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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An error in Wikipedia? (trigonometry)

https://en.wikipedia.org/wiki/N-sphere In "Spherical coordinates" section the hyperspherical coordinates are results of arccosinus function. In some other sources there is arccotangent instead: ...
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Find coordinates for points on circle given R, 2 Points, and angle or 2 points and center?

I would like to find coordinates for points on a circle given: Radius of circle Coordinates of 2 points on the circle Angle of point 1, center, and point 2. Ultimately, I would like to write a ...
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11 views

Parabolic Coordinates Radius

Given Cartesian $(x,y,z)$, Spherical $(r,\theta,\phi)$ and parabolic $(\varepsilon , \eta , \phi )$, where $$\varepsilon = r + z = r(1 + \cos(\theta)) \\\eta = r - z = r(1 - \cos( \theta ) ) \\ \phi ...
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18 views

Find coordinates for point on circle

We got two points on circle and we know about center angle between two points.If we know coordinates of center $(x_1,y_1)$ and point $A=(x_2, y_2)$ and angle $\alpha$, how can we find the coordinates ...
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15 views

Fit cartesian coordinate system to point cloud

I have a cloud of points that initially lie in a plane and have a coordinate system attached to them. I then displace the points slightly, and I want to find how a 'best fit' of the coordinate system ...
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1answer
20 views

Angle between planes , when only two points are given

Find the equation of plane passing through points $[1,0,0]$ and $[0,1,0]$, and making an angle of $45°$ degree with the plane $x + y - 3 = 0$.
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40 views

Tangent definition

As far as the definition of a tangent goes it is a line that touches a curve only at one point. Now let us consider the sine function .At (pi)/2 it attains its maximum value and so does it at ...
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1answer
22 views

rotation matrix to axis angle

from wikipedia the above rotation matrix has a rotation of -74 degrees. What does it mean "around the axis (−1⁄3,2⁄3,2⁄3)"? How can I determine how many degrees is rotated on X axis, Y axis and Z ...
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44 views

“Rigorous” definition of Cartesian coordinates

I, like most, first learned about Cartesian coordinates very early on in my educational career, and so the most instructional way to think about them was that you place down some perpendicular lines ...
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1answer
29 views

Convex Sets and extreme supports

Let the set $S$ in $R^n$ consists of the origin $0$ and $n$ lineary independent vectors $T_1, \ldots, T_n$. Show that $C(S)$, the convex hull of of $S$, is the intersection of its extreme supports, ...
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34 views

Geometric reasoning and triangular coordinates

The following is from a book: I do not understand the sentence "... the point $(t_1, t_2, t_3)$ can be plotted by plotting $(t_1 = t_3, t_2 = t_3)$...", what is meant by the point $(t_1 = t_3, t_2 = ...
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1answer
13 views

Rotation of velocity vectors in Cartesian Coordinates

I want to rotate a $(X,Y,Z)$ coordinate-system around it $Z$-axis. For the coordinates this can be done with the rotation matrix: $$ R_Z(\theta)= \begin{pmatrix} cos \theta & -\sin(\theta) & ...
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1answer
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Scalar products and partitions of Hypercubes

My questions relate to scalar products defined in $\mathbb{R}^{n}$ and partitions of hypercubes. Take $s \in \mathbb{R}$, $\xi, \eta \in \mathbb{R}^{n}$. My first question is why is it possible to ...
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1answer
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How to draw a straight line and determine the gradient from the graph?

The following gives experimental values of two variables $x$ and $y$ which are known to be connected by a relation of the form $xy=a+bx$. So, this information was given in a table. $x=0.4,y=22.0$ ...
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17 views

How to move coordinate systems using rotation matrices.

I am having some trouble with this question. I understand that the rotation matrix will be 4x4 and that the first 3 columns will just be $u$, $v$ and $n$ transposed but I dont know what I am ...
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1answer
37 views

Using Cylindrical Coordinates to Compute Curl

I am given a vector field $\vec{A} = A_\rho \space \hat{e_\rho} + A_\phi \space \hat{e_\phi} + A_z \space \hat{e_z}$, and I am supposed to use the unit vectors (provided below) in cylindrical ...
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30 views

How to find the center of one side of a Quadrilateral

If I have a rectangle drawn in perspective and I know the coordinates of points A, B, C, D, how do I calculate the coordinates of point E? Which equates to the center of the bottom line if not drawn ...
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23 views

Find the coordinates of P.

