The Math Department Joke Drawer

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The Math Department
Joke Drawer
Jokes from my bottom desk drawer, sorted by course,
plus the old proof that 1 = 2, and the exact step where it cheats

Arithmetic · Algebra · Geometry · Statistics · Calculus · 1 = 2 · Office Hours
Good afternoon. Please take out a sheet of paper. (Just kidding. There's no quiz.)

My name is James Farrell, and I've taught mathematics at a community college here in Spokane, Washington, since the fall of 1979. Twenty years, give or take a sabbatical. I teach everything from the basic arithmetic review to second-quarter calculus, and I've had students who were seventeen and students who were seventy-one, and they all, every one of them, start packing up their books about five minutes before the end of class.

So in about 1981 I started using those last five minutes for a joke. One joke, after the homework is on the board and before anybody leaves. A student had asked me that spring whether math teachers had a sense of humor, and I couldn't think of a single joke to prove it, so I went home and wrote one. Then another. They live in the bottom left drawer of my desk, on index cards, one manila folder per course, and the drawer no longer closes all the way.

A few ground rules. Every joke here is my own, written for a particular class on a particular day. You won't find the famous ones; those belong to everybody and you've heard them all. No student is ever named, in a joke or out of one. And like every course in the catalog, each joke has a prerequisite.

Arithmetic

Seven and eight got married. Fifty-six people came to the reception. To this day nobody can say who invited them.
Prerequisite: your sevens and eights, which everybody gets wrong at least once.

A fraction is just a whole number that's been through something.
Prerequisite: fractions; having been through something.

Zero is the humblest number there is. All by itself it's worth nothing. But stand it behind somebody and they're suddenly worth ten times as much. Every office has a zero like that. Be the zero.
Prerequisite: place value; a job.

The remainder is the only part of long division that gets to leave early.
Prerequisite: long division; a ride home.

Subtracting a negative is like cleaning out my desk: the more bad things I take away, the better off I am.
Prerequisite: integers; believing that minus a minus is a plus, which nobody does the first time.

I asked a class to estimate an answer. One fellow said "about seven." I said, "Seven what?" He said, "About."
Prerequisite: rounding; the end of a long day.

Algebra

I asked the class what they'd do with an equation that had two unknowns. A woman in the back row said she'd introduce them and let them work it out themselves.
Prerequisite: systems of equations; an aunt who sets people up.

FOIL is the only rule in algebra named after something you wrap leftovers in.
Prerequisite: multiplying binomials; a refrigerator.

x has been missing since the second week of the quarter. Every test, the whole class goes out looking for it. It always turns up exactly where it was the whole time: on the other side of the equals sign.
Prerequisite: solving for x; patience.

The slope of my driveway is undefined. That's why I park on the street.
Prerequisite: slope, especially vertical lines; a house on the South Hill.

The number i came into my office and said, "Everybody says I'm only imaginary." I said, "Square yourself and tell me how you feel." It said, "Negative."
Prerequisite: imaginary numbers; a bad Monday.

A polynomial walked into a tavern and offered to buy a round for every term in the place. The bartender said, "Like terms only."
Prerequisite: combining like terms; being twenty-one.

Geometry

A circle has no corners, which is why it wins every argument. You can never back it into one.
Prerequisite: the definition of a circle.

The hypotenuse is the longest side of a right triangle, and it has never once let the other two sides forget it.
Prerequisite: the Pythagorean theorem; an older sibling.

A tangent line touches the circle at exactly one point and then goes politely on its way. My mother would have called that the ideal visit.
Prerequisite: tangent lines; a mother with standards.

An obtuse angle is just a right angle that has relaxed a little since high school.
Prerequisite: measuring angles; a twentieth reunion.

Two triangles are congruent if they match side for side and angle for angle. My two brothers and I are congruent on exactly one subject, which is our mother's pot roast. On everything else we're merely similar.
Prerequisite: congruent and similar triangles; brothers.

Statistics

A survey found that four out of five people who answer surveys enjoy answering surveys. The fifth one hung up.
Prerequisite: sampling and bias.

The standard deviation of student excuses is remarkably small. Nearly all of them fall within one printer of the mean.
Prerequisite: the normal curve; a printer.

