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Study proofs geometrically?

  1. Oct 15, 2011 #1
    For proofs such as the derivative of cos or sin.. should I study them both analytically and geometrically? By analytically I mean to derive them by algebraic means. Or should I also study the geometrical "intuition" behind it?

    I love proofs but aren't completely fond of the geometrical "proofs", I was watching MIT opencourseware and stumbled upon the geometrical "proofs" of things like derivatives of cos and sin. Question is, should I even bother to understand them?

    For a little background: I love mathematics and I'm pursuing theoretical physics. I'm only up to calculus at the moment and I'm trying to understand as much of the proofs as possible; simply because I find it fun and worthwhile. Is it necessary to start developing the geometrical intuition behind some proofs? Would it help for my further studies? As of the moment I see it as a waste of time, and enjoy the "real" proofs much more.
  2. jcsd
  3. Oct 15, 2011 #2
    Yes, try to understand both proofs. The more point-of-views you get on a certain subject, the easier it will be to apply this subject later on.

    Actually, I don't really see what you mean with "geometrical proof", but I guess it's probably some argument that gives intuition behind things. This intuition is very important. So do try to understand it.

    In general: the more you study right now, the easier it will be later on. I wish somebody told me this when I was young...
  4. Oct 15, 2011 #3
    Yes, I said geometrical "proof" because its not really a proof at all. I don't really see how the intuition behind the geometry of it is very important, I feel like I completely understand the concept through the regular proof.

    I'm also on the same boat, I wish I would have paid attention to high school algebra. I remember my calculus test the other week.. I completely aced eveything calculus related, only to get stumped on problems dealing with application of linear equations of which were roughly 1/9 the grade of the test.

    Though I suppose I caught this problem earlier than you, I'm only on calculus I at the moment. =p
  5. Oct 15, 2011 #4


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    It's impossible to "understand too much" IMO.

    Certainly you ought to be able to relate simple trig formulas to geometry. It won't hurt if you realize that [itex] \cos^2 \theta + \sin^2 \theta = 1[/itex] is exactly the same as Pythagoras's theorem, for example.
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