Coordinates Definition and 1000 Threads

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

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  1. N

    Set of vectors whose coordinates are integer (is a subspace?)

    Homework Statement For a set of vectors in R3, is the set of vectors all of whose coordinates are integers a subspace?The Attempt at a Solution I do not exactly understand if I should be looking for a violation or a universal proof. If x,y, z \in Z then x,y,z can be writted as...
  2. M

    How Do You Calculate θ_dot in Polar Coordinates?

    Homework Statement A particle moves with const speed v along the curve r(θ) = a(1+cos θ). Starting with the general expression for the velocity vector v in polar coordinates solve for θ_dot in terms of v, k, and θ. What does the sign of θ_dot signify?Homework Equations v = r_dot*r_hat +...
  3. O

    MHB Solving Polar Coordinates in System of Equations

    given that x'=f(x,y) y'=g(x,y) iff the vector function (r, θ) is a sloution of the system r'=f(rcosθ,rsinθ)cosθ +g(rcosθ,rsinθ)sinθ am trying to show that this is true but i just don't get where the sinθ and cosθ come from, how do i get to that
  4. B

    MHB Triple Integrals in Spherical Coordinates

    Hi all, I'm not sure how to get the boundaries in terms of both the spherical and cylindrical coordinates for this question. Here are the boundaries we were given in the solution. How was \frac{\pi}{4} for φ and \frac{1}{\sqrt{2}} for r obtained? Thanks!
  5. PsychonautQQ

    Question about cylindrical Coordinates

    I'm confused why when using cylindrical coordinates three unit vectors are needed. My book says that the three unit vectors are one for the radial direction which is bound to the xy plane and then a unit vector in the z direction. It goes on to say that there is another unit vector associated...
  6. J

    MHB How do I Find the Vector Coordinates to Solve for Trihedral Angle?

    Hi everyone, Here's the problem I have. Given two unit vectors A, B and angle φ between them. Find the coordinates (in 3D) of a unit vector C so that the angles between C and A,B be α and β respectively. α + β => φ and α + β + φ <= 360° It looks trivial to me and yet here I am asking for...
  7. N

    Taking partial derivative in polar coordinates

    In a problem that requires converting from cartesian to polar coordinates, I need to take \frac{dr}{dx}. I tried doing it two different ways but getting two completely different answers.. Method 1: r=\sqrt{x^2+y^2} \frac{dr}{dx}=\frac{1}{2}\frac{1}{\sqrt{x^2+y^2}}2x \;\; =...
  8. T

    Double Integrals using Polar Coordinates

    Homework Statement ∫∫Rarctan(y/x) dA, where R={(x,y) | 1\leqx2+y2\leq4, 0\leqy\leqx Homework Equations x=rcos(θ) y=rsin(θ) x2+y2=r2 The Attempt at a Solution I know that the range of r is 1 to 2 but I can't figure out how to change the second part into θ. If I change y and x to...
  9. H

    Finding Potential (Spherical coordinates )

    1. . An electric dipole located at the origin in free space has a moment p = 3ax −2ay +az nC·m. Find V at r = 2.5, θ =30◦, φ =40◦. I find it difficult to solve when its in spherical co-ordinates.2.Relevent Eq V =P.(r-r')/( 4∏ε|r−r'|2)(|r-r'|)I am confused how to find a unit vector on spherical...
  10. M

    Divergence of curl in spherical coordinates

    Hey pf! I was thinking about how div(curl(f)) = 0 for any vector field f. However, is this true for div and curl in spherical coordinates? It doesn't seem to be. If not, what needs to happen for this to be true in spherical coordinates?? Thanks all!
  11. J

    Write a triple integral in spherical coordinates

    Homework Statement Write a triple integral in spherical coordinates that represents the volume of the part of the sphere X^2+Y^2+Z^2=16 that lies in the first octant(where x,y, and z are coordinates are all greater than or equal to zero) Homework Equations So i know this is in...
  12. B

    Why Does the Radius in Parabolic Coordinates Involve √(εη)?

