## Judge This Joke By Its Size, Do You?

Most everyone knows the classic 7-8-9 joke:

What is 6 afraid of 7?

Because 7 8 9.

I recently heard a Star Wars variation:

According to Yoda, why is 5 afraid of 7?

Because 6 7 8.

This joke isn’t funny unless you understand the syntax often used by Yoda, which involves inverting the word order. See www.yodaquotes.net for some examples.

There are two other variations that have long been part of my arsenal. My favorite is:

Why don’t jokes work in base 8?

Because 7 10 11.

When I told this joke to my seven-year-old son, he said, “I don’t get it.” I asked him how 7, 10, and 11 would be represented in base 8. He thought for a second then said, “7… 8… oh, yeah… yeah, that works.”

That’s why I call this version a *joke grenade*. You pull the pin, and five seconds later, people laugh. Well, *some* people will laugh. Not everyone. I estimate that 5% of the population would understand this joke, and only about 1% would find it funny.

The last variation is multicultural:

What is ε afraid of ζ?

Because ζ η θ.

If you’re thinking, “That’s all Greek to me,” you’re right. The translation is, “Why is epsilon afraid of zeta? Because zeta eta theta.” The Greek alphabet proceeds, in part, as, “…δ (delta), ε (epsilon) ζ (zeta), η (eta), θ (theta), ι (iota)….” But as with all jokes, if it has to be explained to you, then you’re probably not going to find it funny.

## A Father’s Day Gift Worth Waiting For

Alex made a Father’s Day Book for me. Because the book didn’t make it on our trip to France, however, I didn’t receive it until this past weekend. It was worth the wait.

The book was laudatory in praising my handling of routine fatherly duties:

I loved when you took me to Smashburger.

I appreciated when you helped me find a worm.

I love when you read to me at night.

I love when I see you at the sign-out sheet [at after-school care]. It means I can spend time with you.

But my favorite accolade — surprise! — was mathematical:

I liked the multiplication trick you taught me. Take two numbers, find the middle [average], square it. Find the difference [from one number to the average], square it, subtract it. (BOOM! Done!)

Priceless.

The trick that I taught him was how to use the difference of squares to quickly find a product. For instance, if you want to multiply 23 × 17, then…

- The average of 23 an 17 is 20, and 20
^{2}= 400. - The difference between 23 and 20 is 3, and 3
^{2}= 9. - Subtract 400 – 9 = 391.
- So, 23 × 17 = 391.
**BOOM! Done!**

This works because

,

and if you let *a* = 20 and *b* = 3, then you have

.

In particular, I suggested this method if (1) the numbers are relatively small and (2) either both are odd or both are even. I would not recommend this method for finding the product 6,433 × 58:

- The average is 3,245.5, and (3,245.5)
^{2}= 10,533,270.25. - The difference between 6,433 and 3,245.5 is 3,187.5, and (3,187.5)
^{2}= 10,160,156.25. - Subtract 10,533,270.25 – 10,160,156.25 = 373,114.
- So, 6,433 × 58 = 373,114.

Sure, it works, but that problem screams for a calculator. The trick only has utility when the numbers are small and nice enough that finding the square of the average and difference is reasonable.

Then again, it’s not atypical for sons to do unreasonable things…

Son: Would you do my homework?

Dad: Sorry, son, it wouldn’t be right.

Son: That’s okay. Can you give it a try, anyway?

I’m just glad that my sons understand math at an abstract level…

A young boy asks his mother for some help with math. “There are four ducks on a pond. Two more ducks join them on the pond. How many ducks are there?”

The mother is surprised. She asks, “You don’t know what 4 + 2 is?”

“Sure, I do,” says the boy. “It’s 6. But what does that have to do with ducks?”

## Math in France

Driving through the French countryside using smartphone GPS for navigation is a lot like driving through rural Pennsylvania with my redneck cousin riding shotgun — there is a significant lack of sophistication, an ample amount of mispronunciation, and myriad grammatical errors.

In Pennsylvania:

Take that there right onto See-Quo-Eye-Ay (Sequoia) Drive.

In France:

At the roundabout, take the second right toward Ow-Bag-Nee (Aubagne).

Take D51 to Mar-Sigh-Less (Marseilles).

And of course, the GPS pronounced the coastal town of Nice like the adjective you’d use to describe your grandmother’s sweater, though it should sound more like the term you’d use to describe your brother’s daughter.

I was half expecting the computer voice to exclaim,

Hey, cuz, watch this!

