinate system?

What's a coordinate system? I was watching a Khan video about coordinates with respect to orthonormal bases. It is mentioned that orthonormal bases make for "good coordinate systems". I didn't ...
2
votes
0answers
31 views

Ellipsoidal Coordinates Geometrically

Is there a quick, geometric, way of writing down (the square root of?) the Cartesian coordinates $$\begin{align} x^2 &= (a^2+\xi)(a^2+\eta)(a^2+\zeta)/(b^2-a^2)(c^2-a^2)\\ y^2 &= ...
0
votes
2answers
181 views

converting kph and heading to xyz velocity vector

I am writing software (in C++) that is required to send out messages from our simulation system to another simulation system. Problem is we track the simulation object's current speed (kph) and ...
1
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1answer
20 views

How to find the $ x,y$ coordinates of a point in between $2$ points in $3$ dimension

Point $1 = (0,0,0)$ Point $2 = (5,6,7)$ Given that point $3$ have a $z$-coordinate of $3$, how can I find the $x,y$ coordinates of point $3$?