A trapezium ABCD, AB parallel to DC, BC is perpendicular to both AB and DC. $A (4, 2), B (16, 8), C (13,14), D(5, 10)$. Lines AD and BC produced to meet at P. Find the coordinates of P. I tried to ...
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Inverse Rotation - Original X / Y values

Really stumped. I'm currently writing a program and I am given a rotated rectangular object on a 2d plane. The object has been rotated about it's center point and I need to find out how to get the ...
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Finding coordinates of nodes in a graph

I have a complete graph in which the edges represent the euclidean distance between the nodes which is known. Assuming a node to be (0,0), I want to find (approximately) the coordinates of other ...
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29 views

A sufficient condition for a convex body to lie completely inside another convex body?

Suppose we have two convex bodies in 3D space. Let’s call them $B_1$ and $B_2$. Let’s denote their projection curves on the xy plane by: $P_{1xy}$ and $P_{2xy}$, on the yz plane by: $P_{1yz}$ and ...
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Detect Regions Described By Lines in Rectangular Coordinates

Need some help from the superior math minds here. This problem is part of a software project. Essentially, I have a Cartesian grid. The user can create lines by plotting points (every 2 points ...
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1answer
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How can I transform coordinate systems with quaternions?

I have a coordinate system 0 which I'd first like to rotate about its z-Axis which gives me system 1, and afterwards rotate system 1 about its y-axis which gives me system 2. See picture: Both ...
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1answer
25 views

Find the equation of the line.

Find the equation of the line passing through the point $(5,7)$ and parallel to the line $5x+4=0$ If I say $m=5$, how should I find $c$? There is no $y$ in the equation!
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Find the equation of the straight line.

Find the equation of the straight line that is parallel to $2y-x=7$ and bisects the line joining the points $(3,1)$ and $(1,-5)$. So, I found the gradient = $\frac{1}{2}$ And I solved the midpoint: ...
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1answer
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Transfer Transformation from Physics to Vector Graphic

Upfront, I am not a professional in Maths and hope that the formulation of my question describes the problem well enough. I am creating a jump'n'run game, which uses a physics engine (Box2D) and SVG ...
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How to use geometry to express unit vectors of spherical coordinate system in terms of Cartesian unit vectors

It's quite easy to express unit vector $\hat{r}$ in sum linear combinations of Cartesian unit vectors $\hat{x}$, $\hat{y}$ and $\hat{z}$. But I am not sure how I can use geomtery to find a Cartesian ...
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How to find coordinates of a point on a 3D cylinder in Cartesian system if any one point on cylinder and dimensions of cylinder are known?

Consider a cylinder of known dimensions inserted in 3D cartesian space. I know the cartesian coordinate of one point located on the surface of cylinder. Using this information I want to find out the ...
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3answers
38 views

Find the coordinates of $P, Q, R$.

In triangle $PQR$, $A(-2,3), B(5,-1)$ and $C(-4,-7)$ are the midpoints of $PQ, QR$ and $PR$ respectively. Find the coordinates of P, Q and R. I really can't understand how to begin....Please hint :'( ...
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1answer
31 views

Mapping points on a plane in space onto a coordinate plane

Is there a way to isometrically map points on a plane in space onto a coordinate plane? So for example, given the three points $\left( 1,1,0 \right)\;, \left( -1,0,2 \right),\; \text{and }\left( ...
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Converting Euler Angle z-y'-x'' sequence to heading

I'm trying to convert a set of Euler Angles to a heading $(0-360)$ degrees. The Euler Angles use the $\ x-y'-x''$ sequence headings, using $\ \psi, \theta, \phi$ as the rotation angles, respectively. ...
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3answers
41 views

Determining if a point is inside two planes

I have two planes(Plane 1 and Plane 2) the normals ($n_1$ and $n_2$) of which are known to me. How do I determine if a point is inside the two planes? By inside I mean the 3d space between Planes 1 ...
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2answers
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How to find the perpendicular distance from B to AC?

