Why do mathematicians celebrate Christmas and Halloween on the same day?
Because Oct 31 equals Dec 25.

What do you get if you cross a dog and a cat?
cat dog sine theta

What do you get if you cross a dog and a mountain climber?
Nothing. A mountain climber is a scalar.

A constant function and e^x are walking on Broadway. Then suddenly the constant function sees a differential operator approaching and runs away. so e to-the x follows him and asks why the hurry. "Well, you see, there's this diff.operator coming this way, and when we meet, he'll differentiate me and nothing will be left of me...!" "Ah," says e^x, "he won't bother ME, I'm e to-the x!" and he walks on. Of course he meets the differential operator after a short distance.

Also in all seriousness, I understand all of them. I do not know if this is good or bad.

The first joke is based on number systems. The octal (that is, base 8) equivalent of decimal (base 10, what we usually use) 25 is in fact 31. To understand this, the place of a digit represents the base value to the (place minus 1)-th power. That is, in the decimal version of this, 5 times 10^0 is 5, and 2 times 10^1 is 20. 20+5 is 25, duh. With octal 31, 1 times 8^0 is 1, and 3 times 8^1 is 24. 24+1 is...25. Thus, they're equal.

The second joke refers to a function in vector calculus, the cross product. If you want the scalar result of the cross of two vectors, it can be found by multiplying the two times the sine of theta (theta being the angle between the vectors).

The third is also cross-product related. You can't cross a vector and a scalar. I'll leave it to you to decide why a mountain climber is a scalar.

In the fourth, it's important to know that if you differentiate a constant, it becomes zero, hence the constant's fear in the joke. If you differentiate e^x with respect to x, it doesn't change (and it's the only function that does that, as far as I know). But, because the differential operator turned out to be d/dy, e^x would be differentiated with respect to y, and since there's no y, it too would become zero.

Remember, in second grade, or so, when you did math and learned about the "ones" column, and the "tens" column, and the "hundreds" column, and so on? Well, keep that idea in mind.

Decimal is what we normally use. It's called "base 10". This means that you count one through nine w/ a single digit, then write ten w/ two digits. Octal is base 8. That means you can only count up to seven w/ one-digit numbers, then you have to write eight w/ two digits. So, eight in octal is written "10". Don't think of "10" as "ten"; think of it as "one-zero".

Picture it in these terms: think of a car odometer. The dial on the right spins from 0 through 9. When it passes 9, it goes back to 0, and the dial one space to the left advances. This keeps repeating until the second dial passes 9, then it goes to 0, and the next one over advances. And so on.

Now replace the dials w/ ones that, instead of going from 0 to 9, go from 0 to 7. When a dial passes 7, the one to the left advances. This odometer will count in octal. So, the numbers in octal go:

0
1
2
3
4
5
6
7
10
11
12
13
14
15
16
17
20
21
22

And so forth. This doesn't mean you can't write the number "eight" or "nine" in octal. "Eight" is written "10" and "nine" is written "11". This is why you should think of "10" as "one-zero", not "ten", when dealing w/ other bases.

Joke, really, but seriously, this stuff can really confuse the minds of even the most mathematically literate around here, including myself.

[ August 11, 2001: Message edited by: Tahna Los ]

I swear to god, I will never take another calculus course again.

[ August 11, 2001: Message edited by: Tahna Los ]