Survey posted 2005-05-16 19:04 by Jon.

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Impeccable TI-89 said 0, so it is 0. Period.

Except for when my TI-92+ crashes when I enter math problems. :) Rare, but it does happen. Also, there are almost certainly problems for which it gives the wrong answer (even symbolic answers, not just approximations).

I wonder where the answers other than "0", "0!", and "Huh?" came from...maybe random guesses?...since anyone who actually used their calc would know that the answer is 0. ;-)

Just some constants that appear ridiculously often in calculus. If it was a trig question there'd probably be answers like 1/2 sqrt ( 2 ) and 1/2 sqrt ( 3 ).
One of the professors of our math departement once told his class to "always guess 0, 1, e or pi if you don't know the answer". (Not that that advice is gonna do you any good though; no points are awarded for answers (even if they are correct) if you don't show work.)

Sorry, what I meant is "Why would people vote for any options besides 0, 0! (for the people who didn't know it was a factorial), and Huh?".

Oh, I thought you wondered how Jonathan came up with the other possible answers. Well, it's complex math, and not exactly the easy stuff (adding complex numbers (especially in rectangular coordinates) is much easier than complex powers). Remember that many of the visitors of this site are still in high school, so this is pretty far beyond them. I think many of those other answers are just people taking a random guess.

I know that pi is 3.14159265, and that i is the square root of -1, and i know that 1 is but what is e

e is the base of the natural logarithm, being approximately 2.718281828... (but it does not repeat, I just do not remember any more). This constant appears in numerous calculus equations, & the shape of r=e^theta (called, confusingly, either a logarithmic or an exponential sprial) appears a lot in nature.

Does the exponential spiral appear in sunflowers?

Something does but I'm not sure if that's it.

That's the Fibonacci sequence.

thats the thing where you take one number and add it to the previous right.

Yes, start with 0 and 1. The next number in the sequence is the sum of the previous two numbers.

F[n] = F[n-1] + F[n-2]
where F[0] = 0

e =~ 2.7182818284 5904523536 0287471352 6624977572 4709369995 9574966967 6277240766 3035354759 4571382178 525166427 (I didn't remember either, but do have Mathematica installed. :P )
Sometimes it appears as if all of calculus is constructed around e; when I'm doing calculus I see e pop up all the time, in the most unexspected places. For instance, f(x) = 1 + x + x^2 / 2 + x^3 / 6 + ... (that is, the infinite series Sum [ x^i / i!, 0 <= i <= infinity ] ) is equal to e^x, which I think is very strange, because e doesn't even appear in the formula.

I think they made calculus first, then started discovering e everywhere in it. I tried to make a system in which a certain number kept popping up everywhere, but it would not work (I could not make it finite).

Isn't that the Tayler Series for e^x?

It makes sense that e should show up there because e is the sum of 1/k! for 0<=k<infinity. This can also be stated that e^1 is the sum of (1^k)/k! for 0<=k<infinity. Also, e^2 would be the sum of (2^k)/k! for 0<=k<infinity, and e^3 would be the sum of (3^k)/k! for 0<=k<infinity. Following the trend, one can predict that e^x would be the sum of (x^k)/k! for 0<=k<infinity (1+x+(x^2)/2+(x^3)/6+(x^4)/24...).

Indeed it is.

My point was "which I think is very strange, because e doesn't even appear in the formula". I know there are a lot of related formulas (like the ones you mentioned), but the basic point remains the same; you've got an infinite polynomial (well, technically that's an oxymoron) which turns out to be the same as a completely different function, which involves an irrational number.
The same goes for the Taylor series for the sine and cosine functions; they look nicely regular and simple, but if you try to find the zeros, suddenly pi pops up out of (seemingly) nowhere.

e is the base for ln (on you calculator) like 10 is the base for log (on you calculator). Also I thought e was a repeating number. Well I guess you learn something every day!

Actually, e is the second most famous non-repeating number (after pi ofcourse).
Also, depending on who you talk to, the base for "log" can be either 10, 2 (for instance in computer science) or e (why those wacky mathematicians want to write 'log' when they mean 'ln' is beyond me though ;) ).

I have never seen a mathematician use log for base e (unless subscripted with an "e"). Maybe the ones I know are more "enlightened." Anyway, log for base 10, lg for base 2, & ln for base e, last I checked. Why not just use the subscript notation (except, of course, for them not being in most programming languages)? Oh, well.

Because subscripting every log you write is rather pointless if it's the same subscript every time. My calculus teachers all had the habbit of using log for logarithm-base-e. That's pretty much the only logarithm they ever use, so why introduce a different notation? Same goes for computer sciences, most of the time (in complexity for instance) you don't even care about the base, so you just write 'log'. In the (quite rare) cases where you do care it's always gonna be logarithm-base-2. So why bother writing the subscript, it's implied.

Actually, *evil grin*, pi = 3.1415926535 897932384 626433832 795028841 971693993 751058209 749445923 078164062 862089986 28034825...

But anyways, e is important for exponential growth/reduction equations (as well as many other things).

& 31 415926535 897932384 626433832 795028841 is prime, as can be checked on a TI-89/92+ easily.

Just wondering, how much time does it take an 89 to verify that primality?
(In Mathematica, PrimeQ[ 31415926535897932384626433832795028841 ] returns True in "0. Second" (that is, in so little time it can't even measure it). BTW, that's on a 1 GHz Pentium III.)

About 25 seconds on my HW2 TI-92+.