Otherwise, the rest of my recent week-long trip to the south of France was intellectually and often mathematically stimulating. The image below shows a -1 used to describe an underground floor (parking) in a hotel:

And though I didn’t get a picture, the retail floor of the parking garage at the Palais de Papes in Avignon was labeled 0, with the three floors below for parking labeled -1, -2, and -3.

This is a country that does **not** fear negative integers.

I also noticed that the nuts on fire hydrants in Aix-en-Provence were squares.

The nuts on American hydrants used to be squares, until hoodlums realized that two pieces of strong wood could be used to remove them, release water into the streets, and create an impromptu pool party for the neighborhood. As a result, pentagonal nuts are now used on most hydrants.

Alas, an adept hoodlum can even remove pentagonal nuts, so some localities have replaced them with Reuleaux triangle nuts, like the ones on hydrants outside the Philadelphia convention center, which can only be removed with a specially forged wrench.

But perhaps the most mathematical fun that France has to offer is the Celsius scale. While there, our cousins taught my sons a poem for intuitively understanding the Celsius scale:

30 is hot,

20 is nice,

10 is cold,

and 0 is ice.

And I was able to teach them a formula for estimating Fahrenheit temperatures, which is easy to calculate and provides a reasonable approximation:

Double the (Celsius) temperature, then add 30.

Or algebraically,

F= 2C+ 30

The actual rule for converting from Fahrenheit to Celsius is more familiar to most students:

F= 1.8C+ 32

This rule, however, sucks. It’s not easy to mentally multiply by 1.8.

My sons were not convinced that the rule for estimating would give a close enough approximation. I showed them a table of values from Excel:

I also showed them a graph with the lines *y* = 1.8*x* + 32 and *y* = 2*x* + 30:

With both representations, it’s fairly clear that the estimate is reasonably close to the actual. For the normal range of values that humans experience, the estimate is typically within 5°. Even for the most extreme conditions — the coldest recorded temperature on Earth was -89°C in Antartica, and the hottest recorded temperature was 54°C in Death Valley, CA — the Fahrenheit estimates are only off by 9° and 20°, respectively. That’s good enough for government work.

And here’s a puzzle problem for an Algebra classroom, using this information.

The Fahrenheit and Celsius scales are related by the formula

F= 1.8C+ 32. But a reasonable estimate of the Fahrenheit temperature can be found by doubling the Celsius temperature and adding 30. For what Celsius temperature in degrees will the actual Fahrenheit temperature equal the estimated Fahrenheit temperature?

It’s not a terribly hard problem… especially if you look at the table of values above.

## Pearls of Wisdom

Although most educators are unaware that the following quotation was coined by Anna Isabella Thackeray Ritchie, almost all of them have heard it before.

Give a man a fish, feed him for a day.

Teach a man to fish, feed him for a lifetime.

It originally appeared in *Mrs. Dymond* as, “If you give a man a fish, he is hungry again in an hour. If you teach him to catch a fish, you do him a good turn.”

A modification of this quotation is similarly poignant and more colorful.

Build a man a fire, warm him for a day.

Set a man on fire, warm him for the rest of his life.

There are more direct modifications of the phrase:

- Teach a man to fish, and you can sell him a ton of accessories.
- Give a man a fish, and you’ll feed him for a day.

Teach a man to fish, and he’ll drink beer all day. - Give a man a fish, feed him for a day.

Don’t teach a man to fish, feed yourself.

He’s a grown man. Fishing’s not that hard, dude.

There are other motivational quotations that I’ve heard throughout my life. One inspired the following image:

A similar pontification has been making its way around the Internet recently, but it gives me pause.

The math of this declaration is highly troubling. Assuming each of the 7 billion people on Earth stood side-by-side and held hands with two other humans, and each of them occupied approximately two feet of width, their entire length would be 2.7 million miles. That’s more than **100 times the distance** around the Earth at the equator.

Using that same estimate — two feet of width per person — it would only take about 65 million people to circle the Earth at the equator. So a better version of this joke might be:

If everyone from California and Texas held hands around the equator, a significant portion of them would drown.

The problem with this modification is obvious. There are those who believe that sacrificing all Californians would be justified if it means being rid of all Texans; and there are those who believe that sacrificing all Texans would be justified if it means being rid of all Californians.

I’ll continue to work on a better modification, but **I’d love to hear some suggestions** from you.

## 13 Math Jokes that are PG-13 (or Worse)

**T****riskaidekaphobia** is an abnormal fear of the number 13. If you suffer from this ailment, then you might want to stop reading now.

Today is the **only** Friday the 13^{th} that will occur in 2014. Which makes it a good day for some trivia questions.

