What is Coordinates: Definition and 1000 Discussions

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. F

    Mathematica Plotting functions and coordinates, Mathematica

    Hi all. Is there a way to plot both functions and coordinates/points on the same graph in Mathematica? The various functions for plotting each seem very incompatible. I would like to compare a probability function to Monte-Carlo-method simulation results. Also, out of curiosity, do...
  2. A

    Rotation of Gridded Spherical Coordinates to the Same Grid

    I have a uniform grid of data in spherical coordinates. e.g. theta = 0, 1, 2, ... 180 and phi = 0, 1, 2, ... 359 which forms a 2D matrix. I wish to rotate these points around a cartesian axis (x, y, z-axis) by some angle alpha. To accomplish this I currently do the following: 1. Convert to...
  3. M

    Find center of mass and coordinates using double integrals?

    Homework Statement Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is bounded by the parabolas y = x^2 and x = y^2; ρ(x, y) = 23√x Homework Equations m = \int\int_{D} ρ(x, y) dA x-bar = \int\int_{D} x*ρ(x, y) dA y-bar =...
  4. lonewolf219

    Find La Placian of a function in cartesian and Spherical Coordinates

    Homework Statement Prove the La Placian of V(x,y,z)=(zx^{2})/(x^{2}+y^{2}+z^{2}) in Cartesian coordinates is equal to that in Spherical coordinatesHomework Equations \nabla^{2}V=0 The Attempt at a Solution I have attempted to calculate all the terms out, and there were A LOT. I was hoping...
  5. I

    MHB Proving Function Polynomial in Coordinates is Differentiable Everywhere

    The question is: Using the chain rule to prove that a function $f:\mathbb{R}^n\rightarrow \mathbb{R}$ which is polynomial in the coordinates is differentiable everywhere. (The chain rule is for the use under function composition circumstances, how to apply it here to prove that the function $f$...
  6. L

    Triple integral in cylindrical coordinates

    Homework Statement Find the volume of the solid that lies between z=x2+y2 and x2+y2+z2=2 Homework Equations z=r2 z=√(2-r2) The Attempt at a Solution So changing this into cylindrical coordinates, I get z goes from r2 to √(2-r2) r goes from 0 to √2 theta goes from 0...
  7. E

    What will be the change in celestial coordinates in 50 years?

    Is it possible to use celestial coordinates which were taken 50 years ago? What kind of inaccuracy can we expect (give the answer in degrees)? Could I say that it will be about 0.3° error assuming that around the year 130 BC, Hipparchus compared ancient observations to his own and concluded that...
  8. G

    Marginal Density of Coordinates Inside an Ellipse

    Homework Statement A point is chosen randomly in the interior of an ellipse: (x/a)^2 + (y/b)^2 = 1 Find the marginal densities of the X and Y coordinates of the points. Homework Equations NA The Attempt at a Solution So this ought to be uniformly distributed, thus the density function...
  9. F

    Geodesic of Sphere in Spherical Polar Coordinates (Taylor's Classical Mechanics)

    Homework Statement "The shortest path between two point on a curved surface, such as the surface of a sphere is called a geodesic. To find a geodesic, one has to first set up an integral that gives the length of a path on the surface in question. This will always be similar to the integral...
  10. M

    MATLAB Solving Heat Equation in Cylindrical Coordinates with MATLAB's pdepe

    hello i am solving heat equation in cylindrical coordinator. i am using MATLAB "pdepe" solver to solve the partial differential equation. can anyone suggest me how to choose the initial condition?
  11. Astrum

    Off center circular motion (polar coordinates)

    Homework Statement A particle moves with constant speed v around a circle of radius b. Find the velocity vector in polar coordinates using an origin lying on the circle. https://www.desmos.com/calculator/maj7t9ple1 Imagine the r starts at (0,0). Homework Equations \frac{d\vec{r}}{dt} =...
  12. N

    Write Vector Expression in n-t and x-y coordinates of Acceleration

    Homework Statement Write the vector expression for the acceleration a of the mass center G of the simple pendulum in both n-t and x-y coordinates for the instant when θ = 66° if θ'= 2.22 rad/sec and θ"= 4.475 rad/sec2 I have attached an image of the question. Homework Equations an =...
  13. M

