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. G

    Coordinate transformation and multiplying with size of J

    Hi, I am using the book "Advanced Engineering Mathematics" by Erwin Kreyszig where I am reading on the transformation of coordinates - when changing from \int f(x,y) to \int f(v(x,y),v(x,y) it is necessary to multiply with the size of the jacobian, |J| - I cannot find the proof in the book...
  2. E

    Vector Coordinate Conversions

    Homework Statement Transform the following vector into cylindrical coordinates and then evaluate them at the indicated points: \vec A = (x + y)\hat x at P_1 (1, 2, 3) Homework Equations r = \sqrt{x^2 + y^2} \phi = \tan^{-1}(\frac{y}{x}) z = z The Attempt at a...
  3. E

    Right-handed coordinate system

    Homework Statement Can someone give me a real rigorous definition of what a right-handed coordinate system is? I can't find one on the internet. Is this true: A coordinate system is right-handed IF AND ONLY IF x-hat cross y-hat = z-hat ? Homework Equations The Attempt at a...
  4. G

    Exploring the Region of R^3: Solving for xyz=0

    Homework Statement Describe in words the region of R^3 represented by the equation or inequality. Homework Equations xyz=0 The Attempt at a Solution I'm not really sure how to look at the equation. I would think its just the point (0,0,0). Can someone explain if this is wrong.
  5. S

    Theory like coordinate geometry

    is one -one correspondence must for a theory like coordinate geometry , polar coordinate ,vector analysis etc to work , i.e theories which work by representing a quantity by a different set of quantities behaving alike
  6. M

    Rolling Cone - (Rotating Coordinate systems)

    Homework Statement A cone rolls on a flat surface. The instantaneous axis of rotation lies parallel to the point where the cone touches the surface and the angular velocity OMEGA. The motion of the center of mass (Vcm) plus a rotation OMEGAcm about the center if mass. Describe this motion by...
  7. C

    Calculating Offsets on the Normal Coordinate System

    I have problem with getting normal coordinates offset. I have cube1 and cube2. cube1 position is 10,10,10 and cube2 position is 10,9,10. Cube 2 offset refers to local coordinate system of cube1. If rotation of cube1 is 0,0,0 i get position offset 0,-1,0. But if cube1 rotation is 45,0,0 i get...
  8. M

    Help neede in coordinate geometry

    Help neede in coordinate geometry! Homework Statement here is the question : If the pairs of lines x^2-2pxy-y^2 and x^2-2qxy-y^2 are such that each pair bisects the angle between the other pair , then pq equals ...??the answer somehow is -1. i think it uses the concept of homogenisation (if u...
  9. Z

    Surjective Homomorphisms of Coordinate Rings

    Homework Statement I want to show that the homomorphism phi:A(X)->k+k given by taking f(x_1,...,x_n)-> (f(P_1),f(P_2)) is surjective. That is, given any (a,b) in k^2 (with addition and multiplication componentwise) I want to find a polynomial that has the property that f(P_1)=a and f(P_2)=b...
  10. P

    Lorentz coordinate transformation

    Homework Statement Frame S' has an x component of velocity u relative to the frame S and at t=t'=0 the two frames coincide. A light pulse with a spherical wave front at the origin of S' at t'=0. Its distance x' from the origin after a time t' is given by x'^2=(c^2)(t'^2). Transform this...
  11. X

    Cylindrical coordinate

    Homework Statement In cylindrical coordinates write a function which describes the surface of the dome (brunelleshci's dome) whose center is not on the central axis but rather one-fifth of the way from the edge. the sides form a shape called quinto acuto, span of base of dome is 143 find...
  12. T

    Relative Velocity coordinate system

    (a) A point is observed to have velocity v_A relative to coordinate system A . What is its velocity to coordinate system B which is displaced from system A by distance R ? ( R can change in time) I think its v_B = v_A - \frac{dR}{dt} . But I am not completely sure why this is the...
  13. S

    Kinematics[polar coordinate] concept problem

    http://p14.freep.cn/p.aspx?u=v20_p14_p_0711201047589252_0.jpg Formula: http://freep.cn/p.aspx?u=v20__p_0711201059233972_0.jpg 1)I need to find out V(\theta). But I remember that r\theta<dot> = \omega = V(\theta) Something seems like contradict Where my concept wrong? How should I...
  14. tony873004

    What is the Cartesian equation for a circle with a radius of 2?

