What is Coordinate: Definition and 908 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. S

    Coordinate Transforms: Idiot's Guide & Rules of Thumb

    Does anyone know of an “Idiot’s Guide to Coordinate Transforms…”, or good rules of thumb to employ to determine the “proper” set of coordinates for a particular problem? I’m not really having any trouble with the mathematical machinery like finding the Jacobian, etc.; my problem is actually...
  2. Y

    Different coordinate system to sketch (x-2y)=sin(pi(x+y))

    can anyone teach me how to use a different coordinate system to sketch the graph of (x-2y)=sin(pi(x+y)). i have totally no idea
  3. H

    Calculate Center of Mass for 1.05cm Baseball Bat with Linear Density Formula

    A baseball bat of length 1.05 cetimeters has a lenear density given by l=.950 + 1.050x^2/l^2 find the x cooridinate of the center of mass in centimeters. How am I supposed to work this problem?
  4. chroot

    Metrics and coordinate transforms

    Hi all, I'm trying to solve Exercise 1.4.3 in Foster & Nightingale's "A Short Course in General Relativity." The question essentially provides the metric for Euclidean space in spherical coordinates and the matrix representing the coordinate transformation from spherical to cylindrical...
  5. M

    World-sheets, manifolds, and coordinate systems

    I'm trying to understand the manifold properties of world-sheets in string theory. I'm told that world sheets are manifolds and that manifolds are locally Euclidean. So I would like to know the characteristics between the space-time coordinates of the world-sheet given as xμ verses the 2D...
  6. K

    What is the Differential of a Vector?

    Greeting A TA has got me very and utterly confused. He won't be avaible for a few days, so I'm asking you guys. Consider the transformation to cilindrical coord. x-->r.con[the] y-->r.sin[the] z-->z I have the Jabobian (no problems here). He then asks the differential da , where a...
  7. M

    How to find angle of a curve in xy coordinate plane?

    Hi, I think it is atan of the derivative of the curve, is that right? Thanks Matt
  8. T

    Is a 4-D Coordinate Plane Possible?

    Is their a 4-D coordinate plane?
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