    Volume of a cone using spherical coordinates with integration

    Find the volume of a cone with radius R and height H using spherical coordinates. so x^2 + y^2 = z^2 x = p cos theta sin phi y= p sin theta sin phi z= p cos phi I found theta to be between 0 and 2 pie and phi to be between 0 and pie / 4. i don't know how to find p though. how...
  14. dexterdev

    Derivation of Del Operator in Spherical & Cylindrical Coordinates

    Hi all, Del = i ∂/∂x + j ∂/∂y + k ∂/∂z in x y z cordinate similarly I require to see the derivation of del in other coordinates too. Please give me a link for the derivation.
  15. E

    Heat Equation in cylindrical coordinates

    Large, cylindrical bales of hay used to feed livestock in the winter months are D = 2 m in diameter and are stored end-to-end in long rows. Microbial energy generation occurs in the hay and can be excessive if the farmer bales the hay in a too-wet condition. Assuming the thermal conductivity of...
  16. L

    I don't have a clue how to find the coordinates

    Homework Statement http://i277.photobucket.com/albums/kk63/lioricsilver/Untitled_zps7cf41f04.png Homework Equations y2=(16)x is the equation on the question The Attempt at a Solution I have got any clue. I do know how to solve motion in 2d. But since time is not given or the...
  17. E

    Cylindrical / Spherical Coordinates

    I'm trying to convert the below Cartesian coordinate system into cylindrical and spherical coordinate systems. For the cylindrical system, I had r,vector = er,hat + sint(e3,hat). While I do have a technically correct answer for the spherical coordinate system, I believe, I was wondering if there...
  18. O

    Cylindrical coordinates, finding volume of solid

    Homework Statement Find the volume of the solid that the cylinder r = acosθ cuts out of the sphere of radius a centered at the origin.Homework Equations Cylindrical coordinates: x = rcosθ, y = rsinθ, z=z, r2 = x2+y2, tanθ = y/xThe Attempt at a Solution So I know that the equation for the sphere...
  19. L

    Transforming double integrals into Polar coordinates

    Homework Statement Show that: I = \int\int_{T}\frac{1}{(1 + x^{2})(1 + y^{2})}dxdy = \int^{1}_{0}\frac{arctan(x)}{(1 + x^{2})}dx = \frac{\pi^{2}}{32} where T is the triangle with successive vertices (0,0), (1,0), (1,1). *By transforming to polar coordinates (r,θ) show that:* I =...
  20. T

    How to find the acceleration with polar coordinates?

    Homework Statement The quality of the image is bad so here's the statement: For an interval of motion the drum of radius b turns clockwise at a constant rate ω in radians per second and causes the carriage P to move to the right as the unwound length of the connecting cable is...
  21. C

    Electrodynamics: Electrostatic field potencial in Cartesian coordinates

    Homework Statement It's given that absolute permitivity is a coordinate function: ε (x, y, z) = Asin(x)cos(y), where A=const Homework Equations We need to find an electrostatic field potential function \varphi in Cartesian coordinate system. The Attempt at a Solution I tired to solve, but...
  22. V

    Find the coordinates of a point where a line intersects the y-axis.

    Homework Statement The following equation describes a straight line: ⟨x, y, z⟩ = ⟨−1, 0, −2⟩ + t⟨1, 2, 2⟩ Find the coordinates of the point where this line intersects the y-axis. Homework Equations Equation of a Line: r = ro + tv The Attempt at a Solution I'm not really sure...
  23. W

    Double integral in polar coordinates

    Homework Statement I know I have the set up done correctly I am wondering where I went wrong because I know I cannot get zero, and I am a little worried I did my integration wrong. please help. http://i1341.photobucket.com/albums/o745/nebula-314/IMAG0107_zps3cde35a8.jpg
  24. T

    Polar Coordinates functional notation.

