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How to draw a logarithmic spiral

  1. May 18, 2012 #1
    I have a simple geometry question hopefully I'm posting this in the right forum. I want to draw a simple logarithmic spiral using only compass and ruler or any other simple mechanical means. The requirement is that each spiral must be halfway from the center to the next spiral. Is there a simple method for drawing this?

    something like the one in this picture.
    Last edited: May 18, 2012
  2. jcsd
  3. May 19, 2012 #2
    This looks like an involute curve. You can draw this by sticking one end of a piece of string and putting a pencil on the other end. You then whirl the string around the disk until the pencil is on the disk. This is your starting point. You then simply unfold the string and you have your spiral.
  4. May 24, 2012 #3


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    No, that gives an arithmetic spiral. Consecutive turns will be equally spaced (by the circumference of the disc).

    The simplest mechanical means I can think of off-hand goes like this:
    Attach one end of a horizontal telescopic rod to an vertical axis at the origin.
    At the other end, a wheel is attached. The wheel is in the vertical plane, but its axis is turned slightly from the line of the rod. I.e. there's a slight elbow at the end of the rod.
    As the wheel is rolled, it should move away from the origin making a constant tangent angle to the origin.
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