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Geometrical interpretation of Taylor series for sine and cosine?

  1. Jul 9, 2007 #1
    I've stumbled upon what might be a geometrical interpretation of Taylor's series for sine and cosine. Instead of deriving the Taylor's series by summing infinite derivatives over factorials, I can derive the same approximation from purely geometrical constructs.

    I'm wondering if something like this has been done before? If so I don't want to go further and reinvent the wheel. Currently I'm stuck at a certain point because the more accurate you want to get, the complexity of this rises exponentially. But preliminary results are conclusive, this could be true. If you are aware of something like this, let me know. In the mean time I'm going to prepare some papers to show you guys if interested.
  2. jcsd
  3. Jul 9, 2007 #2
    Just off the top of my head I'm not aware of anything like that, but I'm just a silly undergrad. Could you describe your derivation in more detail?
  4. Jul 9, 2007 #3


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    You might want to check the "http://www.maa.org/pubs/monthly.html" [Broken]] (1970-presesnt) for "visual proofs" or "proof without words" along these lines.
    Last edited by a moderator: May 3, 2017
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