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. J

    Vague question about polar coordinate basis

    I hae a kind of strange, vague question. We know that any vector in R^2 can be uniquely represented by unique cartesian coordinates (x, y). If we wish to be more rigorous in our definition of "coordinates" we consider them to be the coefficients of the linear combination of the standard basis...
  2. S

    General Orthogonal Coordinate System: Line Element Explained

    A general orthogonal coordinate system (u,v,w) will have a line elemet of the form: ds^2 = f^2 du^2 + g^2dv^2 + h^2dw^2 I have done a lot of vector calculus, but for some reason I can't figure out what this means! What is a line element? I know about the differential length element and its...
  3. F

    Dot product of basis vectors in orthogonal coordinate systems

    I'm doing a series of questions right now that is basically dealing with the dot and cross products of the basis vectors for cartesian, cylindrical, and spherical coordinate systems. I am stuck on \hat R \cdot \hat r right now. I'll try to explain my work, and the problem I am running into...
  4. H

    Locacal coordinate system in GR observed?

    Local coordinate system in GR observed. If one considers coordinate systems in General Relativity. I think, if I understand it well enough, that in GR space & time and or in space-time a coordinate system depends on locality, e.g. on an average distance between galaxies an the total amount...
  5. J

    Combining coordinate transformations

    I have a vector (<1, 0, 0>) that needs to be transformed from an initial 3d rectangular coordinate system M1 through M2 and M3 to a final 3d rectangular system M4. I'm currently doing this by applying sequential rotations omega, phi, and kappa about the x', y', and z' axes, respectively, for...
  6. H

    Mathematica Coordinate plane in mathematica

    How can I graph single points on the graph in Mathematica? Or draw whole coordinate plane, with *boxes*, like this one: (and then plot) Can't find the informations in the tutorial I'm using presently, Thanks,
  7. Y

    Why is the Tortoise Coordinate Called That?

    Hi. I have been reading the forums for quite sometime now, but this is the first time I decided to join in the fun. :biggrin: I am wondering why the tortoise coordinate is called tortoise coordinate (why not turtle or hippo... :-p) . I have tried searching for the answer online but couldn't find...
  8. T

    Superellipse and a good coordinate system

    Hello guys, at the link http://mathworld.wolfram.com/Superellipse.html you can find the definition of superellipse. Now consider the particular super ellipse \frac{x^{2n}}{A^{2n}} +\frac{y^{2n}}{B^{2n}} = 1 In which A,B, are constant and n is a positive integer. What is the...
  9. T

    Closed curve and orthogonal curvilinear coordinate system

    Hello, I have a "simple" problem for you guys. I am not expert in math and so try to be simple. I explain the problem by starting with one example. The polar coordinate system has the following main property: with two parameters, rho and theta, each point is described as the intersection of...
  10. D

    Where to learn coordinate gepmetry?

    I am currently learning about coordinate geometry. But I need to brush it up a little also. I want to know geometry about the straight line. Can anyone give me a website for this. i searched in the google but can't get any results that I need. Thanks alot.
  11. Q

    Coordinate Transformation Help

    Hello, I was wondering how one would go about finding the coordinate transformation that diagonalizes: 2(x1)^2+2(x2)^2+(x3)^2+2(x1)(x3)+2(x2)(x3) Thanks a bunch.
  12. A

    Frame of Reference vs. Coordinate System

    What is the difference between a frame of refernce and a coordinate system. For example, I know that a rotating frame of reference is non-intertial, but is this also a non-intertial coordinate system? Thanks.
  13. I

    How Do You Calculate the Coordinates of a Point Based on Distance and Gradient?

    Not actually homework, but just a general query... I'm trying to write a program that will predict the trajectory of a moving point by analysing several positions through which the point has passed. Part of this involves finding the coordiantes of a point B, given the coordinates of another...
  14. T

    Find Roots of Polar Coordinate Equation x^2 + 2x + 5 = 0

    x^2 + 2x + 5 = 0.Find the root of this eqn.can use polar system. is the answer=(-1+2i) @ (-1-2i)?? pls help... thanx...
  15. B

    3-D coordinate systems problem

    Pleas help me with this exercises(this is not a homework): Determine whether the points lie on a straight line. a) A(5,1,3), B(7,9,-1), C(1,-15,11) b) K(0,3,-4) L(1,2,-2), M(3,0,1) Should I draw the graph, then find the slopes? Or is there any other way to approach? Pleas help...
  16. daniel_i_l

    Think about SR as different observers using different coordinate

    Is it correct to think about SR as different observers using different coordinate systems depending on their speeds? This would meen that their measurements would differ since space, time, mass,etc.. measurements depend on the system used. I find it very easy to understand SR when I think...
  17. JasonJo

    What Are the Different Coordinate Systems Used in Calculus?

