July 23

[Scooter]

Originally Posted by evay

I know pi is used in measuring circles, and i is the square root of -1 (so the square root of -4 is 2i), but what's "e" in mathematical terms?

It's a constant roughly equal to 2.7 and has to do with natural logarithms. If I remember correctly e is the limit as n approaches infinity of (1 +1/n)^n. Right, math-heads?

Not very applicable to my chosen field of ancient history. But if anyone asks I can always say Caesar invented it. People usually believe that. (He did invent military cryptography, which has as mathematical basis, so we're not too far afield...)

[Asky]

you could always look it up on Wikipedia or something and use your newfound knowledge to pretend to be smarter than you really are...

[Scooter]

Originally Posted by Asky

you could always look it up on Wikipedia or something and use your newfound knowledge to pretend to be smarter than you really are...

A little unfair. I did (much to my surprise) remember the concept and the formula, but I cop to double-checking it before posting. Figures I get called on it anyway.

As for pretending to be smart: I'm a college professor, it's a marketable skill.

[PointyHairedJedi]

Originally Posted by Celeste

math makes my head hurt.

And dentistry makes my mouth hurt.

[admiral sab]

wow. I have no idea what anyone has just said. Except about the head hurting. I get that.

And e of pi were you talking about my pic? It's edited with Photofiltre, and not really edited. I'm no iconic genius, I just cropped her pic over the 5mv logo and 50/50'd the opacity. Apparently making it transparent. Have no idea how to do anything else with it.

[e of pi]

Ah. Okay. I might recommend a new one, as the current one kinda looks like she has antenna.

[admiral sab]

lol she has a bow in her hair... I actually have Photoshop but I have NO idea what I'm doing with it. I could read the help files, but I don't really have the time right now.

[Zeke]

Originally Posted by evay

I know pi is used in measuring circles, and i is the square root of -1 (so the square root of -4 is 2i), but what's "e" in mathematical terms?

Scooter's correct, except about Caesar. (And he is right about Caesar where cryptography is concerned. Caesar devised the Caesar shift, rot-3 in modern parlance, which is why I had the Romulans use it.)

Anyway, e is as deeply embedded in calculus as pi is in geometry. y = C × e^x is the only function which is its own derivative. As such, it's the best base for logarithms (just as pi is the best basis for angle measurement), so logs to the base e are called natural. Common logs, i.e. to base 10, are strictly for engineers and the occasional number theorist.

e also arises in accounting. If you have $1 in the bank at 100% simple interest, your balance will be $2 in a year. If the interest is compounded semiannually, that rises to $2.25. Compound it monthly and you'll end up with $2.61. It turns out that there's a limit to this process, representing a sort of continuous compounding of interest, and that limit is e dollars.

A third way e can be found is through infinite series. e is the sum of the series 1/0! + 1/1! + 1/2! + 1/3! + ..., where the exclamation point is a factorial sign. (4! = 4 x 3 x 2 x 1, and so on. Before you ask, there is a double factorial sign, and it's the only kind of double exclamation point I can stand.) Any of these three properties of e can be, and has been, used as its definition; you can derive the other properties from the one you start with.

As you can see, it's easy to get me talking about this stuff. I did some quality math-related ranting in this LJ post, for anyone interested.

[Scooter]

Originally Posted by Zeke

Anyway, e is as deeply embedded in calculus as pi is in geometry. y = C × e^x is the only function which is its own derivative. As such, it's the best base for logarithms (just as pi is the best basis for angle measurement), so logs to the base e are called natural. Common logs, i.e. to base 10, are strictly for engineers and the occasional number theorist.

Wow, that is the most lucid explanation of a mathematical concept I've seen in ages. Cool.

I bet if we'd been born with 2.7 fingers, then base 10 would never have even been invented. Except that base 10 would be base e, since our numbering system would have developed using an e-based place value...

[mark726]

Actually, I heard somewhere that mathematics would have developed a lot faster if we had 4 fingers on each hand. We would have realized the base 2 system a lot quicker and all sorts of fun stuff like that.

Also, Zeke, what the devil is up with how e^(-i*pi) = -1? My calc teacher explained it to me once...but I was lost. It had something to do with infinite series, I think, but I was really confused.

[Hotaru]

I am so confused.

Math is the devil in numerical form.

[NeoMatrix]

Originally Posted by Hotaru

I am so confused.

Math is the devil in numerical form.

So math tempts you to sin by partying too hard at math camp?

[danieldoof]

well at least he doesnt have to sit in the sun..cos if he would go out he would tan

(OMG no .. I am hiding now for those cheap puns)

[Kristina]

Is that a sine?
*hides, too*

On another note, my new title gave me a good laugh - thanks, Zeke!

[Nate the Great]

I may as well bring up the Mathematicians Rouser:

e to the x, dy dx
e to the x, dx
secant, cosine, tangent, sine
three point one four one five nine
integral, integral
rah rah rah!

[Derek]

Actually, I went to Georgia Tech, and that's pretty close to one of our cheers.

E to the X dy dx,
E to the X dx,
Tangent Secant Cosine Sine,
3.14159,
Square roots, Cube roots, Poisson brackets,
Dis-integrate ‘em Yellow Jackets!

[Nate the Great]

I suppose as one math professor tells it to a class, who teaches it to the students they TA later, and so forth, it will mutate. Or maybe it's a byproduct of Hodgekin's (or however the heck you spell that name) Law of Parallel Planet Development. In any event, I related the version I was taught.

[Chancellor Valium]

Brek-ek-ex, Bro-ax, Bro-ax!
Brek-ek-ex, Bro-ax, Bro-ax!

[Nate the Great]

Zizzy Zuzzy Zik!

[Sa'ar Chasm]

Brek-ek-ex, Bro-ax, Bro-ax!

Somebody croak that chorus.