I wear my brown tie on test days, and it has rained on every test day this year. I've explained to the class that correlation is not causation. They still want me to burn the tie.
Prerequisite: correlation; a brown tie.

A statistician's wife asked him if he loved her. He said, "With ninety-five percent confidence." She asked about the other five percent. He's been sleeping on the couch ever since, give or take a night.
Prerequisite: confidence intervals; knowing when to stop talking.

The mode is the most popular number in the set, and, like most popular things, it isn't always the most useful.
Prerequisite: mean, median and mode; high school.

My chances of winning the lottery are just about the same whether I buy a ticket or not. I've been very consistent about not buying one.
Prerequisite: probability; restraint.

Calculus

A limit is how close you can get to something without ever actually reaching it. My wife Lynnette says that's also my plan for cleaning out the garage.
Prerequisite: limits; a garage.

The constant of integration is the plus C that everybody forgets. It's the cousin who never says a word at the reunion but would be very hurt not to be invited.
Prerequisite: antiderivatives; a large family.

Integration by parts: take something hard, split it in two, and hope the second half is easier. It's also how I put together bookshelves.
Prerequisite: integration by parts; a hex wrench.

Every function wants to be continuous. Some of them just have a lot going on at home.
Prerequisite: continuity; compassion.

L'Hôpital's rule is for when you get zero over zero, which is also what I get when I ask an eight o'clock class whether there are any questions.
Prerequisite: L'Hôpital's rule; an 8 a.m. section.

The derivative of my salary with respect to time has been very close to zero since about 1993.
Prerequisite: derivatives; the state budget.

Proof That 1 = 2
(and where it cheats)

This one is older than I am and older than anyone I know. I show it to every algebra class in the last week of the quarter, and I give them the weekend to find the trick before I tell them. Here it is. Read each step and ask yourself whether it's legal.

Start with two numbers that are equal. Call them a and b, and let them both be 1.

Step 1	a = b Given. Both are 1.
Step 2	a² = ab Multiply both sides by a.
Step 3	a² - b² = ab - b² Subtract b² from both sides.
Step 4	(a + b)(a - b) = b(a - b) Factor both sides. The left is a difference of squares; the right has a common factor of b.
Step 5	a + b = b Divide both sides by (a - b).
Step 6	2b = b Since a = b, replace a with b: b + b = b.
Step 7	2 = 1 Divide both sides by b.

Found it? Don't scroll yet if you want to try. Get a cup of coffee and come back.

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It's Step 5.

Look at what we divided by: (a - b). But a and b are equal. So a - b is 1 - 1, which is zero. Step 5 divides both sides by zero, and that's the one thing in arithmetic you are never, ever allowed to do.

Here's how you can see it with your own eyes. Put the numbers in. In Step 4 the left side is (1 + 1)(1 - 1), which is 2 times 0, which is 0. The right side is 1 times (1 - 1), which is 1 times 0, which is 0. So Step 4 says 0 = 0. Perfectly true. Every step up to there is true.

Then Step 5 "cancels" the zero from each side, as if 2 times 0 and 1 times 0 being equal meant 2 and 1 were equal. They aren't. Anything times zero is zero, so knowing that two things times zero came out the same tells you nothing at all about the two things. That's exactly why division by zero is against the rules. If it were allowed, you could prove any number equals any other number, and my paycheck would equal the president's. (Step 7 is fine, by the way. It divides by b, and b is 1.)

The moral, which I write on the board in yellow: before you divide by anything, make sure it isn't zero. In algebra, the zeros hide inside the parentheses.

Next Door

Every drawer needs a neighbor. Mine is Mr. A's Periodic Table of Puns, from a retired high school chemistry teacher in Wisconsin who opened every class with a pun for thirty-four years and rates them all on his Groan-O-Meter. He opened with his. I close with mine. Between the two of us, we have the whole period covered.

And if you're one of my students and you came here looking for the homework: it's on the board. It was always on the board. See Office Hours.

You are student number

in this section since January 1998. (A prime, as of this morning.)

Jokes for the drawer, or questions about your homework:
[email protected]

Last updated Thursday, September 23, 1999
Fall quarter started this week. The drawer is open.