Teacher: “Would you like a pocket calculator?”

Student: “No, thanks. I already know how many pockets I have.”

Thanks, Alden!

Of course, that reminded me of this gem from Spiked Math:

And one final pocket joke:

The department chair said to the math teachers, “I have good news, and I have bad news. The good news is, we have enough money for a new microwave in the staff lounge.” The teachers cheered! Then one of them asked, “What’s the bad news?” The chair said, “It’s still in your pockets.”

Ouch.

]]>McDonald’s sells 75 hamburgers every second.

But I’m a math guy, so there’s no doubt where my mind turned after that emotion passed:

How many cows is that?

Have at it, internet.

]]>What do you get when you divide the circumference of a bovine by its diameter?

Cow pi.What is the favorite course at Bovine College?

Cowculus.A mathematician counted 196 cows in the field. But when he rounded them up, he got 200.

Good morning! It’s National Dictionary Day. Ever wonder what the shortest word is? Technically, it’s a toss-up between the single letter words

andI, but sinceais always capitalized, I’d sayIis just a little shorter.a

Is there anything more powerful than a language arts joke to get the day off to a good start?

I have no words to describe today. I do, however, have a ton of obscene gestures.

So, what’s the shortest **math** word? Technically, *e* and *i*, but if you don’t like constants, then you’ll have to settle for the three-letter words *set* and *box*.

And what’s the longest math word — at least based on the list at Math Words? It has 17 letters, and you’ll get a big hint if you check the time.

What two math words, both having the same number of letters, are equally appropriate to describe a triangle whose sides are congruent?

And what’s the funniest math word? Personally, I think it’s *syzygy*, but according to Tomas Engelthaler, it’s *logic*. In Humor Norms for 4,997 English Words, Engelthaler and Hills (2017) describe a method for determining which words are funniest. I emailed Engelthaler to ask which math word is funniest, and he responded as if it were a completely reasonable question. Without hesitation, he shared a list of math words and their humor rankings, and these five were at the top of the list:

- logic
- math
- theory
- science
- graph

The overall funniest English word, according to Engelthaler’s research? *Booty*. Go figure.

While you may not think that any of those words, mathy or otherwise, are laugh-out-loud funny, this isn’t debatable; it’s based on science.

If you take issue with this research, you’ll need to discuss it with Engelthaler and his colleagues. Please write to him directly to say that you’re bumfuzzled, that his research is malarkey, or that you think he’s a nincompoop.

]]>But the probability of doing that four times in a row is much lower, somewhere closer to 0.0039, or about 1 in 250.

Now, imagine flipping 100 coins four times, and getting the same number of heads each time. The odds of that happening are only slightly better than impossible. In fact, if every person *in the entire world* were to flip 100 coins four times, it would still be highly unlikely that this would ever happen.

That’s how rare it is, and it gives you some idea of what Major League Baseball player Khris Davis just pulled off. The Oakland Athletics outfielder just finished his fourth consecutive season with a batting average of .247. That’s right — the same average four seasons in a row.

Davis had some advantage over our coins, though. For starters, he wasn’t required to have the same number of at-bats every year. Moreover, batting averages are rounded to three decimal places, so his average wasn’t *exactly* the same during those four years; it was just really, really close:

**2015**: .24745 (97 hits in 392 at-bats)**2016**: .24685 (137 in 555)**2017**: .24735 (140 in 566)**2018**: .24653 (142 in 576)

How could something like this happen? According to Davis, “I guess it was meant to be.“

Perhaps it *was* predestination, but I prefer to put my faith in numbers.

Empirically, we can look at the data. From 1876 to present, there have been 19,103 players in the major leagues. The average length of an MLB career is about 5.6 years, which means that an average player would have about three chances to record the same batting average four seasons in a row. It’s then reasonable to say that there have been approximately 3 × 19,103 = 57,309 opportunities for this to happen, yet Khris Davis is the only one to accomplish this feat. So experimentally, the probability is about 1 in 60,000.