    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 = \phi why is it obvious, looking at the pictures (Is my picture right or is it...
  13. J

    Position vector in curvilinear coordinates

    The position vector ##\vec{r}## in cartesian coordinates is: ##\vec{r} = x \hat{x} + y \hat{y}##, in polar coordinates is: ##\vec{r} = r \hat{r}##. But, given a curve s in somewhere of plane, with tangent unit vector ##\hat{t}## and normal unit vector ##\hat{n}## along of s, exist a definition...
  14. P

    MATLAB [Matlab] Replace pixels of an image with theta of Polar Coordinates

    Dear Math and Physics fans You have always been so helpful in the past and I was hoping that I could call on your expertise once again. I want to make a wedge filter in MATLAB so I can determine the orientation of the ellipse of a centered 2D fft. I tried to make an new image where...
  15. C

    Integration and Laplacian in polar coordinates

    Homework Statement I have a function y that is axisymmetric, so that y=y(r). I want to solve for r such that ∇2y(r) = Z. Can anyone tell me if I'm following the right procedure? I'm not sure since there are two "∂/∂r"s present... Homework Equations ∇2 = (1/r)(∂/∂r)(r*(∂/∂r)) +...
  16. A

    Is the motion of a pendulum restricted by a cycloid surface cyclical?

    the coordinates of cycloide are ##x= a (\theta- sin \theta)## ##y= a(cos \theta -1)## If i use ##\theta =\omega t## this is a example of cycloid but, if i use ##\theta=\cos (\omega t)##, ¿this is a cycloid? My teacher says that in a cycloid pendulum ##\theta## must be oscillatory...
  17. bsmithysmith

    MHB Finding Coordinates on a circle with time/speed

    Marla is running clockwise around a circular track. She runs at a constant speed of 3 meters per second. She takes 46 seconds to complete one lap of the track. From her starting point, it takes her 12 seconds to reach the northernmost point of the track. Impose a coordinate system with the...
  18. U

    Spherical coordinates choice for an electric field problem

    I am finding the electric field from a spherical shell at a point on the z-axis outside the shell. The shell is centered at the origin,and I am only allowed to use coulomb's law. I want to find dE in spherical coordinates first then transform it to Cartesian before integrating to get E. So I...
  19. P

    Canon shooting area in polar coordinates

    Homework Statement hi,guys. The directions of shooting e=cos\alphacos\varphii+cos\alphasin\varphij+sin\alphak 0<\varphi<=2π;\varphi -horizontally \alpha[0,π];\alpha is vertically initial speed=v0 I need to calculate the surface equation of canon shots (where it hits). In other words equations...
  20. T

    Finding the volume using spherical coordinates

    Homework Statement Let V be the volume of the solid enclosed by the sphere x^2 + y^2 + z^2 - 2z = 0 , and the hemisphere x^2 + y^2 + z^2 = 9 , z ≥ 0. Find VHomework Equations Using spherical coordinates: x^2 + y^2 + z^2 = ρ^2 z = ρcos(ø) The Attempt at a Solution So I changed both of them to...
  21. A

    Polar Coordinates - Graphing the points of when theta<0

    Polar Coordinates --- Graphing the points of when theta<0 Hi everyone, I'm working with an online graphing program desmos.com. It's great, and actually tons of fun. I'm currently working with polar coordinates but the only flaw of this grapher is that when working with polar coordinates...
  22. S

    Transforming a vector in spherical coordinates

    I've got a Green's function in which all the impulses are on the line from the north pole to the origin (polar angle θ=0) and terminating with a point impulse at the north pole. I've found its gradient at a field point, and I want to rotate everything to a new coordinate system with the source...
  23. J

    Triple Integral Problem in Cylindrical Coordinates

    Homework Statement Use cylindrical coordinates to find the volume of the solid that the cylinder r = 3cos/theta cuts out of the sphere of radius 3 centered at the origin. Homework Equations Why do we evaluate theta from 0 to pi instead of from 0 to 2pi? Don't we want to go all the...
  24. N

    Limits if polar coordinates (conceptual explanation)

    1. Homework Statement [/b] Suppose the lim(x,y) →(0,0) (xy)/SQRT[x^2 + y^2] if it exists find the limit. The Attempt at a Solution x = rcosΘ y = r sinΘ r = SQRT[x^2 + y^2] ∴ lim[SUB]r → 0 (r2cosΘrsinΘ)/ r = rcosΘsinΘ \leq r and so -r \leq(xy)/SQRT[x^2 + y^2] \leq r ... ... I can...
  25. U

    Spherical coordinates length from differential length

    is it logical to ask this question in Spherical coordinates: Using the differential length dl , find the length where r=1 0<Θ<∏/4 ∏/2< θ <∏/4 where Θ is the azimuthal angle. What I mean by ∏/2< θ <∏/4 is that the line is a "diagonal" line which has an ascention of ∏/4 from the xy...
  26. N