- Is there at least one Friday the 13th every year? If so, prove it. If not, provide a counterexample.
- What is the maximum number of times that Friday the 13th can occur in a (calendar) year?
- What is the average number of times that Friday the 13th occurs in a year?

You can check out my previous post Good Luck on Friday the 13th to find the answers to those questions.

This is also a good day for some off-color math jokes. Then again, is there a bad day for off-color math jokes?

Why is 1 the biggest slut?

It goes into everything.What has six balls and abuses the poor?

The lottery.Math is a collection of cheap tricks and dirty jokes.

What do calculus and my penis have in common?

Both are hard for you.Old statisticians never die.

They just get broken down by age and sex.Algebraists do it in fields.

Or do they do it in groups?What do you call an excited quadrilateral?

An erectangle.What covers the genitalia of a hexahedron?

Cubic hair.A knight with a 20-inch penis told a wizard that he wanted a smaller penis. The wizard told him to propose marriage to an enchanted princess. He did, and the princess said, “No.” His penis instantly shrunk to 16 inches. Happy with this result, he asked her again. Again she said, “No,” and his penis shrunk to 12 inches. He realized that each time she said, “No,” his penis shrunk by 4 inches. So he asked one last time. “How many times do I have to refuse you?” she asked. “No! No! No!”

How is math like sex?

I don’t get either one.How is sex like fractions?

It’s improper for the larger one to be on top.Why did you break up with that math student?

I caught her in bed, wrestling with three unknowns.13 is the square root of 169. What is the square root of 69?

Ate something.

## 2 Truths and a Lie (Mathematician Version)

Here’s the question that started all of the nonsense that follows:

You come to a fork in the road. One fork leads to the village, the other leads to almost certain death. There are three guards stationed at the fork: two always tell the truth, and one always lies. What one question can you ask to one of the guards to find out which fork leads to the village?

There is a truly logical answer to this question, but my favorite answer is:

Did you know they’re giving away free beer in the village?

and then follow all three of them as they sprint toward the village.

A similar question that got me thinking:

A kind but eccentric king has three beautiful daughters. The eldest daughter always tells the truth, the middle daughter always lies, and the youngest daughter will answer any question randomly, either yes or no. To be sure, you would like to marry the one who always tells the truth; but, you are willing to settle for the one who always lies, because at least you’ll always know where you stand. Under no circumstances would you like to marry the crazy one.

The king offers you the hand of one of his daughters in marriage. He allows you to ask one yes/no question of one of the daughters. What question should you ask to ensure that you don’t marry the crazy one?

Variations of this question have been discussed on Straight Dope and xkcd.

And those two questions got me thinking about the icebreaker game *Two Truths and a Lie*, wherein each person at a social gathering tells two truths and one lie about themselves, and the others have to discern fact from fiction.

So I imagined…

What would happen if the most famous mathematicians in history played

Two Truths and A Liewith one another?

The following is what I suspect some of them might say. (The answers follow below.)

**Isaac Newton**

- Newton’s Cannonball is named after one of my thought experiments.
- The city of Newton, MA, is not named after me, but Newton Township, OH, is.
- The Fig Newton, manufactured by Nabisco, is named after me.

**Rene DesCartes**

- I did not get out of bed most days until 11 o’clock in the morning.
- I posited that boiled water freezes more quickly than other water.
- I started college at the age of 10.

**Abraham de Moivre**

- I noted that I was sleeping 15 minutes longer each day, and using that arithmetic progression, I predicted that the day I would sleep for 24 hours would be the exact day of my death — and I was correct.
- I was unable to garner a university post in England, but I was appointed to a Commission of the Royal Society to determine if Newton or Leibniz was the first to discover the calculus.
- I gained great and immediate notoriety for discovering the normal (bell) curve.

**Euclid**

- My name is a Greek word that means “good glory.”
- Abraham Lincoln would often quote me in his speeches.
- I proved the infinitude of primes using a proof by contradiction.

**Gottfried Wilhelm Leibniz**

- I discovered the calculus.
- I invented the first four-function calculator.
- My vast estate was left to my son after my death.

**Leonardo Pisano (Fibonacci)**

- I love rabbits!
- I sometimes used the name Bigollo to refer to myself, which means “good-for-nothing traveler.”
- The 20th century pianist Liberace created his stage name from a contraction of my book title,
*Liber Abaci*.

**Grace Murray Hopper**

- In 1973, I was the first American and the first woman to be elected a Distinguished Fellow of the British Computer Society.
- I invented the computer language COBOL.
- I received 36 honorary degrees.