Theoretically, we can look at the number of ways a player could finish a season with a .247 batting average. In 2007, the Phillies’ Jimmy Rollins recorded an astounding 716 at-bats. That’s the most ever by a Major League Baseball player. So using a sample space from 1 to 716 at-bats, I determined the number of ways to achieve a .247 batting average:

- 18 hits, 73 at-bats
- 19 hits, 77 at-bats
- 20 hits, 81 at-bats
- 21 hits, 85 at-bats
- 22 hits, 89 at-bats
- 36 hits, 146 at-bats
- …
- 161 hits, 652 at-bats
- 161 hits, 653 at-bats
- …
- 177 hits, 716 at-bats

And, of course, there are the examples above from Davis’s last four seasons.

It’s interesting that it’s not possible to obtain a batting average of .247 if the number of at-bats is anywhere from 90 to 145; yet it’s possible to hit .247 with 161 hits for either 652 or 653 at-bats. I guess it’s like Ernie said: “That’s how the numbers go.“

All told, **there are 245 different ways to hit .247** if the number of at-bats is 716 or fewer.

That may sound like a lot, but consider the alternative: there are 256,441 ways to **not** hit .247 with 716 or fewer at-bats.

So, yeah. No matter how you look at it, what Davis did is pretty ridiculous. Almost as ridiculous as what happened to Saul…

Saul is working in his store when he hears a voice from above. “Saul, sell your business,” the voice says. He ignores it. His business is doing well, and he’s happy. “Saul, sell your business,” the voice repeats. The voice goes on like this for days, then weeks. “Saul, sell your business.” Finally, Saul can’t take it any more. He finds a buyer and sells his business for a nice profit.

“Saul, take your money, and go to Las Vegas,” the voice says.

“But why?” asks Saul. “I have enough to retire!”

“Saul, take your money to Las Vegas,” the voice repeats. It is incessant. Finally, Saul relents and heads to Vegas.

“Saul, go to the blackjack table and bet all your money on one hand.”

He hesitates for a moment, but he knows the voice won’t stop. So, he places his bet. He’s dealt 18, while the dealer has a 6 showing. “Saul, take a card.”

“What? The dealer has…”

“Saul, take a card!” the voice booms.

Saul hits. He gets an ace, 19. He sighs in relief.

“Saul, take another card.”

“You’ve got to be kidding me!” he pleads.

“Saul, take another card.”

He asks for another card. Another ace, 20.

“Saul, take another card,” the voice demands.

But I have 20!” Saul shouts.

“TAKE ANOTHER CARD, SAUL!”

“Hit me,” Saul says meekly. He gets another ace, 21.

And the voice says, “Un-fucking-believable!”

]]>**Want to amuse your friends, irritate your students, or annoy people you’ve just met? Download a PDF version of the One-Letter Quiz (without answers).**

- The letter used to represent the square root of -1.
- This letter is often added to indefinite integrals to show that any function with at least one antiderivative has an infinite number of them.
- The most frequently occurring letter in English words.
- The letter most recently added to the modern, 26-letter English alphabet.
- The letter represented by four dots in Morse Code.
- A type of road intersection with three arms.
- Although long out of use, this letter was used in the middle ages as the Roman numeral to represent 90.
- This letter is used for the temperature scale in which the boiling point is 212 degrees and the freezing point is 32 degrees.
- The most common blood type.
- The rating from the Motion Picture Association of America that requires children under 17 to be accompanied by an adult.
- The 43rd President of the United States.
- The only vowel that does not appear in the spelling of any single-, double-, or triple-digit numbers.
- Behind
*s*and*c*, the third most common letter with which English words begin. - With
*plan*, the letter used to refer to a typically less desirable alternative. - The Roman numeral for 500.
- The symbol for potassium on the periodic table.
- The most common variable in algebra.
- The Roman numeral for 5.
- The “score” used to indicate the number of standard deviations a data point is from the mean.
- The letter commonly used to refer to the vertical axis on a coordinate graph.
- Although every adult can recognize the loop-tail version of this lowercase letter in print, less than one-third of participants in a Johns Hopkins study could correctly pick it out of a four-option lineup.
- The clothing size that increases when preceded by an X.
- The shape of the “happiness curve,” which implies that most people are least happy in their 50’s.
- The shape of a logistic growth curve, which increases gradually at first, more rapidly in the middle, and slowly at the end, leveling off at a maximum value after some period of time.
- The only letter that does not appear in the name of any US state.
- The answer to the riddle, “It occurs once in a minute, twice in a moment, but never in a thousand years.”