    I've always been curious why points in polar coordinates are defined as (r,θ) when all equations (including parametric equations formed from them) are defined as r=f(θ). Considering that point in cartesian coordinates are defined as (x,y) where y=f(x). Also a,b=(r,θ) ∫1/2[f(θ)]2 further...
  25. P

    Using polar coordinates to find the distance traveled

    Homework Statement A tourist takes a tour through a city in stages. Each stage consists of 3 segments of length 100 feet, separated by right turns of 60°. Between the last segment of one stage and the first segment of the next stage, the tourist makes a left turn of 60°. At what distance...
  26. D

    Integration of Polar coordinates

    Homework Statement Find the area in the polar curve r = sin2θ between 0 and \frac{\pi}{2}. The way to do this is to say the area of a tiny bit of this polar curve, dA = \frac{1}{2}r^{2}dθ so the integral is just \frac{1}{2}\int^{\frac{\pi}{2}}_{0}(sin2θ)^{2}dθ if we did say a function...
  27. J

    Graphing Covariant Spherical Coordinates

    I am studying Riemannian Geometry and General Relativity and feel like I don't have enough practice with covariant vectors. I can convert vector components and basis vectors between contravariant and covariant but I can't do anything else with them in the covariant form. I thought converting the...
  28. L

    Finding limits on spherical coordinates

    Homework Statement find the limits on spherical coordinates. where ε is the region between z²=y²+x² and z = 2(x²+y²) no matter what i try i can't seem to find the limits, especially for "ρ", so far i got 0<θ<2Pi and 0<φ<Pi.
  29. U

    What's wrong with my Jacobian of polar coordinates?

    Homework Statement Change of coordinates from rectangular (x,y) to polar (r,θ). Not sure what's wrong with my working.. Homework Equations The Attempt at a Solution
  30. N

    Spherical, Cyndrical or Polar Coordinates

    Spherical, Cylindrical or Polar Coordinates Homework Statement I have attached an image of the problem. I know that the solution is number 1 but I'm having some difficulty understanding why. In solution one is it using cylindrical coordinates> My first response to this question had been to...
  31. B

    How to graph spherical coordinates

    Homework Statement given I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ the bounds of the integrals: left most integral: from 0 to pi middle integral: from 0 to pi/2 right most integral: from 1 to 3 i have no idea how to graph this, i was hoping someone would be able to recommend some techniques.
  32. B

    Converting a triple integral from spherical to cartesian, cylindrical coordinates

    Homework Statement Consider the interated integral I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ -the bounds of the first integral (from left to right) are from 0 to pi -the bounds of the second integral are from 0 to pi/2 -the bounds of the third integral are from 1 to 3 a)express I as an interated...
  33. M

    Angular momentum and coordinates

    let us denote the joint eigenstate of \hat{L^{2}}and \hat{L_{z}} by ll,m> and we know that if we are in spherical coordinates, \hat{L^{2}} and \hat{L_{z}} depend on θ and ∅, so we denote the joint eigenstate by: <θ∅l l,m>.. why?
  34. M

    Cartesian to cylindrical coordinates (integration question)

    There has been a few times when I switch from Cartesian to cylindrical coordinates to integrate I would get the wrong because I used the wrong substitution. For instance I would use x = rcos(θ) and y = rsin(θ) where r and θ are variable when I was suppose to leave r as a constant. Question...
  35. T

    Solving Poisson-Boltzmann equation in Cylindrical and Spherical Coordinates

    Homework Statement I don't have a specific problem in mind, it's more that I forgot how to solve the particular equation from first principles. \nabla^{2} \Phi = k^{2}\Phi Places I've looked so far have just quoted the results but I would like the complete method or the appropriate...
  36. M

    Understanding Spherical Coordinates

    questioning what ρ does. What is the difference between the two equations? Let k be the angle from the positive z-axis and w be the angle from the pos x-axis parametric equation of a sphere with radius a paramet eq. 1: x = asin(k)cos(w) y = asin(k)sin(w) z= acos(k) 0≤w≤2pi 0≤k≤pi...
  37. A

    Generalized coordinates - Rotating pendulum

    My question is kinda simple but it has been causing me some trouble for a while. In the problem of the pendulum rotating about an axis, why isn't the angle of rotation about the axis a generalized coordinate? The doubt appears when i try to write the hamiltonian for the system and i don't know...
  38. M

