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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6
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1answer
224 views

Minimum number of lines covering n points

Let there be n points in the plane. I want to know the minimum number of horizontal and vertical lines covering all the points in the plane. My initial approach started like this, 1) for each point I ...
1
vote
0answers
46 views

Linejoin for fat lines?

I draw a figure with 2 fat lines. I need to draw a join between these lines correctly. Long red lines are in a middle of each fat line. What I know: coordinates of white points. the angle between ...
0
votes
2answers
161 views

Converting $(4,-4{\sqrt3}, 6)$ from rectangular to cylindrical coordinates

I'm getting the wrong answer for $\theta$. What am I doing wrong? $$(4,-4{\sqrt3}, 6)$$ $$r =\sqrt{4^4 + (-4\sqrt{3})^2} = 8$$ $$z = 6$$ $$\tan\theta=\frac{-4\sqrt{3}}{4}$$ $$\tan\theta=-\sqrt{3}$$ ...
1
vote
3answers
2k views

finding out the area of a triangle if the coordinates of the three vertices are given

What is the simplest way to find out the area of a triangle if the coordinates of the three vertices are given in x-y plane? One approach is to find the length of each side from the coordinates given ...
1
vote
1answer
133 views

Perpendicular unit vectors

I have a known unit vector $p (a,b,c)$. First I want a unit vector $q$ which is perpendicular to $p$ and passing through a known point $V(X_0,Y_0,Z_0)$. Then a another unit vector $r$ which ...
0
votes
0answers
557 views

How do I calculate roll, pitch, yaw from a unit vector?

I am provided a unit vector giving a direction in x, y, z coordinates, and that the roll is defined as about the x axis, pitch around y, yaw around z. I'm trying to determine how to calculate roll, ...
3
votes
1answer
43 views

Cauchy-Riemann equations in arbitrary coordinates?

The CR equations in rectangular coordinates can be written as one equation in the following way: $$\frac{\partial f}{\partial x} = \frac{1}{i} \frac{\partial f}{\partial y}$$ Likewise, in polar ...
0
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0answers
15 views

Parametrically defined Spheres in $R^n$

So I have 2 questions here which are closely linked: How do you parametrically define the circle $(x')^2 + (y')^2 = r^2$ using (x') and (y') as coordinates on the plane ax + by + cz = 0 that are ...
0
votes
1answer
25 views

Calculate $x_1$ $x_2$ $y_1$ $y_2$ from center coordinates,height and width

What i have here is a rectangle or square.I have the center coordinates $x$,$y$, width and height.How do i go about finding the $x_1$, $x_2$,$y_1$ and $y_2$ from these.
1
vote
1answer
53 views

show that the straight lines $(a^2-3b^2)x^2+8abxy+(b^2-3a^2)y^2=0$ form with the lie $ax+by+c=o$ an equilateral triangle

show that the straight lines $(a^2-3b^2)x^2+8abxy+(b^2-3a^2)y^2=0$ form with the lie ax+by+c=o an equilateral triangle whose area is $\frac{c^2}{\sqrt{3}(a^2+b^2)}$ is there any other way to solve ...
0
votes
2answers
114 views

equation representing 2 straight lines

Let us assume this equation is given to us we have to factorize it $$12x^2 +7xy-10y^2+13x+45y-3=0$$ By solving we get that this represents two straight lines. But how to factorize it? Is there a ...
0
votes
4answers
138 views

How to find equation from points

I have a list of 218 points. Is it possible to find an equation for a line that passes through the points? Update : Is there a software that can generate the equation from the points?
0
votes
3answers
405 views

Straight line problem : Find the number of points which lies between the figure : $(0,0) , (0,21); (20,0)$

Problem: Find the number of points which lies inside the triangle : $(0,0) , (0,21); (20,0) $ Approach : Let us take point $A = (0,0)$, $B = (0,21)$, and $C = (20,0)$. Since the figure ...
0
votes
1answer
125 views

How to project 3D plots on a 2D coordinate system without losing the metric scale?

I've been collection data of a river bank last week and I need to plot the cross sections of the data. The issue is, that the data taken consists of 3 coordinates: easting, northing and elevation. ...
2
votes
1answer
62 views

Find direction, angle or co-ord of unknown vertices using only distance?

My current issue is that I have a triangle, where I know all the line distances as well as an origin coordinate. Is there any way I can then gain the coordinates of the other vertices with this ...
0
votes
0answers
20 views

How to set dihedral values to null?

I have a protein with many residues, but I would like to set the phi and psi angles of residue 15 to value of null. I have a file containing all residues and Cartesian coordinates, and I have another ...
0
votes
1answer
168 views

How to show that a line pass through a point?