**Leonhard Euler**

- All of my work, now collected in
*Opera Omnia*, contains over 70 volumes. - In 1735, Guillaume De L’Isle and I prepared a map of the Russian Empire.
- I was the first to use the notation
*f*(*x*) for a function,*e*for the base of natural logs,*i*for the square root of –1, and π for the ratio of circumference to diameter of a circle.

**Diophantus of Alexandria**

- It is believed that I lived to 84 years of age, based entirely on a problem that appeared in a Greek anthology compiled by Metrodorus.
- I was a potato farmer.
- I proved that 24
*n*+ 7 cannot be expressed as the sum of three squares, for integer values of*n*.

**Evariste Galois**

- I was home-schooled until age 12.
- I was killed in a duel, but history is unsure of the other duelist or the reason for the duel.
- I transcribed most of my ideas for what is now called
*Galois theory*the night before the duel.

The third statement from each mathematician was their lie. Below is explication.

Isaac Newton: The Fig Newton is named after the town of Newton, MA, where it was first manufactured.

Rene DesCartes: Actually, he started college at the age of 8.

Abraham de Moivre: In fact, de Moivre’s discovery of the normal curve went almost unnoticed.

Euclid: While many claim that Euclid’s proof of the infinitude of primes uses a proof by contradiction, Michael Hardy and Catherine Woodgold debunk this belief in *Mathematical Intelligencer*, Vol. 31, No. 4, pp. 44–52. Hardy claims that the proof written by Euclid is simpler and more elegant than the proof often attributed to him.

Gottfried Wilhelm Leibniz: He had neither a vast estate nor a son. He was never married, and he died nearly destitute.

Leonardo Pisano (Fibonacci): Though it would be a great piece of trivia, Liberace’s name had nothing to do with Fibonacci. Liberace was a family name; he was born Władziu Valentino Liberace, but he used only his last name on stage.

Grace Murray Hopper: She received at least 37 honorary degrees, perhaps more.

Leonhard Euler: Euler deserves credit for a lot of things, but he does not deserve credit as the first to use π. That distinction belongs to William Jones who used the symbol in 1706.

Diophantus of Alexandria: Though he claimed that 24*n* + 7 cannot be expressed as the sum of three squares, he had no proof of it.

Evariste Galois: The myth that he basically transcribed Galois theory the night before his death is greatly exaggerated. He wrote a lot that evening, but he published three papers in the year before his death, which collectively contained most of his work.

## Peanut Distribution

When we recently bought honey roasted peanuts at the grocery store, Eli speculated that there were 215 peanuts in the jar.

“I think there are less,” Alex said. “My guess is 214.”

“Okay, so now we have to count them,” Eli said.

“No,” I said, explaining that I didn’t want them touching food that others would be eating. I then showed them the back of the jar, which said that one serving contained **about 39 pieces** and the whole jar contained **about 16 servings**. They knew that 39 × 16 would approximate the number of pieces, and they estimated that the jar contained 40 × 15 = 600 pieces.

But then they wanted the actual value, and I wondered how we could use the estimate to find the exact product. More importantly, I wondered if it was possible to find an algorithm that would allow an easily calculated estimate to be converted to the exact value with some minor corrections.

My sons’ estimate used one more than the larger factor and one less than the smaller factor; that is, they found (*m* + 1) × (*n* – 1) to estimate the value of *mn*. A little algebra should help to help to provide some insight.

The product had a value of 600, so further refinement led to:

This led to an algorithm:

- Find an estimate with nice numbers.
- Add 1.
- Add the larger factor.
- Subtract the smaller factor.

This gives 600 + 1 + 39 – 16 = 624. And sure enough, 39 × 16 = 624.

This method works any time you want to find the exact value of a product when the larger factor is one more than a nice number and the smaller factor is one less than a nice number. Just estimate with the nice numbers, then follow the steps. The method can be modified if the larger factor is one less than a nice number and the smaller factor is one more than a nice number:

- Find the estimate.
- Add 1.
- Subtract the larger factor.
- Add the smaller factor.

So if you want to find the product 41 × 14, then the larger factor is one more than 40 and the smaller factor is one less than 15. The estimate is again 40 × 15 = 600.

Then 600 + 1 – 41 + 14 = 574. And sure enough, 41 × 14 = 574.

The same idea can be extended to numbers that aren’t the same distance from nice numbers. But that’s not the point. The intent was not to find general methods for every combination; instead, the hope was to use an easily calculated estimate as the basis for an exact calculation. I’m not sure this method completely succeeds, but it was fun for an afternoon of mental gymnastics.