Category: Humor

Red card

As I visited our student workroom one afternoon, a small group of students were killing time by kicking a miniature soccer ball around. As tried to walk by, one student tried to trap an errant pass and gave me a good kick in the shin. Of course, he was mortified.

Naturally, I had the only reasonable response to this stimulus: I quickly spotted a dark red index card and held it silently in the air in his direction.

That Makes It Invertible!

There are several ways of determining whether an n \times n matrix {\bf A} has an inverse:

  1. \det {\bf A} \ne 0
  2. The span of the row vectors is \mathbb{R}^n
  3. Every matrix equation {\bf Ax} = {\bf b} has a unique solution
  4. The row vectors are linearly independent
  5. When applying Gaussian elimination, {\bf A} reduces to the identity matrix {\bf I}
  6. The only solution of {\bf Ax} = {\bf 0} is the trivial solution {\bf x} = {\bf 0}
  7. {\bf A} has only nonzero eigenvalues
  8. The rank of {\bf A} is equal to n

Of course, it’s far more fun to remember these facts in verse (pun intended). From the YouTube description, here’s a Linear Algebra parody of One Direction’s “What Makes You Beautiful”. Performed 3/8/13 in the final lecture of Math 40: Linear Algebra at Harvey Mudd College, by “The Three Directions.”

While I’m on the topic, here’s a brilliant One Direction mashup featuring the cast of Downton Abbey. Two giants of British entertainment have finally joined forces.

More on divisibility

Based on my students’ reactions, I gave my best math joke in years as I went over the proofs for checking that an integer was a multiple of 3 or a multiple of 9. I started by proving a lemma that 9 is always a factor of 10^k - 1. I asked my students how I’d write out 10^k - 1, and they correctly answered 99{\dots}9, a numeral with k consecutive 9s. So I said, “Who let the dogs out? Me. See: k nines.”

Some of my students laughed so hard that they cried.

There are actually at least three ways of proving this lemma. I love lemmas like these, as they offer a way of, in the words of my former professor Arnold Ross, to think deeply about simple things.

(1) By subtracting, 10^k - 1 = 99{\dots}9 = 9 \times 11{\dots}1, which is clearly a multiple of 9.

(2) We can use the rule

a^k - b^k = (a-b) \left(a^{k-1} + a^{k-2} b + \dots + a b^{k-2} + b^{k-1} \right)

The conclusion follows by letting a = 10 and b =1.

From my experience, my senior math majors all learned the rule for factoring the difference of two squares, but very few learned the rule for factoring the difference of two cubes, while almost none of them learned the general factorization rule above. As always, it’s not my students’ fault that they weren’t taught these things when they were younger.

I also supplement this proof with a challenge to connect Proof #2 with Proof #1… why does 11{\dots}1 = \left(a^{k-1} + a^{k-2} b + \dots + a b^{k-2} + b^{k-1} \right)?

(3) We can use mathematical induction.

If k = 0, then 10^k - 1 = 0, which is a multiple of 9.

We now assume that 10^k - 1 is a multiple of 9.

To show that 10^{k+1}-1 is a multiple of 9, we observe that

10^{k+1}-1 = \left(10^{k+1} - 10^k \right) + \left(10^k - 1\right) = 10^k (10-1) + \left(10^k - 1\right),

and both terms on the right-hand side are multiples of 9. (I also challenge my students to connect the right-hand side with the original expression 99{\dots}9.)

\hbox{QED}

Bad puns

I thought I saw an eye-doctor on an Alaskan island, but it turned out to be an optical Aleutian.

No matter how much you push the envelope, it’ll still be stationery.

A dog gave birth to puppies near the road and was cited for littering.

A grenade thrown into a kitchen in France would result in Linoleum Blownapart.

Two silk worms had a race. They ended up in a tie.

Time flies like an arrow. Fruit flies like a banana.

Two hats were hanging on a hat rack in the hallway. One hat said to the other: ‘You stay here; I’ll go on a head.’

I wondered why the baseball kept getting bigger. Then it hit me.

A sign on the lawn at a drug rehab center said: ‘Keep off the Grass.’

The midget fortune-teller who escaped from prison was a small medium at large.

The soldier who survived mustard gas and pepper spray is now a seasoned veteran.

A backward poet writes inverse.

In a democracy it’s your vote that counts. In feudalism it’s your count that votes.

If you jumped off the bridge in Paris, you’d be in Seine.

A vulture carrying two dead raccoons boards an airplane. The stewardess looks at him and says, ‘I’m sorry, sir, only one carrion allowed per passenger.’

Two Eskimos sitting in a kayak were chilly, so they lit a fire in the craft. Unsurprisingly it sank, proving once again that you can’t have your kayak and heat it too.

Two hydrogen atoms meet. One says, ‘I’ve lost my electron.’ The other says, ‘Are you sure?’ The first replies, ‘Yes, I’m positive.’

Did you hear about the Buddhist who refused Novocain during a root-canal? His goal: transcend dental medication.

There was the person who sent ten puns to friends, with the hope that at least one of the puns would make them laugh. No pun in ten did.

green lineAnd now for some math puns:

What’s purple and commutes? An Abelian grape.

What is lavender and commutes? An Abelian semigrape.

What’s purple, commutes, and is worshipped by a limited number of people? A finitely-venerated Abelian grape.

What do you get when you cross a mountain goat with a mountain climber? You can’t — a mountain climber is a scalar.

How does a linear algebraist get an elephant in a refrigerator? He splits the elephant into components, stuffs the components in the refrigerator, and declares the refrigerator closed under addition.