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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1answer
9 views

Calculate X Y Z from two specific degrees on a sphere

I am a programmer, don't know much about advanced math. I would need the exact formula(s) that could achieve this, so I can translate it to my programming language. I am having a headache trying to ...
0
votes
0answers
23 views

How to check if a set of coordinates creates a polygon?

Well, hello. I've got a set of coordinates and i want to check if it creates one polygon or 2 (or more) polygons. Coordinates are being read from input stream, one after another, for example: ...
0
votes
2answers
15 views

Finding the co-ordinate vector

I can find the co-ordinate vectors for all $x$ in $R^n$ but I can't wrap my head around the ones for $x$ in $P_n$. Here is a question: Let $V$ be the space $P_3$ of all polynomials of degree at ...
0
votes
1answer
17 views

Coordinates of a vector under a basis in a Hilbert space?

Given an arbitrary basis $\{m_1, \dots, m_n \}$of a Hilbert space $H$ (or just think it as $\mathbb R^n$, and I think the methods should be the same) with given inner product, how can we find the ...
0
votes
1answer
25 views

How to find the equation of lines passing through the origin and perpendicular to the lines $xy-3y^2+y-2x+10=0$

Problem : How to find the equation of lines passing through the origin and perpendicular to the lines $xy-3y^2+y-2x+10=0$ My working on this : Two lines are perpendicular if the sum of ...
0
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2answers
28 views

Find the co-ordinates of the point of intersection

I have the function $$y=2x^2-3x$$ How do I find the co-ordinates of the point of intersection of the lines tangent to the curve at $y=-1$? One point where $y = -1$ is when $x = \dfrac 12$. I took ...
0
votes
1answer
24 views

Orthogonal parameterization

Consider the function $$f(a,b,c,d):=\frac{\left(a^*\right)^2b^2-\left(b^*\right)^2a^2+\left(c^*\right)^2d^2-\left(d^*\right)^2c^2}{a^*a+c^*c}$$ With complex parameters $a,b,c$ and $d$ Now find any ...
0
votes
1answer
17 views

Deal with non standard form of conic

I want to know how can I calculate latus rectum, tangent at vertex, vertex and axes of a parabola whose equation is not standard. For example, the parabola: $$ 4x^2 - 4xy + y^2 - 10 y - 19 = 0 $$
2
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0answers
24 views

Calculate the distance between any points in two different circles

I have two overlapping circles (C1 and C2) for which the distance between their centers is know. Inside each circle theres's random number of points (P11... P1n and P21... P2n) for which the distance ...
0
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0answers
12 views

Cordinate geometry problem

The base of a triangle passes through fixed point $(1,1)$ and its sides are bisected at right angle by the lines $y^2 - 8xy - 9x^2 =0$. If the locus of its vertex is a circle of radius ${(k/2)}^{1/2} ...
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0answers
12 views

coordinate geometry passage problems [closed]

Passage $1)$ Let $A( 0, B)$ , $B ( -2 , 0)$ and $C (1 ,1)$ be vertices of a triangle then $Q1)$ Angle $A$ of triangle $ABC$ will be obtuse if $B$ lies in that is the range of $B$ is $a)$ $( -1, ...
3
votes
3answers
145 views

Drawing a Right Triangle With Legs Not Parallel to x/y Axes?

I have been presented with an interesting problem. How can I decide whether a right triangle with given side lengths can be placed (with integer coordinate vertices) on a Cartesian plane so that the ...
0
votes
2answers
21 views

Divergence of vector in spherical coordinates

How should I calculate the divergence for $$\vec{V}=\frac {\vec{r}}{r^2}$$ Is it possible to convert it from spherical coordinates to cartesian?
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votes
0answers
12 views

Why is the Laplace/Helmholtz equation only separable in a finite number of coordinate systems?

On MathWorld one finds that the Helmholtz equation $$(\nabla^2+k^2)\psi=0$$ is only separable in 11 coordinate systems. Similar statements can be found about the Laplace equation and maybe other ...
0
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0answers
23 views

In need of formula: Gravity at Specific Coordinates [closed]

Doing Research on the gravitational pull at a specific set of coordinates. Does anyone know how to solve this mathematically? Please Help. Thanks
1
vote
1answer
4 views

finding the coordinates of a point third of the way along a line segment

if you have a line segment and you know the coordinates of the two endpoints how do you find the coordinates of the point a third of the way along the line? In general how do find the coordinates ...
2
votes
1answer
25 views