**Answers (and Notes of Interest)**

- I
- C
- E
- J : in 1524, Gian Giorgio Trissino made a clear distinction between the sounds for
*i*and*j*, which were previously the same letter - H
- T
- N : see Wikipedia for a list of other Roman numerals used in medieval times
- F
- O
- R
- W : should probably be “Dubya” instead of “Double U,” but whatever
- A
- P : as you might expect, more English words start with S than any other letter; based on the ENABLE word list, P is the second most common initial letter, followed by C
- B
- D
- K : the symbol K comes from
*kalium*, the Medieval Latin for*potash*, from which the name*potassium*was derived - X
- V
- Z
- Y
- G : a lowercase
*g*can be written in two different ways, and the more common version in typesetting (known as the “loop-tail*g*“) can be recognized but not written by most adults, as recounted on the D-Brief blog - L
- U : see this article from
*The Economist*, especially this image - S
- Q
- M

]]>

If each piece of candy corn sold in a year by Brach’s — the top manufacturer of the waxy confection — were laid end to end, they would circle the Earth 4.25 times.

In writing that post, I inadvertently formulated a statistic that rather surprised me:

If all the players on an NFL team were laid end to end, they’d stretch from the back of one end zone to the opposite goal line.

That the players would almost line the entire field struck me as an amazing coincidence. And it got me to thinking — might this be true for other sports?

Not one to let sleeping dogs — or professional athletes — lie, I decided to investigate. Based on that research, here’s a simple, one-question quiz for you.

**Which of the following comparisons is the most accurate?**

- If all of the players on an
**NHL (hockey)**roster were laid end to end, they would reach from**one end of the rink to the other**. - If all of the players on an
**NBA (basketball)**roster were laid end to end, they would reach from**one end of the court to the other**. - If all of the players on an
**NFL (football)**roster were laid end to end, they would reach from**one end line to the other**. - If all of the players on an
**MLB (baseball)**roster were laid end to end, they would reach from**home plate to second base**. - If all of the players on an
**MLS (soccer)**roster were laid end to end, they would reach from**one end to the other**.

As you begin to think about that question, some notes:

- Every professional baseball stadium has different measurements. Fenway Park (Boston) is a mere 310′ from home plate to the right field wall, whereas Comerica Park (Chicago) extends 420′ from home plate to straightaway center. Consequently, the distance from second to home is used in the fourth answer choice, because it’s the same for every field.
- To my surprise, MLS stadiums are not uniform in length and width. Who knew? The length of the field must be at least 100 meters, at most 110 meters, and anywhere in between is fine. Assume an average length of 105 meters for the fifth answer choice.

Before you read much further, let me say how much fun I’ve had discussing this question around the dinner table and at the local pub. In spite of hard facts, there is resolute disagreement about player height, roster size, and field dimensions. And the shocking (or should I say predictable?) results raise an eyebrow every time. I only mention that to persuade you to think about the question, alone or with some friends, before continuing.

Okay, you’ve cogitated? Then let’s roll.

In researching the answer to the question, I was struck by how close the total length of all players on the roster is to the length of the field, court, or rink. Coincidence? Of course, a larger field requires more players, so perhaps this is the evolution of roster size that one would expect.

To answer the question, you need to know the height of an average player, the number of players on a roster, and the dimensions of professional venues. All of that data can be found in a matter of minutes with an online search, but I’ll save you the trouble.