    Identify the curve by finding a Cartesian equation for the curve. r=2 My attempt: r=2 makes a circle with a radius of 2, so: \begin{array}{l} x^2 + y^2 = r^2 \\ y^2 = r^2 - x^2 \\ \\ y = \pm \sqrt {r^2 - x^2 } \\ \\ y = \pm \sqrt {2^2 - x^2 } \\ \\ y...
  15. H

    Find the x Coordinate of the Center of Mass of 3 Chocolate Blocks

    Homework Statement Three odd-shaped blocks of chocolate have the following masses and center-of-mass coordinates: (1) 0.310 kg, ( 0.200 m, 0.310 m); (2) 0.410 kg, ( 0.110 m, -0.380 m); (3) 0.200 kg, ( -0.280 m, 0.610 m). Find the x coordinate of the center of mass of the system of three...
  16. Y

    How to Calculate 3D Fillet Tangent Points and Center in Excel?

    Homework Statement I have 3 known point, with coordinate P1-(X1, Y1, Z1), P2-(X2, Y2, Z2), P3-(X3, Y3, Z3). straight line is draw from P1 to P2, P2 to P3. they are "not" collinear. I would like to fit a round fillet to the conner with a "Known" radius of R, and I would like to know...
  17. S

    Divergence in cylindrical coordinate system

    I am trying to understand the derivation of the divergence formula in cylindrical coordinates. www.csupomona.edu/~ajm/materials/delcyl.pdf paper does a good job of explaining it but I don't understand 2 things that the author does. \frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi} and...
  18. R

    Coordinate Transformation

    If we want to transform vector A from cooedinate ei to ei', then this formula occur: Aj' = aij Ai But I have a question, if I have found all components of Aj', then I want to transform it back to Ai, what should I do? I have tried Ai = aij Aj' but it won't give me the same number. Thanks...
  19. G

    Relativity: Inertial vs. Coordinate Systems Explained

    Can anyone explain me what is the difference between inertial system and coordinate system in relativity? Please make me understand.
  20. R

    3 dimension coordinate systems

    Homework Statement Describe in words the region of R3 (3 dimension) represented by the following inequality. 1)xyz=0 Homework Equations none i know of The Attempt at a Solution no idea where to start. I know that this means one variable must be equal to 0, but i don't...
  21. S

    Coordinate transformation to flat space

    Homework Statement find the transformation that turns this metric: ds^2=-X^2dT^2+dX^2 into the minkowski metric: diag(-1,1). The Attempt at a Solution attempt 1: I transformed the above metric into the coordinates that use the lines that define the light cone as the axes. Namely, u=T+ln(X)...
  22. N

    Solve Geometry Coordinate Homework: |Z-1|+|Z+1|=7

    Homework Statement Given that Z is a complex number with condition |Z-1|+|Z+1|=7 Illustrate Z on Argand Diagram and write out the equation of Locuz Z I attempted to figured out the equation of locus Z, |Z-1|+|Z+1|=7 |x+yi-1|+|x+yi+1|=7 \sqrt{}[(x-1)^2+y^2] + \sqrt{}[(x+1)^2 + y^2] =...
  23. P

    Coordinate charts to cover a circle?

    4 charts seem to cover it. BUt only 2 will do for a minimal number? Just like 2 charts will do to cover a sphere? Even though there are 6 all together.
  24. F

    Solve Coordinate System Problem: Find Acceleration & Tension

    Hi everyone, wondering if anyone can help me with this little problem... An object with mass m1 , resting on a frictionless horizontal table, is connected to a cable that passes over a pulley and then is fastened to a hanging object with mass m2. Find the acceleration of each object and the...
  25. H

    Coordinate Geometry Q: Intersecting Lines & Parallelogram

    Question Statement The straight line y=mx -2 intersects the curve y^2=4x at the two points P(x1,y1) and Q(x2,y2). Show that 1) m>-1/2, m not equal to 0. 2) x1 + x2 = 4(m+1)/m^2 3) y1 + y2 = 4/m If the point O is the origin and the point T is a point such that OPTQ is a parallelogram, show...
  26. M