    Need help in understanding W paremeter for homogeneous coordinates

    First I would like to apologize first if this is the wrong place for posting this problem. I don't really understand what is the importance of w in the homogeneous coordinate (x,y,z, w). One of the example i have read is about a parrallel line extended to infinity, and both line would...
  27. S

    MHB Give all the polar coordinates corresponding the rectangular point

    Give all the polar coordinates corresponding the rectangular point (-1, \sqrt{3}) Am i setting this up right? so would I use (r, \theta) so x = rcos(\theta) y = rsin(\theta) r^2 = x^2 + y^2 so: (-1)^2 = (-1*\frac{2\pi}{3})^2 + (-1*\frac{11\pi}{6}) ?
  28. L

    MHB Finding the curve coordinates of the point nearest to P in the curve

    Find the curve coordinates of the point nearest to P in the curve 5x2 -6xy +5y2 = 4 P = (0,0) oK x2 + y2 =D2 But how can i solve for x or y ? Maybe by expliciting derivative
  29. S

    MHB Sketching graphs in polar coordinates

    I don't understand why I am screwing this up so bad. Sketch the graph of the equation r = 2 + 4cos(\theta) in polar coordinates. So I did: 0 = 2 + 4cos(\theta) = -\frac{1}{2} = cos(\theta) Then got cos(\theta) is -\frac{1}{2} @ \frac{2\pi}{3} and @ \frac{4\pi}{3} Then i plotted points to...
  30. JasonHathaway

    Unit vectors in different coordinates

    Hi everyone, I've some points I want to make sure of. 1- When converting a "POINT" from a coordinate system to another, I'll just use the derived equation to convert (e.g. (1,2,3) from cartestian to cylindrical: \rho=\sqrt{x^{2}+y^{2}}, \phi=tan^{-1}\frac{y}{x}, z=z 2- When converting an...
  31. J

    Spherical Coordinates: Distance Between 2 Points

    Hello, I am looking into finding geodesic distances for an ellipsoid. I will designate two points then find the distance between them. This will be my geodesic distance. I have put together a schematic (attached) for reference. Ultimately I need to know the distance D as shown on the...
  32. C

    What Are Rosen Coordinates in Gravitational Wave Analysis?

    I see a number of gravitational wave analytic solutions with the metric given in terms of Rosen coordinates. I have no idea what these coordinates are. How do I perform a coordinate transformation from Rosen coordinates to traditional (t,x,y,z) Euclidean\Cartesian coordinates? Also, is there a...
  33. S

    MHB How Do You Plot and Find Alternate Polar Coordinates?

    Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r < 0 so I did \frac{\pi}{3} + 2\pi = \frac{7\pi}{3} \therefore r > 0 and did \frac{\pi}{3} + \pi = - \frac{4}{3} \pi \therefore r < 0 so i have (2,7pi/3)...
  34. M

    Speed in radial coordinates and angular coordinates

    Homework Statement First off, I am not a physics student. I am a math major taking a maple software course and there is a question that I can not figure out. The question gives me a radial coordinates r r:= \frac{a*t^{2}*e^{-b*t}}{1+t^{2}} And angular coordinates: θ:=b+c*t^{2/3} Where...
  35. H

    Charge density of a disk with radius a in cylindrical coordinates

    To write the uniform charge density of a disk with radius a in cylindrical coordinates, If we do this form: \rho (x)=\frac{A\delta(z)\Theta (a-\rho)}{\rho} (A is constant that sholud be determined and \theta is step function), we get A=\frac{Q}{2\pi a} and so: \rho (x)=\frac{\frac{Q}{2\pi...
  36. P

    Solving Circle Equation with 2 Intersecting Vectors

    Thank you for taking time to read my post, I hope I am putting into the correct area of the physics forum. I am working with a programmer to complete a project that involves 2 intersecting vectors and a circle. The vector coordinates are known, we are trying to solve the circle equation...
  37. J

    Connection between cesaro equation and polar coordinates

    First, I'd like that you read this littler article (http://mathworld.wolfram.com/NaturalEquation.html). The solution given by Euler that coonects the system cartesian (x, y) with the curvature κ of the "cesaro system" (s, κ), is that the derivative of the cartesian tangential angle φ* wrt arc...
  38. J

    Which is orientation of tangential angle in polar coordinates?