    Stress Tensor in Spherical Coordinates

    Homework Statement Calculate the deformation of a sphere of radius R and density \rho under the influence of its own gravity. Assume Hooke's law holds for the material. Homework Equations Not applicable; my question is simply one of understanding. The Attempt at a Solution I want...
  39. C

    MHB Circle problem finding coordinates of points

    Continued from; Originally Posted by Jameson http://www.mathhelpboards.com/f2/understanding-how-deal-fractions-using-brackets-2596/#post11674 What is the full problem you are trying to solve? I can't make sense of your post until I know that. I have a circle problem and am trying to find...
  40. zonde

    Limit of Rindler coordinates

    It seems that acceleration at some point in Rindler coordinates completely determines it's distance from rindler horizon, right? If we have two rockets with equal hight and experiencing equal acceleration at the bottom there are no other parameters we can vary to get different results for two...
  41. C

    Double integration when switching to polar coordinates

    Homework Statement Take the double integration of http://webwork.usi.edu/webwork2_files/tmp/equations/08/1294e87299342c0ccfe2f8a97055da1.png when f(x)=sqrt(4x-x^2) Homework Equations x=rcos(theta) y=rsin(theta) The Attempt at a Solution I know I plug in the r*cos(theta) and...
  42. P

    Expressing a complex function as polar coordinates

    Homework Statement Consider the complex function f (z) = (1 + i)^z with z ε ℂ. 1. Express f in polar coordinates. Homework Equations The main derived equations are in the following section, there is no 'special rule' that I (to my knowledge) need to apply here. The Attempt at a...
  43. F

    Evaluate integral by using spherical coordinates

    ∫03∫0sqrt(9-x2)∫sqrt(x2+y2)sqrt(18-x2-y2) (x2+y2+z2)dzdxdy x=\rhosin\varphicosθ y=\rhosin\varphisinθ z=\rhocos\varphi Change the integrand to \rho and integrate wrt d\rhodθd\varphi I don't know how to find the limits of integration. Normally I would draw a picture and reason it out...
  44. W

    Spherical Coordinates Question

    In spherical coordinates we have three axes namely r, θ, ∅ the ranges of these axes are 0≤r≤∞ 0≤θ≤∏ 0≤∅≤2∏ what will happen in a physical situation if we allow θ to change from zero to 2∏
  45. S

    Christoffel Symbols of Vectors and One-Forms in say Polar Coordinates

    Hello all, I've been going through Bernard Schutz's A First Course In General Relativity, On Chapter 5 questions atm. Should the Christoffel Symbols for a coordinate system (say polar) be the same for vectors and one-forms in that coordinate system? I would have thought yes, but If you...
  46. D

    Can tensors be defined without using coordinates in a physics-friendly way?

    My class is starting to cover E&M in Lorentz covariant form, and obviously the subject of tensors came up. The problem is that my prof defines tensors in terms of coordinates, which is ugly and against the spirit of relativity. Is there a way of doing tensors coordinate-free in a physics...
  47. O

    Transformation from cartesian to cylindrical coordinates

    Homework Statement I'm trying to get to grips with Godel's 1949 Paper on Closed Time-like Curves (CTCs). Currently I'm trying to confirm his transformation to cylindrical coordinates using maple but seem to keep getting the wrong answer. Homework Equations The line element in cartesian...
  48. A

    How Does Spacetime Curvature Affect Tangential Light Speed Measurements?

    The coordinate speed of light relative to its speed at infinity is calculated as (1-2M/r)c (at infinity) yes?? SO it makes sense that local measurements made with local rulers and clocks which are contracted and dilated respectively would still be c for radial measurements. But how does that...
  49. M

    Double integral using polar coordinates

    The question is in the paint document I wanted to know why they integrated from 0 to pi and not from 0 to 2pi
  50. L

    Solid hemisphere center of mass in spherical coordinates

    Hello, I am struggling with what was supposed to be the simplest calc problem in spherical coordinates. I am trying to fid the center of mass of a solid hemisphere with a constant density, and I get a weird result. First, I compute the mass, then apply the center of mass formula. I divide...
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