"Find the area of triangle $ABC$ with vertices $A(2, 1), B(12, 2) $and $C(12, 8)$. Hence or otherwise, find the perpendicular distance from $B$ to $AC$." I found the area, which is 30 units by find ...
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Find the point on the y-axis which is equidistant from the points $(6, 2)$ and $ (2, 10)$.

Find the point on the y-axis which is equidistant from the points $(6, 2) $ and $ (2, 10)$. Please help, there are no examples of this kind of sum in my book! I don't know how to solve it.
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Why are the axes in coordinate geometry perperndicular?

In coordinate geometry, the $x$ and $y$ axis are perpendicular to each other. But is there any special reason for this (other than to make it simple)? Will coordinate geometry have contradictions if ...
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2answers
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Show that the four points given below are the vertices of a rhombus.

Show that the four points, $(5, 8), (7, 5), (3, 5)$ and $(5, 2)$ are the vertices of a rhombus. I tried solving it, by finding out the distances by using the formula $\sqrt{(x_{2}-x_{1})^2 + ...
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What do we know about non linear coordinate systems?

I first learned about coordinate systems by Gelfand and I knew that we basically have two axis x and y with origin O and some unit vectors $\hat i$ and $\hat j$ and if $\vec{OA}=x\hat i+y\hat j$ then ...
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3answers
216 views

What is wrong with this method for a rotated and shifted parabola?

$(x+2y)^2=4(x-y)$ Disecting the above parabola is the question. (vertex, axis,tangent at vertex,etc). So at first what I thought of was making its equations at LHS and RHS perpendicular. I thought ...
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A method of calculation coordinates in order to implement it to a code language!

lets say that we have three points A(xa,ya,za), B(xb,yb,zv), C(xc,yc,zc) with known coordinates in 3d space. Is there a method to calculate the coordinates (x,y,z) of another point D for which the ...
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Given U,V<->X,Y trnslation formula explanation

Well in a text book (about numerical analysis methods to do a polynomial interpolation in bivariate functions). The following piece of text/functions is just given, without much explanation. The goal ...
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3answers
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How to find location of a point for a rectangle

I have a circle with a line that is drawn through it at two points. I have the coordinate for the center of the circle, the two coordinates where it intersects the circle and the radius as well. I ...
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1answer
24 views

Equation of a plane through intersection of two and parallel to other

I have got two planes $$x+y+z=1$$ and $$2x+3y-z+4=0$$ . I am required to find a plane by intersection of two and parallel to $x$ axis . I think the plane parallel to $x$ axis so Simply $P1+kP2=0$ ...
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Best way to plot a 4 dimensional meshgrid

I have $4$ variables $X$, $Y$, $Z$ and $C$, and I want to plot these on a graph. Usually I would just plot the surface $X$, $Y$, $Z$ and then use color to represent the $4$th dimension, as shown ...
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Proving the existence of a ____ number of conditions under a rotation of coordinates.

I'm reading a section on Rotation of Coordinate Systems and this is throwing me off: 'In n-dimensional space, the rotation matrix will have $n^2$ elements, upon which orthogonality relations place ...
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1answer
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Coordinates of sector of circle

I know the coordinates of one point on a circle, this point is part of a sector. I know the angle of the sector at the centre of radius, I know the radius and I know the arc length. How do I calculate ...
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1answer
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Get yaw to point at X and Y values (2D)

I have $X$ and $Y$ coordinates. I also have another object. I need to figure out how set the yaw of the second object to point at the $X$ and $Y$ coordinates. How can I go about doing this?
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Let PQR be a right angled isosceles triangle right angled at P (2,1). If equation of line QR is $2x+y=3$, equations of PQ&PR

Let PQR be a right angled isosceles triangle right angled at P (2,1). If equation of line QR is $2x+y=3$, find combined equation of pair of lines PQ and PR.
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solving 3-d coordinates from x, y and z distance

I working with WiFi positioning and i want to know the exact coordinate where I am. Here is the problem..
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How to get coordinates of some area

I have a rectangle and I divide it into 8 triangle with same size. Top left corner is origin. I want to check that if a point is inside the black area or not. Lets say point's x coordinate is pointX ...
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2answers
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What is (fundamentally) a coordinate system ?

Consider the following construction of vectors and points. Let's start with a vector space, or more specifically a coordinate space $F^N$ over a field $F$ and of $N$ dimensions. The elements of this ...