Recent content by JsStewartFan

I fell in love with math in junior college because of two professors who genuinely loved the subject and spent quality time with our small group of students - treated us like fellow-researchers. A big part of why I loved it was the group of students who studied together diligently every...

http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Lambert.27s_proof Sorry - same page as above.

OK, I'm way down here on understanding, but wanted to ask cmcraes what "since we know i is not" meant, with explanation, please. Thanks!

For radius 1/(2pi), the circumference of a circle is 1, rational, but the radius is irrational. The radius and circumference are incommensurable, can't both be measured in any unit so that one is a multiple of or proportional to the other. Am I on the right track?

I would run a few numbers in a table and get a feel for how your numbers would work. What if n = a^3 + b^3 is an even number? What does that say about a and b? Also, your problem sounds like an "or" problem, as in n = a^3 + b^3 or n = c^3 + d^3, where a, b, c, d are distinct. Not an expert...

Thanks, ehild and gb7nash! I wish I could think of how such a pattern could be generated. WTMTOMH, I guess.

Thanks! And you didn't recognize it, did you, as a well-known number?

Is 2.71771177711177771111... irrational? Homework Statement I'm student teaching 8th graders Numbers and Operations. This is from an 8th grade activity I inherited with no "answer key." Is this decimal (with a pattern but not a repeating pattern) irrational? I am guessing it is, but I want to...

Good job. Thanks for showing the solution. A future high school math teacher Terry

QuarkCharmer: I think I've proved this two ways - one I found in Sullivan's Algebra & Trigonometry book (proved in the text), ed. 7, page 793. The other one I proved using the difference of limits as I wanted to, but I had to separate the proof into the four quadrants, since the hyperbola is not...

I finally found the homework and course work section under Science, so I'm OK there. Thanks, Terry

Oh, I read your question wrong. I think since Mr. Stewart only explained slant asymptotes in terms of the limit definition, that he's expecting me to use it here. This is a problem right after that section. I know I can use setting the hyperbola to zero instead of 1 (saw that in another post...

By the limit difference, I just meant the definition for the asymptotes that says if the limit as x approaches infinity of (f(x) - (mx + b)) equals zero, then that y=mx+b is an asymptote of the function f(x), which is the hyperbola in question. It's listed under related equations. I wasn't...

Dear HallsofIvy, Thanks for your easy-to-follow explanation of why you replace the 1 with a zero to find the asymptotes. I had gotten that tidbit from another website, but they didn't explain why you set the original equation to 0 instead of 1.

Homework Statement Prove the equation(s) for the asymptotes of a standard hyperbola. That is, prove that the asymptotes for the hyperbola x^2/a^2 - y^2/b^2 = 1 are y = -(b/a)x and y = (b/a)x where foci are at (c,0) and (-c,0); vertices are at (a,0) and (-a,0); difference in distances...