League |
Average Height (in.) |
Players on a Roster |
Combined Height, Laid End to End (ft.) |
Dimensions |

NHL | 73 | 23 | 140 | 200 feet (from end to end) |

NFL | 74 | 53 | 327 | 120 yards (360 feet, from end to end) |

NBA |
79 |
14 |
92 |
94 feet (from end to end) |

MLB | 73 | 23 | 140 | 127 feet (from home to second) |

MLS | 71 | 28 | 166 | 105 meters (345 feet, from end to end) |

As it turns out, the MLS comparison is the least accurate. The combined heights of soccer players is only 48% of the length of their field. The NHL comparison is a little better, with players’ heights extending 70% of the length of the field. But the NFL and MLB are both very close, with the players’ heights equalling 91% of the field length and 110% of the distance from home to second, respectively. Astoundingly, if the players on an NBA team were laid end to end, they’d come just 22 inches short of covering the entire court, accounting for a miraculous 98% of the length!

So there you have it. **D**, final answer.

One last thought about this. I play ultimate frisbee, a sport with a field that measures 120 yards (360 feet). For tournaments, our rosters are capped at 29 players, and I suspect my amateur teammates are, on average, shorter than most professional athletes. If we assume a height of 5’10” for a typical frisbee player, then the combined height is 172 feet. That puts us in the realm of soccer, with our combined length covering just 48% of the field.

If, like me, you play a sport that isn’t one of the Big 5 in the U.S., I’d love to hear about your sport’s field and roster size, and how it ranks with the comparisons above.

]]>Coffee House Press claims that the novel is about “treachery, death, academia, marriage, mythology, history, and truly horrible poetry.” I mean, what’s not to love?

I bought *The Grasshopper King* because of how much I enjoyed *How Not to Be Wrong*, but I had no intention of enjoying it nearly as much as I did. From the first page, though, I was enthralled with Ellenberg’s style. To amalgamate several of the Amazon reviews, “this is an unusual book,” but it is beautiful because of “the finely tuned precision of the writing itself.”

This is not a math book, but occasionally Ellenberg turns a phrase that reminds you he’s a mathematician. When Grapearbor’s girlfriend claims that New York is ninety-five percent liars and snobs, he replies, “In Chandler City it’s ninety-nine. Point nine repeating.” Other times, he’ll include mathematical terms that are, in fact, completely appropriate and economical, but not altogether necessary:

a grasshopper, stirred by some unguessable impulse, heaved itself out of the drench mess, rose and fell in a perfect, inevitable

parabolawhoseinterceptwas the exposed stripe of Charlie’s backthe pressure of the water made

concentric circlesbehind my clenched-shut eyelidsthe agricultural buildings were at

discreet distancesfrom one another

And, yes, I know that last one isn’t a math phrase… but I can’t help but read it as *discrete distances*.

If you like Pynchon or Wolfe or anything off the beaten path, then you’ll like this book. The characters are quirky and memorable, and the writing is unforgettable. I recommend spending a few hours with it during what you have left of this summer.

]]>- If all the atoms in your body were laid end to end, they would be able to encircle the Earth over 41 billion times, a length of almost 56 light years. (Trove 42)
- If you laid the Knicks’ top six big men from end to end, you would get 41 feet and 4 inches of pain, and enough sore necks, feet, knees and ankles to fill a modest orthopedic ward. (
*New York Times*, April 11, 2013) - If all of the fiber optic cable in the world were laid end to end, it would encircle the Earth 25,000 times. (NPR)

- If all the rolls of toilet paper used in the United Kingdom in a year were laid end to end, they would reach further than Mars. (@ThomasCrapperCo)
- If you laid all the DNA from all your cells side by side, their combined length would be about twice the diameter of the Solar System. (Science Focus)
- If your blood vessels were laid end to end, they would be over 100,000 miles long for an adult and 60,000 for a child. (Franklin Institute)
- If you laid all the M&M’s produced in a year end to end, they would stretch for a million miles. (MF4MF)

Though ubiquitous, these comparisons are often unreliable:

I checked with Google to see just how long the [Aleppo] souk actually is, if all its streets were laid end to end, and found it to be, variously, seven, eight, ten, twelve, thirteen, sixteen, and “about 30” kilometres. (Jonathan Raban)

But accuracy be damned. The point of these comparisons is not to demonstrate precise computational ability. Instead, they are meant to provide a reference point for a statistic that would be otherwise difficult to interpret.