    Double integral coordinate transform

    Basically I want to find the new limits w,x,y,z when we make the valid transformation \int^{\infty}_0 \int^{\infty}_0 f(t_1,t_2) dt_1 dt_2 = \int^w_x \int^y_z f(st, s(1-t)) s dt ds I've tried putting in arbitrary functions f, and so getting 4 equations constraining the limits, but I end up...
  27. K

    Coordinate speed of light vs. gravitational time dilation?

    I know there is: A gravitational length contraction by the factor of \sqrt{1-2GM/rc^2} A time slowing by the factor of \sqrt{1-2GM/rc^2} I would have thought the former and latter affect the notions of wavelength and frequency of light respectively, am I not right? However, then...
  28. D

    Any Standard Notation for Multiple Coordinate Systems?

    Homework Statement Given variables in one coordinate system, give the notation used to refer to the variables in another system. The known variable is x Homework Equations The transformation is an arbitrary one. My question has to do with notation and not mathematical procedures...
  29. D

    How many coordinate charts does it take to cover a surface?

    I was wondering about this, I've never seen any general theorem. Obviously it takes more than one, but I would think that in general it can take quite a few, for I can't see how to cover a torus with only 2. Is there any sort of general result on this?
  30. A

    What are the values of A, B, and C for rotating a line about the x-axis?

    Homework Statement Let L be the line y=7, x=7z. If we rotate L about the x-axis, we get a surface whose equation is Ax^2 + By^2 +Cz^2=1 What are the values of A, B, and C? Homework Equations Listed above. The Attempt at a Solution Since y=7, my first point that I plugged into...
  31. L

    A Query on Sun and Moon Coordinate data

    Hello everyone, I was wondering where I could get complete ecliptic longitude/latitude data over the course of as many years as possible of the Sun and Moon. Of course, by definition the ecliptic latitude of the Sun would be zero. The equatorial coordinates would be fine. Thank you for...
  32. N

    Coordinate transformation of lagrangian

    Hey all, According to my physics textbook, if the potential energy of a particle is a homogeneous function of the spatial coordinate r, one can transform r by some factor a and t by some factor b=a^(1-.5k) such that the Lagrangian of the particle is multiplied by a^k. I understand all of this...
  33. M

    Frame fields vs. Coordinate bases

    What is the difference, if any, between frame fields and coordinate bases?
  34. C

    Rotating 2D coordinate geometry/conic sections into 3D - how?

    I know basic 2D coordinate geometry/conic sections and some vectors and calculus. What I am trying to find out is, if you rotate a conic about its axis by an angle of pi, you should get a surface in 3D. How would you go about rotating this though?
  35. P

    Rigid Body: Rotation of a coordinate axes made up of rods

    Homework Statement A rigid body consists of three uniform rods each of mass, and length 2a, held mutually perpendicular at their midpoints (choose and axis along the rods). a) Find the angular momentum and kinetic energy of the body if it rotates with angular velocity w about an axis...
  36. J

    Converting between coordinate planes

    How would you go about converting from a Cartesian coordinate plane to one where (0,0) is in the top left hand corner?
  37. E

    Express for Operator of coordinate in momentum representation

    Homework Statement 1. Obtain an expression for operator of coordinate in momentum representation. To this end begin with definition of the average coordinate x = ∫ψ*(x)xψ(x)dx express the wave functions as wave packets in terms of plane waves, and rewrite the expression for average...
  38. H

    Locus of Q in Coordinate Geometry: Find the Answer

    The points Q moves such that the length of the tangent from Q to the circle x^2+y^2+4x+8y+9=0 is equal to the distance of Q from the origin ). Determine the locus of Q. I am basically clueless about this question...but I will try to provide as many work I have done on this question. I assume...
  39. L

    What Coordinate Transformation Converts a Complex Metric to Minkowski Space?

