You know you're a nerd when...

... I woke up at 1:00 am and suddenly a math problem I'd been working on made sense.

I had to write it down.

It's important. I'm teaching this stuff to a billion college students in a month.

You see, when finding an integral, you're finding the area under a function curve.

You can approximate it using rectangles (find the area of a set of rectangles you've fit under the curve).

As you may guess, the more rectangles you fit under there, the more accurate your approximation is.

So, in my mind, I knew that what students tend to want to say is that the integral (or the exact area), is the area when there are infinitely many rectangles under the curve.

But that's not exactly right language.

So for the past few weeks I've been trying to remember the right thing to say.

At 1:00 this morning I remembered.

The integral is the sum of all the rectangles when the size of the base of each rectangle is essentially zero.

I woke up, turned on the light, wrote it down, and went back to sleep.

Glad we could get that taken care of. :)