Geometrical interpretation of Taylor series for sine and cosine?

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SUMMARY

The discussion centers on a geometrical interpretation of Taylor series for sine and cosine functions, suggesting an alternative derivation method that relies on geometric constructs rather than traditional calculus. The author expresses uncertainty about the originality of this approach and seeks confirmation from others in the forum. Preliminary results indicate potential validity, although increasing accuracy leads to greater complexity. The author plans to prepare papers to share findings and invites further elaboration on existing derivations.

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  • Understanding of Taylor series and their mathematical significance.
  • Familiarity with sine and cosine functions and their properties.
  • Basic knowledge of geometric constructs in mathematics.
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Mathematics students, educators, and researchers interested in innovative approaches to understanding Taylor series and their geometric interpretations.

waht
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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.
 
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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?
 
You might want to check the "http://www.maa.org/pubs/monthly.html" ] (1970-presesnt) for "visual proofs" or "proof without words" along these lines.
 
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