Knowing the punchline is half the fun

OK, so there I am the other day, tooling along in class, talking about one of the coolest numbers on the planet when I seemed to forget I was not in the classroom alone. I had warned the students previous to this event that this might happen occasionally. Once in a while, my inner geek rises to the surface and—BLAMMO!—unwary onlookers are left in the dust.

The number responsible for this is e. It is just as cool as π but gets almost no press. You never hear of people memorizing e. As far as pop culture goes, e is getting short shrifted. Just what is a shrift anyway? And does size matter?

One more common way of describing where the value e occurs is in the following expression:

Ready for what seems like a mathematical paradox? The value for n can increase without bound. Pass Go, get your $200 and don't even slow down. Yet the overall value of the expression has a limit. It will never get bigger than e ≈ 2.71828 18284 59045 23536 ... Isn't that cool?

Can you tell my geek personality has taken control of my body right now? A similar thing happened in class. I was sharing the next occurrence of e with the students: pick a random number between 0 and 1. Go ahead, you've got an infinite amount to choose from. Now pick another number and add it to the first one. Keep picking and adding until the sum is 1 or greater. When it is stop and count how many numbers you had to pick. Then repeat the process; keep summing random values between 0 and 1 until the sum is greater than 1. When you've repeated the process a goodly number of times, find the average number of numbers you had to pick to exceed 1. That average will be—you guessed it—e.

It was right at this moment, this exciting climax when a student calmly asked: if we know the value of e why do we have to keep determining it?

(sigh) I felt I was in the room alone. Oh, well. I had a good time and hopefully my enthusiasm will prove contagious someday. Today was just not the day.

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Ode to e (and other math jokes/rhymes)
If (1+x) (real close to 1)
Is raised to the power of 1
Over x, you will find
Here's the value defined:
2.718281...

It takes a peasant to multiply.