How to show that a line pass through a point? Two fixed straight line $OX$ and $OY$ are cut by a variable line at the points $A$ and $B$ respectively and $P$ and $Q$ are the feet of the ...
0
votes
1answer
184 views

Given 2 points/coordinates, how do I express in $ax + by + c = 0$ form?

Given 2 points eg. $(x_1, y_1), (x_2, y_2)$ how do I express in $ax + by + c$ form? I am supposed to find the intersection of 2 lines. I have 2 points for 1 line, and the other line will be ...
0
votes
0answers
13 views

The velocity of a set of axes with respect to themselves

I am reading Whittaker's Analytical Dynamics. This is chapter 8 Non Holonomic Systems. Dissipative systems. Paragraph 88 is Equations of motion relative to axes moving in an arbitrary way. Let $G$ be ...
0
votes
1answer
46 views

locus difficult

A fixed point is at a perpendicular distance a from a fixed straight line and a point moves so that is distance from the fixed point is always equal to its distance from the fixed line.Find the ...
2
votes
1answer
92 views

Find the locus of the point which divides segment AB internally in the ratio 1:2.

A and B are variable points on X and Y axis respectively,such that l(ab)=4.Find the locus of the point which divides segment AB internally in the ratio 1:2. I think that it must be a circle . or ...
1
vote
1answer
69 views

Cylindrical coordinate system

Let us consider a fixed reference point P and another point Q in space. Suppose you want to express the position of Q with respect to P in cylindrical coordinate system. Now in the cylindrical ...
0
votes
0answers
65 views

Gradient definition of the unit vector

Given some coordinate system ($q_1,q_2,q_3$), it seems that the unit vectors $\hat{q}_i$ can be defined by $$\hat{q}_i = \frac{\nabla q_i}{||\nabla q_i||},$$ that is, the normalized gradient of $q_i$. ...
1
vote
0answers
66 views

Parameterizing a spherical cap in cylindrical coordinates

In calculating the mean curvature for a surface of the form $(f(z)\cos(\theta), f(z)\sin(\theta), z)$ I need to use some checks to ensure I haven't made any mistakes along the way. The one I would ...
3
votes
1answer
117 views

Are cartesian coordinates “more fundamental” than other coordinates, and are they inherently tied to $\mathbb R^n$?

Are the Cartesian coordinates more "fundamental" than other coordinate systems? When someone says $\mathbb R^n$ do we implicitly mean the set of points PLUS Cartesian coordinate system? Sometimes I ...
1
vote
1answer
21 views

coordinate of shorter line

If I have a line segment with endpoints AB,CD. The length of the line is 5 units. If I make the line shorter (eg. 3 units), and one of the endpoints is still AB, how do I figure out what the new CD ...
0
votes
1answer
45 views

Geometry finding area problem

A regular 2N -sided polygon of perimeter L has its vertices lying on a circle. Find the radius of the circle and the area of the polygon.
4
votes
1answer
76 views

Calculate the X,Y values of an ellipse

I guess am confused somewhere. I have the length(l) and breadth(b) of an ellipse enclosing rectangle. I know the center point and the angle(x) that the line makes with the center. I want to know the ...
3
votes
0answers
60 views

Changing coordinate system with non standard definitions

The standard coordinate transformation to polar coordinates is $$ \begin{cases} x=r\cos(\varphi)\\ y=r\sin(\varphi) \end{cases} $$ with $r\in[0,\infty), \ \varphi\in[0,2\pi)$ The question is whether I ...
1
vote
1answer
298 views

How to calculate the coordinates of orthocentre.!!

How to calculate the coordinates of orthocentre.!! I was surfing through the net and got this formula.. $$x-\rm coordinate= \frac{x_1\tan A+x_2\tan B+x_3\tan C}{\tan A+\tan B+\tan C}$$ ...
2
votes
0answers
1k views

Converting an equation from cartesian to cylindrical coordinates

This is going to seem pretty basic, but I'm trying to figure out if there is a problem in my homework's text or if it's just not clicking for me. I have to find the volume for the paraboloid $$z = 6 ...
1
vote
3answers
77 views

How to find the integral by changing the coordinates?

Let R be the region in the first quadrant where $$3 \geq y-x \geq 0$$ $$5 \geq xy \geq2$$ Compute $$\int_A (x^2-y^2)\,dx\,dy.$$ I tried to use $ u= y-x, v= xy$ as my change of coordinates, but then I ...
1
vote
1answer
468 views

How to determine gradient of vector in cylindrical coordinates?

I am wondering how to actually determine the gradient of a vector in cylindrical coordinates. I have seen a lot of websites that just say what the general form is but I cannot seem to understand how ...
4
votes
1answer
129 views

Are spherical coordinates unique orthogonal coordinates on sphere?

