Archive for October, 2010
Math Jokes for Halloween
Tom Lehrer said, “Base eight is just like base ten, really… if you’re missing two fingers!”
Ever notice that cartoon hands only have four fingers? There’s a very simple reason for that — it’s easier to draw a hand with four fingers than with five fingers. But have you ever wondered what it would be like to have only four fingers on each hand? For one thing, you’d count in base eight, not base ten. For another, you’d never be able to give someone a high five.
Base eight and base ten are relevant to a math joke that’s appropriate for today:
Why do mathematicians sometimes confuse Halloween and Christmas?
Because Oct 31 = Dec 25.
It’s a wonderful coincidence that October 31 and December 25 both happen to be days with significance, which is why that joke works. It’s no coincidence, however, that the abbreviations for October (Oct) and December (Dec) could also be the abbreviations for the octal (base 8) and decimal (base 10) number systems. In the old Roman calendar, October was the 8th month, and December was the 10th month. When the Julian calendar was created, July and August were added in the middle of the year, pushing October and December to the 10th and 12th slots, respectively.
Math and Disks
Math is only one of my passions. Ultimate Frisbee is the other. I’m playing this week at the USA Ultimate National Championships in Sarasota, FL.
Many mathy folks love Ultimate Frisbee, and I think that has to do with the beautiful physics of a disk in flight. One of my favorite quotes:
When a ball dreams, it dreams it’s a Frisbee.
– Stancil Johnson (Disc Golf Hall of Fame 2003)
I have several mathy jokes about various types of disks. For computer scientists…
How am I supposed to back up my hard disk if I can’t find the reverse switch?
For physicists…
There was a young fellow named Fisk,
A swordsman, exceedingly brisk.
So fast was his action,
The Lorentz contraction
Reduced his rapier to a disk.
And for mathematicians…
What is the volume of a disk with radius z and height a? pi · z · z · a
Song: New Math
Bo Burnham is an offcolor, singing comedian. His song New Math, while slightly distasteful and potentially offensive, is catchy, funny, and filled with many jokes for mathy folks. When I listened to the song on his live CD, I noticed that some of the funniest jokes elicited almost no laughs from the audience. So below, I provide annotations for the math in the song, knowing full well that things just aren’t as funny if they have to be explained. As E. B. White said, “Humor can be dissected as a frog can, but the thing dies in the process and the innards are discouraging to any but the pure scientific mind.” Oh, well.
So here’s a song that takes something that’s not so fun — math — and makes it offensive.
What’s a pirate minus the ship? Just a creative homeless guy.
And an anteater plus a large hungry mutant ant? An ironic way to die.
And what’s domain, domain, range? A kid with too much in his pants.
Domain refers to x‑coordinates and range refers to y‑coordinates. So “domain, domain, range” implies XXY, the genetic makeup for a male with Klinefelter’s syndrome.
And two balls minus one? Six titles at the Tour de France.
A reference to Lance Armstrong, who survived testicular cancer.
Split a decision with long division,
Take the circumference of your circumcision.
Live like your data, and when you’re all “set,”
Put it all together, and whatever you get…It’s new math.
What’s a bag of chips divided by five? Well, that’s a Nike worker’s meal.
And Santa Claus multiplied by i? Well, I guess that makes him real.
The imaginary part of a complex number contains i, the imaginary value equal to the square root of ‑1. Since i × i = 1, the product of two imaginary numbers is a real number. The implication is that Santa Claus, being imaginary, becomes real when multiplied by the imaginary number i.
And the square root of the NBA is Africa in a box.
How do you trace a scatterplot? Give the pencil to Michael J. Fox.Take the approximate moral proportion
Of the probable problem of a prolife abortion.
Live like your data, and when you’re all “set,”
Put it all together, and whatever you get…It’s new math.
And if you made a factor tree
Of the factors that caused my girl to leave me,
You’d have a tree…
Full of Asian porn.
Well, CAL, see you later.
A clever way to divide and pronounce the word calculator: CALCULATOR.
Mathematical minds make industrial smog.
And what’s the opposite of ln(x)? Duraflame, the unnatural log.
ln(x) is the natural log, so it’s opposite would be an unnatural log.
Support the farmers with a pro‑tractor.
One of my favorite jokes!