    1) Rewrite the following expression in polar coordinates: (second derivative of z with respect to x) + (second derivative of z with respect to y) where x=rcos(theta) y = rsin(theta) i had first derivative of z with respect to x = (dz/dx)(dx/dr) + (dz/dx)(dx/d(theta)) same concept for...
  18. M

    Vectors and Coordinate Systems

    Hi, I'm a first year university student and I don't understand vectors and the coordinate system. I tried reading the book, but it doesn't make sense to me like the magnitude of theta and sigma or the oval with the vertical line through it. If someone could help me with the concept of it and...
  19. N

    Rate of Change in a coordinate plane

    Hi. I am drawing a complete blank on this calc problem. Point a moves along the x-axis at the constant rate of 'a' ft/sec while point b moves along the y-axis at the constant rate of 'b' ft/sec. Find how fast the distance between them is changing when A is at the point (x,0)and B is at...
  20. W

    Cylindrical and Spherical Coordinate systems

    I have a question about the equation mechanics of cylindrical and spherical coordinate systems This is basically about the velocity and acceleration equations of both Let me just give an example from cylindrical \vec v = \dot r\hat e_r + r\dot\theta\hat e_\theta + \dot z\hat k and...
  21. T

    Coordinate transformations and acceleration

    So often students question the validity of the twin paradox and how acceleration is involved in looking at round trip scenarios that I am asking why not just give them the tools to transform between the coordinates of an inertial frame and those of an accelerating frame. It is not hard to do and...
  22. B

    DOFs in coordinate mapping if metrics specified?

    I am trying to determine a mapping between two coordinate systems, given only the metric tensor written for each system. How much freedom do I have available in specifying the mapping once the metrics have been given? I know that the transformation equations of the metric tensor components...
  23. D

    How Can I Visualize 3D Rotation Transformations in Linear Algebra?

    These problems are actually for my classical mechanics class, but they are linear-algebra based. I can construct a transformation matrix, but I have trouble visualizing the rotations, particularly in 3-space. So if someone could help me get a pictorial idea of what's actually happening, then...
  24. B

    Dynamics, polar coordinate system

    i have been set the following question theta = 3r^2 find the magnitude of the acceleration when r=0.8 m dr/dt = 4ms^-1 d^2r/dt^2 = 12 ms^-2 my working followed the process of calculating angular velocity with these conditions and angular acceleration with these conditions then...
  25. Z

    What is coordinate system and how to find angles b/w lines

    hi i want to know what is cordinate system and how to find angle b/w two connected lines
  26. P

    How can I solve a 3D coordinate problem involving rotation and a given point?

    I have been thinking about this problem for awhile, but have no idea to even begin solving it. Was wondering if anyone has a clue to help me started? There's a point (x0,y0,z0) in 3D. There is a line on the X-Y plane. This line is say theta degrees (0 - 360) about the Y-axxis. If the point...
  27. M

    Rotating a Vector in a Coordinate System: Explaining the Formula

    Say, i have a vector a, defined in a coordinate system, x-y-z and i rotate the axes by an angle theta around the z-axis, so i have my z-component invariant in this change of basis. Can someone show me why, a_x' = a_x cos\theta + a_y sin\theta and a_x' = -a_x sin\theta + a_y cos\theta...
  28. G

    Solve Coordinate Geometry Puzzle: Find Relationship Between a & b

    Hi all (<--new user) I've spent the last 6 months trying to learn A-level mathematics in a vacuum after 9 years of letting my GCSE knowledge slide into oblivion, this is the first time however, I've hit a question for which how the book arrives at its answer is completely frying my brain. The...
  29. P

    Finding Eigenvectors for Coordinate transformation

    I'm wondering if anyone here might have a solution to a problem I've having. This is a Quantum Mechanics problem I'm doing. I calculate a 4 by 4 complex Hermitian matrix (H = Hamiltonian) in a basis where it is not diagonal. I diagonalize it numerically (using eispack) and get eigenvalues...
  30. N

    General Coordinate Transformations

    Gents, Could you please help me: Speaking about General Coordinate Transformations, one speaks always generally. Are there any explicit expressions for General Coordinate Transformations? Like in SR speaking about Lorentz Transfrmations one recalls Lorentz Matrixes. Maybe I'm not quite...
  31. S

    Div an curl in different coordinate systems

    To calculate the divergence of a vectorfield in cartesian coordinates, you can think of it as a dot product, and to calculate the curl, you can think of it as a cross product. But how can you calculate the div and curl when you have spherical or cylindrical coordinates, without explicitely...
  32. C

    How Do I Solve a Complex Coordinate Geometry Problem with Parabolas?

    Hi there, I've been struggling with this question for days :cry: :confused: , the first part where they call me to prove that equation, i could do it...the second one i don't know how to do...could anyone help me? how do i find the locus equation? its so confusing... ty in advance. If...
  33. O

    How Do Cartesian Components Transform into Cylindrical Coordinates?

    Hi. I’ve just started learning about tensors on my own and am still trying to understand coordinate transformations. If I begin with a vector whose Cartesian components are (x, y, z) and apply the tensor transformation to cylindrical polars, I end up with (r, 0, z) – is this right? I...
  34. A

    Coordinate Geometry II TRIANGLES

    The question is in the attached picture. i can't seem to find a relevant formula and when i do i can't get a suitable answer, if some one can help, i'll highly appreciate it. Thanks in advance.
  35. V

    Can the Spherical Coordinate Integral be Simplified using a Substitution?