Consider the family of lines $a(3x+4y+6)+b(x+y+2)=0$ Find the equation…

Question : Consider the family of lines $a(3x+4y+6)+b(x+y+2)=0$ Find the equation of the line of family situated at the greatest distance from the point P (2,3) Solution : The given equation can ...
0
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0answers
18 views

coordinate geometry high level problems

If the lines $aX^2 + 2hXY + bY^2 =0$ form two sides of a parallelogram and the line $lX + mY =1$ is one diagonal, prove that the equation of other diagonal is $Y(bl – lm) = X(am – hl)$
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0answers
20 views

coordinate geometry proving problems [closed]

If XcosA +YsinA = p where p = – sin^2A/cos^2A be a straight line prove that prependiculars on these straight lines from the points ( m^2 , 2m ) , (Mm , M+m ) , ( M^2 ,2M ) form a geometric progression ...
-3
votes
0answers
35 views

About coordinate geometry [closed]

The sides of triangle are $U_r = x\cos A_r + y\sin A_r – P_r$, where $P_r$ is the offset which can be set to zero. $r = 1,2,3$. Show that orthocentre is given by $U_1 \cos(A_2 – A_3) = U_2\cos(A_3 – ...
0
votes
1answer
45 views

What happens when this turns to $dx$?

I have this equation: $$ ds^2=c^2dt^2-dx^2-dy^2-dz^2. $$ And I've also been given $$ x=x'\cos(\Omega t)-y'\sin(\Omega t), $$ which I need to substitute into the first equation. I've squared $x$ to get ...
0
votes
0answers
15 views

Direct computation of hyperboloid-line intersection in 3d

I was wondering if a solution to this problem that doesn't involve coordinate space transformations. I have two points in 3d space, and am interested in locations where the difference of the ...
3
votes
0answers
53 views

Computing volume element in spherical coordinates

Suppose $y = (r, \theta^1, \theta^2)$ are spherical coordinates in $(\mathbb{R}^3,g)$. What is the $d\text{vol}$ in these coordinates? I solved it but I don't know if it's right. My solution: We ...
1
vote
2answers
47 views

Prove that $\mathbb{R}^\infty$ is an infinite-dimensional vector space

I am busy studying for a Linear Algebra test and came across this question in Section 4.4 of Elementary Linear Algebra (Application Version) $11^{th}$ edition. This is not part of my work that needs ...
0
votes
1answer
22 views

Calculate the gradient of the curve

Calculate the gradient of the curve y=(x+1)^3 (x-1) at the points where it crosses the x-axis
19
votes
1answer
380 views

Infinite staircase to a circle

Suppose you start at $(0,0)$ on the unit disc and repeat the following procedure again and again: Face east and walk half-way to the circumference. Face north and walk half-way to the circumference. ...
0
votes
1answer
37 views

Convert coordinates to a different coordinate axis

Sorry for any forum rules I have broken, I needed a quick answer. I want to create a plane including 3 nonlinear points on a 3d coordinate system, one being the origin. I also need to create a ...
0
votes
3answers
54 views

Find 3rd and 4th co-ordinates for a square given co-ordinates of two points?

To construct a square we need 4 points . In my problem 2 points are given we can find 3rd and 4th point . e.g. A (1,2) B(3,5) what should be the co-ordinate of 3rd (C) and 4th (D) points . Please ...
0
votes
1answer
16 views

Using an offset data point with x, y coords to find the true centre of a circle

I have a data point at (0, 0) where measurements of a tank's shell are taken from. I have used this data point to plot the circle in a graph. However, this data point is not the true centre of the ...
2
votes
1answer
33 views

Is there an efficient way to prove orthogonality of a coordinate system?

Suppose we define a new orthogonal coordinate system, such as spherical coordinates defined by $$x = r \sin \theta \cos \phi, y = r \sin \theta \sin \phi, z = r \cos \theta.$$ Is there an efficient ...
-1
votes
1answer
17 views

$12x^2 +7xy -py^2-18x+qy+6=0$ represents a pair of $\perp$ straight lines. Find $p$ and $q$. [closed]

I'm sorry I can't show you what I've tried because I don't know how to start. For those who start from behind: p=12,q=1. Any help would be appreciated. :) thanks.
2
votes
2answers
56 views

Find the equation of the locus of a point which has its sum of distance from (0,3) and (0,-3) equal to 8.

I know the answer but due to various expressions under root, I'm unable to reach there. Is there something which I'm missing to make the solution easier? By the way the answer given is ...
0
votes
2answers
63 views

What is this kind of geometry called?

I want to get Cartesian coordinates of the points of a curve (e.g. a bezier curve) based on the distance (e.g length of the arc) from the start point on the curve. To make this more clear, suppose I ...
-1
votes
0answers
109 views

Minimum number of points that should be added to obtain a square?