    In the wiki, there is an explanation for what is the tangential angle in cartesian and polar coordinates. However, the orientation these angles aren't specified. In cartesian coordinates, I believe that the tangential angle φ is measured from the x-axis, in polar coordinates the tangential angle...
  39. J

    Conversions between intrinsic/extrinsic coordinates

    I noticed that in wiki there is the follows conversion: that is the conversion beetwen the cartesian coordinates and the intrinsic (arc length, curvature) "coordinate". In this case, the system is 2D. There is the 3D case too: However, is missing the (x, y, z)...
  40. A

    Intersection coordinates in lattice

    On the drawing below is a hexagonal lattice. For the basis vectors one can choose either the set of arrows in black or the set in yellow. The intersection coordinates of the plane in green seems to be the same regardless of choosing the black or the yellow basis. Why is that? My teacher said it...
  41. S

    Wave function simplification in relativistic coordinates?

    My textbook says ψ(x,t)=exp(i(p_{0}x^{0} + p^{→}\cdotx^{→})/h)=exp(i*p\cdotx/h) (note that by h I mean 'h-bar'...couldn't find the symbol). I don't recognize (like my text implies I should) how the first equation equals the second. Where did the p_{0}x^{0} go? Sorry for my stupidity here. Any...
  42. dwn

    Polar Coordinates Homework: Integral w/ Image & Equations

    Homework Statement Image attached Homework Equations r2=x2+y2 The Attempt at a Solution ∫∫ re-r^2 drdΘ I'm not sure how to establish the boundaries. This is an online class so if you can offer any additional tips for evaluating types of integrals of this sort, that would be...
  43. M

    Vector calculus: angular momentum operator in spherical coordinates

    Note: physics conventions, \theta is measured from z-axis We have a vector operator \vec{L} = -i \vec{r} \times \vec{\nabla} = -i\left(\hat{\phi} \frac{\partial}{\partial \theta} - \hat{\theta} \frac{1}{\sin\theta} \frac{\partial}{\partial \phi} \right) And apparently \vec{L}\cdot\vec{L}=...
  44. JasonHathaway

    Unit vector in cylindrical coordinates

    Hi everyone, I've two vectors in cylindrical coordinate - (-1,\frac{3\pi}{2},0),(2,\pi,1) - and I want to find the perpendicular unit vector of these two vector. Basically I'll use the cross product, then I'll find the unit vector by \hat{u}=\frac{\vec{u}}{||\vec{u}||}. But do you I...
  45. C

    Is the metric tensor constant in polar coordinates?

    I've been watching the Stanford lectures on GR by Leonard Susskind and according to him the metric tensor is not constant in polar coordinates. To me this seems wrong as I thought the metric tensor would be given by: g^{\mu \nu} = \begin{pmatrix} 1 & 0\\ 0 & 0\\ \end{pmatrix} Since...
  46. G

    Coordinates in general relativity

    Hello fellow PF go-ers I am having trouble with coordinates in curved space time lately, allow me to demonstrate my issue. Take the metric of flat space in spherical coordinates for example, a diagonal metric with values 1,r^2 and r^2sinΘ. It appears to me that only when we know that the Θ and...
  47. H

    Surface integral, spherical coordinates, earth

    Homework Statement Find the surface area of the Earth (as a fraction of the total surface of the earth) that lies above 50 degrees latitude North. Homework Equations $$A = \int_R\sqrt{|\det(g)|}d\theta d\phi$$ The Attempt at a Solution Hence I get $$\int_0^{360}...
  48. T

    Are 3D coordinate angles restricted to certain values?

    Homework Statement In 3d coordinate space any two of the coordinate angles must A. Sum to less than one B. Be greater than ninety but less than one eighty. C. Each be greater than forty five degrees D. Sum to greater than 90 ( if they are both less than 90) E. Have cosines less than...
  49. D

    Fourth point given three coordinates

    1.Hi, Need to find fourth point S coordinate, given the below: 1. coordinates of P,Q,R, 2. torsion angle between PQR and QRS, 3. the bond length RS and 4. bond angle QRS. Can anybody give me the way out? 2. Equaltions for Torsion angles b1=PQ b2=QR b3=RS where PQ,QR and RS are all...
  50. K

    Finding base circle with coordinates of two points of involute curve

    Hi, I have an involute gear and measured co-ordinates of two arbitrarily chosen points (on the involute portion) of a tooth. Can I find out the base circle with this information? Thanks.
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