    My professor said this problem is straightforward in spherical coordinates, \int_{|\vec{r_1}|\leq a } \int_{|\vec{r_2}|\leq a } \frac{1}{|\vec{r_1}-\vec{r_2}|} d^3 r_2d^3r_1 i set up the integral in spherical coordinate and found it really ugly...
  36. A

    What is the Method for Finding Points Inside a Triangle Using Inequalities?

    Coordinate Geometry II HARD! 1a). TriangleABC has vertices A(4,6), B(-3,4) and C(-1,-3). Write down the three inequalities whose intersection is the interior of triangleABC. 1b). Prove that triangleABC is a right angled isosceles triangle. 2a). The lines L1 and L2 have the equations...
  37. N

    Homework help (normal and tangential coordinate problem)

    Problem : A baseball player releases a ball with v_0= 100 ft/sec at an angle of \theta= 30 degrees. Determine the radius of curvature of the trajectory (a) just after release and (b) at the apex. For each case compute the time rate of change of the speed. I really wasn't sure how to do the...
  38. F

    Unit Vector z in Spherical Terms: (1, 0, 0)

    at (2,3,-4) express the unit vector z in spherical terms. express the unit vector r in rectangular terms. for the first part, would it just be (1,X,0) fi should be zero because that's the angle the line makes with the z axis, and since this is going to be parallel to the z-axis this...
  39. R

    Coordinate Geometry: Point Division in Ratio 2 : 5

    Hi i'm stuck on this question . please could someone guide me in the right direction ? A = (1, - 2,4) and B = (8,12, - 3). Find the co-ordinates of the point which divides AB in the ratio 2 : 5. thanx roger
  40. B

    Orthogonal projection, orthonormal basis, coordinate vector of the polynomial?

    Hey there I'm working on questions for a sample review for finals I'm stuck on these three I think I'm starting to confuse all the different theorem, I'm so lost please help 1) Find the coordinate vector of the polynomial p(x)=1+x+x^2 relative to the following basis of P2: p1=1+x...
  41. T

    Converting a Shifted Circle into Polar Coordinates

    How do I express this in polar coordinates? (x-h)^2+(y-k)^2= h^2+k^2 It is a circle with k and h greater than 0.
  42. B

    Convenient Coordinate System for Dog, Acrobat, and Submarine Analysis

    Identify a convenient coordiante system for analyzing each of the followling situations: A. a dog walking along a sidewalk B. an acrobat walking along a high wire C. a submarine submerging at an angle of 30 degrees to the horizontal. This should be rather easy, it was number one of the...
  43. W

    Coordinate transformation matrix?

    Can anyone tell me: 1) How to understand the defination to orthogonal transformation matrix? Defination: A(i,j)A(k,j)=q(i,k) where q is Kronecker delta. 2) Why the inverse of this orthogonal matrix is equal to its transpose? Will.
  44. U

    Arghhh Coordinate geometry question

    Hi everyone. This is a question that was attempted in class but no on (including our teacher) could solve in the time we had left. It's not actually homework, but it's really getting on my nerves! The quadrilateral ABCD, where A is (4,5) and C is (3, -2), is a square. Find the coordinates of...
  45. G

    Coordinate geometry - circles.

    I'm just introducing myself to coordinate geometry in the xy plane of cirlces. Here's a question I'm having trouble with: Q11: The line with equation y=mx is a tangent to the circle with equation x^2 + y^2 - 6x - 6y + 17 = 0. Find the possible values of m. At first i thought i'd try...
  46. E

    Epsilon Pi's ideas on coordinate independence

    Tensors, a reason of great schism in physics? Yes, this application of that aristotelian principle, you have described so well, where the third is excluded and as so uncertainty is the reason why there won`t be a quantum gravitation theory, and a reason why physical laws must not be expressed...
  47. H

    Taking Time as the Fourth Coordinate What are the implications?

    As Einstein said, when we talk of higher speeds close to the speed of light, time becomes an important factor...So much that the time coordinate that was almost non-existent before, becomes a dominant force... So if we move at speeds close to the speed of light, the time coordinate become...
  48. denian

    Solve Rhombus: Coordinate Geometry Question

    just want to ask a simple question a quadrilateral has the vertices A ( 1,4 ), B (9,5 ) , C ( 5,-2) and D (-3,-3). show that the quadrilateral is a rhombus what i do is find gradient AB, CD, AD and BC. and then state which and which have the same gradient... and hence the opposite sides...
  49. denian

    Coordinate Geometry: Triangle Vertices & Point P Movement in OAB Plane

    the vertices of a triangle are 0, and the points A (a, 0) and B (0,a) where a>0. the point P moves in the plane OAB such that OP square + AP square + BP square = k square, where k is a positive constant. show that k mst be bigger than (2/3)a X square root of 3 i tried. but can't even know...
  50. E

    Help with accelerated coordinate system question

    Ok, so if a ball is thrown vertically upward with velocity v on the Earth's surface. (Air resistance being neglected). I have to show that the ball lands a distance (4wsin(beta)v^3/3g^2) to the west where w is the angular velocity of the Earth's rotation and beta is the colatitude angle...
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