Given a set of N points. How to find the minimum number of points that should be added to the given set in order to obtain at least one square whose vertices belong to the points in the given set ? ...
2
votes
2answers
208 views

How to rotate a vector by 90 degree?

Suppose I am given a vector in 2-D as $AB = {(x_1,y_1) ,(x_2,y_2)}$. Now , what will be the co-ordinates if I rotate the vector about the point $(x_1,y_1)$ both clockwise and counter-clockwise ?here ...
0
votes
1answer
20 views

Find the co-ordinates of the point on the curve

Calculate the points on the curve $y=(1-x)^4$ at gradient = -4 I solve little bit $\frac{dy}{dx} = 4(1-x)^{4-1}\cdot \frac{d}{dx} (1-x)\\ = 4(1-x)^3 \cdot (-1 )$ the gradient is =-4 so I put ...
0
votes
2answers
43 views

double integral over an arbitrary triangle

Assume we have an arbitrary triangle ABC in x-y plane and we want to integrate a function $f(x,y)$ over surface of this triangle as shown in fig. 1: We can define another coordination system [x' ...
0
votes
1answer
8 views

When to use transformation of variable and when transformation of differentials

I was reading the book: Mathematical Methods in the Physical Sciences by M. Boas and I came across this statement; I wasn't quite sure why this was the case. Is it because in the curvilinear ...
0
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0answers
10 views

Orientation of a given coordinate system - Calculation of angles

Hi dear math community, How do you calculate the orientation angles of a given reference frame? To be more precise, by rotating which angle values about base's X,Y,Z do you get this reference frame? ...
0
votes
1answer
14 views

How to determine whether point is on the left of right side of the line

I have a line, for example $y=-\frac{1}{9}(x+6)-3.5$. And I also have a point, for example $A(-5, 2)$. How to determine whether this point is on the line, on the right or on th left side? Just put A ...
1
vote
1answer
64 views

Reaching a point B in Cartesian coordinate via Euler angles knows its initial point A Euler angles and Cartesian coordinates

I have a point A:- Known it's Cartesian coordinates (X,Y,Z) and its Euler angle Aka body rotation (R,P,Y) respectively Roll (rotation around X axis) , Pitch (rotaion around Y axis) and Yaw (rotation ...
1
vote
1answer
17 views

Find a change of coordinates matrix

Find the change of coordinates matrix that changes coordinates in the basis $1$, $1+t$ in $P_1$ to the coordinates in $1-t$, $2t$.
1
vote
4answers
80 views

locating any point on a real number line

So my question is really simple (and may be a bit naive): The claim is, I can locate any point in a 2D-plane by recursively applying the following method (possibly infinite number of times): For ...
-1
votes
2answers
24 views

Prove radius chord theorem without using congruent traingles

Suppose that $P(a,b)$ and $Q(c,d)$ are two points on the unit circle $x^2 + y^2 = 1$, and let $M$ be the midpoint of chord $PQ$. (Without using congruent triangles), prove that $OM$ is perpendicular ...
0
votes
0answers
16 views

How to visualize a vector from its components (in spherical coordinates)

Let $$\mathbf{v} = A (1 + \cos \theta) \cos \phi \mathbf{\hat{u}}_{\theta} + A (1 + \cos \theta) \sin \phi \mathbf{\hat{u}}_{\phi}$$ be a vector; $\mathbf{\hat{u}}_{\theta}$ and ...
1
vote
0answers
15 views

Insert Coordinate into best place within list of coordinates in a route

I have a list of coordinates: ...
2
votes
3answers
171 views

Explanation of formula for distance between triangles in a triangular grid

Lets say you have a triangle similar to the one below, with each triangle numbered $(N, i) $ where $N$ is the row number and $i$ is the position within the row. From any triangle, you are allowed ...
0
votes
1answer
21 views

Show P, Q and R are non collinear

If P $\equiv$ $(-sin(\beta - \alpha), -cos\beta)$, Q $\equiv$ $(cos(\beta - \alpha), sin\beta)$ and R $\equiv$ $(cos(\beta - \alpha + \theta), sin(\beta - \theta))$, where $$0 \lt \alpha, \beta, ...
0
votes
0answers
22 views

Move a distance $d$ from $x_i, y_i, z_i$ using yaw, pitch, roll angles as 'headings'

I'm trying to write some code for 3D turtle graphics for a Lindenmayer System, which is similar to how a plane moves. I have a current position in Cartesian coordinates. I know a set of current ...
2
votes
3answers
65 views

How to determine if a triangle can be drawn with the given points.

Given $3$ points $$(x_1, y_1), (x_2, y_2), (x_3, y_3),$$ how does one determine whether they are vertices of a triangle? Thanks.