Link Kennedy and Lincoln with a common factor.
Numerologists have made a lot of hullaballoo about the coincidences between Kennedy and Lincoln. You can read about them, and their veracity, at snopes.com.
Live like your data, and when you’re all “set,”
Put it all together, and whatever you get…Yeah, it’s new, it’s new, it’s new, it’s new…
It’s new math.Okay, word problems…
If there’s a fat guy in a pastry shop with a $20 bill and he’s ready to buy,
In order to predict his volume change, you need to know the value of π.
A pun since π could refer to the mathematical constant (pi) or to the dessert (pie).
And if there’s a metal train that’s a mile long
And at the very back a lightning bolt struck her,
How long till it reaches and kills the driver,
Provided that he’s a good conductor?
Another pun, conductor referring either to a train engineer or an electrical conduit.
And if 10% of men are gay,
And 20% of men are Chinese,
What are the odds that a man chosen at random
Spends his free time and his mealtime while on his knees?And if Kim is half as old as Bobby,
Who is two years older than 12‑year old Tory,
For how many more 30‑day months
Will their threesomes be considered statutory… rape?
A distasteful reference to standard algebra age problems.
Because math can be sexy…
Cause having sex is like quadratic expansion —
If it can’t be split, then it’s time to stop.
A trinomial expression (in the form ax^{2} + bx + c) can often be factored into two binomials. But the general rule for high school algebra classes is to simplify the expression only if it divides nicely; otherwise, leave it alone.
And having sex is like doing fractions —
It’s improper for the larger one to be on top.
An improper fraction is a fraction where the numerator is larger than the denominator.
And having sex is like math homework —
I do it best when I’m alone in my bed.And squaring numbers are just like women —
If they’re under 13, just do them in your head…
In school, students are often expected to memorize the values of the squares of small positive integers.
Science Festival
If you’re in Washington, DC, this weekend, check out the USA Science and Engineering Festival.
With over 1,500 exhibits for math, science, and engineering, the National Mall will be filled with geeksaplenty. NCTM will be participating in the event, running an activity based on the Bears in a Boat lesson from Illuminations. (I’ll be manning the exhibit on Saturday; if you’re there, stop by Booth 410 to say hello.)
A mathematician, an engineer, and a physicist are scheduled to appear at a science and engineering festival. Arriving in Washington, DC, they spy a festival (*) on the National Mall.
The physicist is driving the car. While stopped at a stoplight, he performs some calculations to determine the exact amount of acceleration needed so that the car will roll to a stop at the entrance to the festival. When the light changes green, he depresses the gas pedal for 2.837 seconds and then releases it. The car accelerates to 22 miles per hour, then slowly decelerates and comes to a stop approximately 150 meters beyond the festival. “Hmm,” he says, perplexed that his calculations failed him.
“You missed,” says the engineer. “My turn.” The engineer and physicist swap seats so the engineer can drive. They return to the same stoplight. The engineer then estimates the distance to the festival based on the position of the sun and the length of the shadow cast by the Washington Monument. He then finds the answer to the problem in a lookup table. He depresses the gas pedal until the car reaches a speed of 21 miles per hour and releases his foot. The car gently rolls to a stop 150 meters short of the festival entrance.
“Well,” says the physicist, “it seems that your method wasn’t very successful, either.”
“What are you talking about?” says the mathematician. “On average, the two of you arrived perfectly!”
(*) How did they know it was science and engineering festival?
The physicist observed that it behaved like a science and engineering festival, so it must be a science and engineering festival.
The mathematician compared it to a festival he had attended a year before, thereby reducing it to a previously solved problem.
The engineer was looking for a science and engineering festival; therefore, it was a science and engineering festival.
Kids’ Favorite Jokes
I have twin sons. They’re 3½ years old, and they love numbers. As shown below, they love calculators, too — Eli (on the left) prefers the TI‑73 Explorer, while Alex prefers the TI‑83 Plus.