    How can I identify the coordinate transformation that turns ds^2 = \left(1+\frac{\epsilon}{1+c^2t^2}\right)^2c^2dt^2 - \left(\frac{\epsilon}{1+x^2}\right)^2x^2 - \left(\frac{\epsilon}{1+y^2}\right)^2y^2 - \left(\frac{\epsilon}{1+z^2}\right)^2z^2 into the Minkowski metric ds^2 = c^2dt^2...
  40. D

    Dative bond confusion (or coordinate bond)

    I am a little confused with this. I know what a dative bond is, but the problem is when it comes to complex ions I do not understand. ok now for example NH_3 + H^+ = NH_4^+ So in this the lone pair of NH3 will fill the s- subshell of H and make it stable, but say in Cu^2^+ when this attracts...
  41. L

    Coordinate Distance of Object at Redshift z: Solving w/ k=0, n<1

    Homework Statement For a universe with k=0 and in which (a/a_0) = (t/t_0)^n where n<1, show that the coordinate distance of an object seen at redshift z is r=\frac{ct_0}{(1-n)a_0}[1-(1+z)^{1-1/n}].2. The attempt at a solution I have used r=f(r)=\int_{t}^{t_0}...
  42. H

    Coordinate Geometry: Proving Chord & Tangent of Rectangular Hyperbola

    The points P(cp,c/p) and Q(cq,c/q) lie on the rectangular hyperbola xy=c^2. Show that the equation of the chord PQ is pqy+x=c(p=q), and deduce the equation of the tangent at the point P. I can do the proving. And I can find the tangent as well if the word "deduce" is not there. How can you...
  43. J

    Expressing Wavefunction psi(x) Using Eigenstates |ai> for State |psi>

    Given a state |psi> and an operator A with (non-degenerate) eigenstates |ai> corresponding to real eigenvalues ai, express the wavefunction psi(x) corresponding to the state |psi> in terms of |psi> Now this was a question in last year's exam that my lecturer went through, but his answer on...
  44. B

    Coordinate conversion calculator

    I know this might be a stupid question, but I wan't to know if any of you know of any sites that convert between RA and dec coordinates to altitude and azimuth coordinates. I mean I found this site: http://home.att.net/~srschmitt/script_celestial2horizon.html But unfortunately you can't...
  45. H

    Sketch Curves: y=5x^(3/4), y=-2x^(-3/2)

    Homework Statement Sketch the curves with the following equations: a) y=5x^(3/4) b) y=-2x^(-3/2) Homework Equations The general equation of curves (circles, parabola, ellipse, hyperbola) The Attempt at a Solution It seems to me that this question is not exactly a coordinate geometry...
  46. D

    Mathematica Mathematical Proof For Lorenz Coordinate Transformation

    Hi, I have a pretty in depth understanding of special relativity. Recently I have been searching for mathematical proof of the Lorenz transformation. I found some information about it, but to tell the truth I didn't understand much of it. Maybe one of you guys can shed some light on the proof...
  47. L

    Find the Intersection Point of a Line and Plane: Step by Step Guide

    coordinate help please :) Hi i just got my home work but don't know where to start. Any help on this just to get me started would be great:) I want to make sure I am doing it right Thank you Work out the coordinates where this line meets this plane. Line x = -4 t + 4, y = -4 t + 6...
  48. Q

    Converting from 2D coordinate Systems

    I am trying to get from one 2D coordinate system to another 2D coordinate system. I found 2 corresponding points and each system. I did the following: [a1 a2 ] * [ x1,y1 ] = [u1,v1] [a3 a4] [ x2,y2] [u2,v2] or A*x = u if I use MATLAB to...
  49. B

    Coriolis forces, rotating coordinate systems

    I know that some people worship Symon's Mechanics 3rd Ed., but I find this book incredibly confusing...especially chapter 7, dealing with rotating coordinate systems. I follow the math, and perhaps the logic, but I can't even find a way to start the homework problems. The guy doesn't give any...
  50. N

    Coordination of Electrons in Covalent Bonds

    Do coordinate covalent bonds have to involve the sharing of a PAIR of electrons or can it just be a single electron? Example: XeF4 Now, since Xe already has a full octet, it would seem correct that the F basically shares electrons to Xe without donating any as well. This would only be true...
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