Spherical coordinates on unit sphere are defined by the following transformation: $$\begin{cases}x=\sin\theta\cos\varphi\\ y=\sin\theta\sin\varphi\\ z=\cos\theta\end{cases}$$ Are these coordinates ...
1
vote
1answer
158 views

sketching regions of three variables

If i had a solid region, V, such that $x^2+y^2+z^2\le9$, $x^2+y^2\le4$, $x\le0$ and $z\ge1$ what would be the easiest method to sketch this region? Can someone run me through steps as how to tackle ...
3
votes
1answer
733 views

Calculate Camera Pitch & Yaw To Face Point

How do you calculate pitch & yaw for a camera so that it faces a certain 3D point? Variables Camera X, Y, Z Point X, Y, Z Current Half Solution Currently I know how to calculate the pitch, ...
0
votes
0answers
27 views

Natural dihedral

Can you help me with this: A body of mass $m$ is moving under gravitational force and resistance force proportional to the square of its speed. Write differential equations of motion of a body in ...
0
votes
1answer
35 views

Algorithm to approximate the closest nonlinear formula(funciton) for an arbitrary set of points?

I have a table which concists of XY points (so I have a set of points hehe), where X represents the Velocity and Y the Real World Speed. Those points are not linear. With two points it's easy to ...
1
vote
2answers
2k views

Finding a line perpendicular to a line and passing through the intersection of other two lines

So here is the question as in my text book Find the equation of the line through the intersection of $2x - 3y + 4 = 0 $ and $3x + 4y - 5 = 0$ and perpendicular to $6x - 7y + c = 0$ so I ...
1
vote
1answer
55 views

Center of Distance

I am given $N$ points in a 2D plane($x$ and $y$ coordinates). I have to find a point in this plane with coordinates $X$ and $Y$ such that: $$\sum_{i=1}^N \max\{|X - A_i|, |Y - B_i|\}\text{ is ...
1
vote
1answer
222 views

Which matrix transforms my vector field $F(r,\theta,\phi)$ from cylindrical to spherical coordinates

I am looking for the matrix that I have to apply my vector at the position $(r,\theta, z)$ to in order to get the appropriate vector in spherical coordinates. I am totally okay, if you could give me ...
1
vote
2answers
154 views

How to calculate the number of integral points inside an area

How many integral solutions (x, y) exist satisfying the equation |y| + |x| ≤ 4 My approach: I have made the graph after opening the the modulus in the above equation by making four equations. Now ...
2
votes
1answer
185 views

Get 2D direction vector from 1D rotation (for game development)

I am working on a game where my object is supposed to move forward based on it's rotation (the direction it's facing) I tried this: increase object x to cos(rotation) increase object y to ...
1
vote
1answer
296 views

Express spherical coordinates with different centers in terms of each other.

Imagine that you have two spheres with a distance $R$ from one center to the other one. Now, it is well known how one would get the cartesian position vector of each point in sphere 1 by using ...
-1
votes
1answer
49 views

Confusion on the given solution to a homework question.

Question: If the line $ x = a+m $, $y = -2 $ and $y = mx$ are concurrent, the least value of $|a|$ is (A) $\sqrt{2}$ (B) $2\sqrt{2}$ (C) $2\sqrt{3}$ (D) ...
0
votes
0answers
70 views

coordinate transformation and scaling

I have a global coordinate system that I need to transform to a local coordinate system. The new and old coordinate systems are shown below. Using transformation rules, I came with with the ...
1
vote
0answers
40 views

What's the mathematical formulation for frames for reference?

In this lecture I've come across an interesting formulation of kinematics and reference frames. When I studied kinematics, the idea of what is meant by a 'frame of reference' was never quite fully ...
1
vote
1answer
90 views

Find the coordiantes of a rectangle using vectors

I have two coordinates which are vertices of a rectangle. They form the diagonal of the rectangle. Is it possible, using vectors, to calculate the other two coordinates? I have tried calculating ...
2
votes
0answers
71 views

Evaluation of oscillating gaussian integral

I've problems to evaluate the following integral $$\int_{\mathbb{R}^3} dx \, dy \, dz \, \frac{e^{-i \Gamma |\vec{r}-\vec{r_0}|}}{|\vec{r}-\vec{r_0}|} \frac{e^{i \Upsilon |\vec{r}|}}{|\vec{r}|} ...
0
votes
2answers
33 views

Given a bunch of rectangles, find an enclosing rectangle.

Given below are a bunch of rectangles whose dimensions are listed in (x, y, w, h) format. Where, x, y are coordinates of left top corner of the rectangle while w ...