They used to enjoy the Alpha‑Lock feature, because they could type their name, our address, and other words. But recently, they’ve been having fun entering expressions to see the result. Their grandpa called the other day, and when he heard they were playing with calculators, he started quizzing them with addition problems. (Understand, I have an issue with the boys “learning” their number facts with a calculator before they understand the concept. That said, I’m pretty sure they understand addition conceptually, and even if they don’t, who am I to prevent Pop Pop from having fun with his grandsons?) He began by giving them some onedigit addition problems: 2 + 3, 5 + 8, etc. They’d enter the expressions and then tell him the answer. (Usually, I’d cover the screen so they couldn’t see the answer, and I’d make them figure the answer in their head first.) Then he asked them, “What is 12 + 12?” Without entering anything, Alex said, “12 is 6 + 6, so 12 + 12 is 6 + 6 + 6 + 6.” He paused to think for a moment, then asked, “How much is four 6’s, daddy?”
“Holy crap,” I said to my wife. “He’s ready for multiplication!”
My wife rolled her eyes. “Easy there, tiger,” she said. “He’s only 3½.”
Then yesterday, Pop Pop called again and asked the boys, “Who wants to give me a math problem?” I could not have been prouder when Eli said,
What do you get when a bird crosses a zero?
Pop Pop was confused by the question until Eli shouted the answer:
A flying none!
(Actually, I suppose I could have been prouder had Eli said, “You can’t cross them, because zero is a scalar.”)
Alex then offered a joke as well:
What did 0 say to 8?
Nice belt!
It seems the rotten apple doesn’t fall far from the infested tree.
Anyway, here’s a math joke about twins…
A statistician’s wife gives birth to twins. Excitedly, he calls everyone to share the good news. When he calls the minister, the minister says, “That’s terrific! Bring them down to church this Sunday, and we’ll baptize them!”
“Uh, let’s just baptize one of them,” says the statistician. “We can keep the other one as a control.”
Fun Factor
Two numbers were having a conversation about their social lives.
28: Did you hear that 284 broke up with 220?
6: I’m not surprised. He’s far from perfect. But at least their breakup was amicable.
28: Yeah, well, I heard she started seeing 12.
6: Really? He doesn’t have abundant charm. Don’t you think 10 would be a better match for her?
28: I don’t know. He seems so solitary!
Speaking of factors, I learned a neat trick this weekend for finding the sum of the factors of a number. Before I share that, consider the method for determining how many factors a number has. Take the number 12, for instance. The prime factorization of 12 is:
12 = 2^{2} × 3
The following array can be used to generate all of the factors of 12:

2^{0}  2^{1}  2^{2} 
3^{0}  1  2  4 
3^{1}  3  6  12 
It’s obvious from the array that there are six factors. But the trick is to notice that each factor in the array is made from a power of 2 times a power of 3 — that is, each factor is equal to 2^{m} × 3^{n}, where 0 ≤ m ≤ 2 and 0 ≤ n ≤ 1. Since there are three possible values of m and two possible values for n, then there are 3 × 2 = 6 factors of 12.
In general, if the prime factorization of the number takes the form a^{p} × b^{q} × c^{r}, then the number of factors is (p + 1)(q + 1)(r + 1) for exponents p, q, and r. (The process could obviously be extended if there are more than three prime factors.)
But look at the array again. The sum of all factors of 12 is equal to sum of all products that occur within the array. However, there is an easy way to find that sum, by taking advantage of the distributive property. The sum of the powers of 2 along the top is 2^{0} + 2^{1} + 2^{2} = 7, and the sum of the powers of 3 along the left side is 3^{0} + 3^{1} = 4. Consequently, the sum of all factors of 12 is equal to:
(2^{0} + 2^{1} + 2^{2})(3^{0} + 3^{1}) = 7 × 4 = 28
In general, if the prime factorization of a number is a^{p} × b^{q} × c^{r}, then the sum of the factors is:
(a^{0} + a^{1} + … + a^{p})(b^{0} + b^{1} + … + b^{q})(c^{0} + c^{1} + … + c^{r})
And again, this could be extended if the number had more than three prime factors.
Cool, huh?
Functional Exponents
Overheard at the NCTM Regional Meeting in Baltimore:
In the expression x^{3}, what do you call the 3?
An exponent.In the expression y^{2}, what do you call the 2?
A y‑ponent.
Speaking of exponents — though apropos of absolutely nothing — here’s an equation that appeared in the 1995 Halloween episode of The Simpsons:
1782^{12} + 1841^{12} = 1922^{12}
Without a calculator, can you determine whether it’s true or false?