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Math Help - 2D to 3D Loci

  1. #1
    Member GAdams's Avatar
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    2D to 3D Loci

    Hi
    I am trying to visualise 3D loci.

    Example: a person is on the London Eye (a type of ferris wheel with a large capsule, see here: The London Eye's official website for the best online ticket prices, guaranteed.). She paces up and down in the capsule as it goes round. What would the path traced out by her look like in 2D and 3D? I am pretty sure I have it in 2D -a straight line the length of the capsule on a circle and repeated periodically over the circumference of the circle, but not sure about 3D.

    Any ideas?

    Thanks.
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    Quote Originally Posted by GAdams View Post
    Hi
    I am trying to visualise 3D loci.

    Example: a person is on the London Eye (a type of ferris wheel with a large capsule, see here: The London Eye's official website for the best online ticket prices, guaranteed.). She paces up and down in the capsule as it goes round. What would the path traced out by her look like in 2D and 3D? I am pretty sure I have it in 2D -a straight line the length of the capsule on a circle and repeated periodically over the circumference of the circle, but not sure about 3D.

    Any ideas?

    Thanks.
    Assuming that the "pacing" is perpendicular to the plane of the circle, imagine a flat wheel rim. The locus will be a zigzag line drawn on that rim.
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    Member GAdams's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    Assuming that the "pacing" is perpendicular to the plane of the circle, imagine a flat wheel rim. The locus will be a zigzag line drawn on that rim.
    The pacing is perpendicular. So the only difference between the 2D and 3D would be the zig zag, where for the 3D, the points would be connected. Is this right? I tried simulating it using Geogebra and the 'trace' function. But it doesn't come out quite right.
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    Hello, GAdams!

    A person is on the London Eye (a Ferris wheel with a large capsule).
    She paces up and down in the capsule as it goes round.

    You mean back-and-forth or end-to-end, don't you?

    What would the path traced out by her look like in 2D and 3D?

    I will assume that the pacing is done in simple harmonic motion.


    Suppose a lap is a walk from one end of the capsule to the other and back.

    Suppose further that she walks 30 laps during one revolution of the wheel.


    Get a huge strip of paper.

    Its length is the circumference of the wheel.
    Its width is the length of the capsule.

    On the strip, fit thirty cycles of a sine curve.

    Tape together the ends of the strip, forming a wheel.


    The sine graph is the path taken by the person.

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