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  1. K

    Parallelogram Paradox!

    Thank you! I clearly do not think in a direct mannerism...Anyone else left-handed? Thanks again to everyone for your help! I always seem to have problems with the simple math problems, yet I find set theory and linear algebra rather straightforward...
  2. K

    Parallelogram Paradox!

    Sorry. Just realized you said this first! Take the comment I made to "HallsofIvy" and apply it to yourself as well! Thank you!
  3. K

    Parallelogram Paradox!

    HOLY CRAP! Thank you so much. I cannot believe I didn't think of that! It makes so much sense. It doesn't seem like it when you think about it though...You would think that the area remains constant...GEEZ! Math is exciting! Thank you all and especially you! Very simplistic solution! USE LIMITS...
  4. K

    Parallelogram Paradox!

    Yes. But what I am saying is that the angle is less than 90 degrees. All I have done is taken the original rectangle and "Pushed it" so that it went "sideways." I am just wondering why the area would not simply be A*B instead of A*B*sin(theta) because if it were A*B and the angle is less than...
  5. K

    Parallelogram Paradox!

    Hi there! My question involves the area of a parallelogram. Now, I know how to prove the commonly used formula (b*h) very easily, however, there is a formula given on Wikipedia as an alternative that states....Given two sides B and C with angle (theta), B*C*sin(theta)=Area of a parallelogram...
  6. K

    Proof of the Possibility of Division!

    Hi there! I have been reading Apostol's "Calculus: Volume 1" and have been trying to prove a few theorems using specific field axioms(note that this is not a "homework" question since I have not been assigned it, but instead, chosen to attempt it out of curiosity). Although I am not a math...
  7. K

    Prove that if ab=ac, then b=c.

    Thanks to all who replied! You have helped me greatly!
  8. K

    Prove that if ab=ac, then b=c.

    Sorry. I have forgotten to include that no division axioms may be used but nonetheless, thank you!
  9. K

    Prove that if ab=ac, then b=c.

    Thank you for the clarification and your reply!
  10. K

    Prove that if ab=ac, then b=c.

    Can someone help me prove that if ab=ac and a does not equal 0, then b=c. You can only use the field axioms. Here is my attempt( I am not sure about the final result). ab=ac then, ab-ac=0 a(b-c)=0 a(0)=0 (Already proved this) since a cannot equal 0, (b-c) must equal zero and we are left...
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