1. Homework Statement
As I was relearning some concepts in calculus, I came across a section on ellipses. What I don't understand is why a and b in the standard equation of an ellipse govern the length of the minor/major axes. Can anyone shed some light? Thank you very much!
2. Homework...
Yes, sorry, I figured this out earlier. Sorry I did not post to say so. I appreciate the time you have taken to explain this to me. Please know that you have helped someone understand even more just how beatiful math can be. Again, I thank you for all your help!
Ok. I understand everything now. Can you just prove to me that if two numbers, say a and b, have the same factor, then their difference is indeed also divisible by that factor.
Thank you so much for your help!
Thank you very much! All of this makes sense except for one bit. Why MUST p divide the difference of two integers? Also, 1 is divisible by a number but it yields a fraction. Why must the result be an integer?
Again, thank you so much for your help. I understand the proof, I just don't...
1. Homework Statement
Euclid's proof
Euclid offered the following proof published in his work Elements (Book IX, Proposition 20)[1] and paraphrased here.
Take any finite list of prime numbers p1, p2, ..., pn. It will be shown that some additional prime numbers not in this list exist. Let P be...
Wow. Thank you for the lightning fast response! Also, I forgot to mention... Merry Christmas to you if you celebrate it and Merry Christmas to everyone else that celebrates it as well! Happy New Year!
1. Homework Statement
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2. Homework Equations
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3. The Attempt at a Solution
I guess I will start here. My question does not necessarily involve equations. In the Calculus book I am currently studying from, I am reviewing some pre-calculus and I came across a section that...