If all the players on an NFL team were laid end to end, they’d stretch from the back of one end zone to the opposite goal line.

(This reminds me, for no good reason, of an entry in the *Washington Post* Style Invitational from some years back, in which entrants were asked to submit bad similes and metaphors: “He was as tall as a 6‑foot, 3‑inch tree.”)

Such end-to-end comparisons are not new, however. According to the Quote Investigator, this type of comparison was used in 1885 to describe the Vanderbilt family’s $200,000,000 fortune:

Enough to buy 40,000,000 barrels of flour at $5 each. If these barrels were placed end to end, they would reach around the Earth on the parallel of Boston, or they would fence in every State in the Union.

Alexander Wolcott, in his 1934 bestseller *While Rome Burns*, quoted Dorothy Parker as saying:

If all the girls attending [the Yale prom] were laid end to end, I wouldn’t be at all surprised.

The most famous of these comparisons, however, is probably the following:

If all economists were laid end to end, they would not reach a conclusion.

Who said it? Who knows. It’s most often attributed to George Bernard Shaw, but it seems that the quip existed a full decade before Shaw was ever credited. It has also been attributed to Isaac Marcosson, Farmer Brown, Stephen Leacock, and William Baumol. Regardless of its originator, it has been reiterated and modified a thousand times:

- If the nation’s economists were laid end to end, they would point in all directions. (Arthur H. Motley)
- If all economists were laid end to end, there would be an orgy of mathematics.
- If all the economists in the world were laid end to end, it would probably be a good thing.

My favorite end-to-end comparisons, like the one attributed to Shaw, are usually garden-path sentences. They begin with an astounding statistic, but just when you think some simpler comparison will be made, they smack you in the nose with a twist:

- Just to be clear, if you carefully removed, and laid end to end, all the veins, arteries, and capillaries of your body, you will die. (Neil deGrasse Tyson)
- If all the world’s managers were laid end to end, it would be an improvement.
- If you laid all our laws end to end, there would be no end. (Arthur “Bugs” Bae)
- If all the salmon caught in Canada in one year were laid end to end across the Sahara Desert, the smell would be absolutely awful.
- If all 206 bones were removed from your body and laid end to end… you’d be dead.
- If all the cars in the world were laid end to end, someone from California would be stupid enough to try to pass them.
- If all the joggers were laid end to end, it would be easier to drive to work in the morning. (Milton Berle)
- If all students who fell asleep in their seats during math class were laid end to end, they’d be a lot more comfortable.

Finally — and with absolutely no bias whatsoever (wink, wink) — I present my all-time favorite end-to-end comparison, gloriously penned by my friend and colleague Gail Englert, and which appears on the back cover of * More Jokes 4 Mathy Folks*:

If you took all the people who fell on the floor laughing when they read this book and laid them end-to-end, you’d have a very long line of people. It’d be a silly thing to do, but at least you’d know who to avoid at a cocktail party.

Do you have a favorite end-to-end comparison? Have at it in the comments.

]]>Last night, I was finally able to carve out some time to binge-watch Season 2 of *Trial & Error*, and I was rewarded with a classic math joke in Episode 1. When lead investigator Dwayne Reed arrives at the house of accused murderer Lavinia Peck-Foster, he says:

There are two things that Reeds don’t trust: doctors, Pecks, and math.

I love it!

Upon realizing that I might be able to get my sitcom-writing career off the ground by reformulating stale math jokes, I promptly submitted my resume to NBC.

But, wait… there’s more!

Earlier in the day, I received NCTM‘s email newsletter *Summing Up*, which contained an unexpected surprise. In the section titled “NCTM Store,” there was a blurb about my most recent book, *More Jokes 4 Mathy Folks*, under the headline **Just Published!**

I had no idea that NCTM decided to sell my book, let alone that they were going to publicize it. My ignorance not withstanding, I couldn’t be more delighted!

If you’re looking for some great, light summer reading — something that can be enjoyed poolside while sipping a mojito — then pick up a copy of ** More Jokes 4 Mathy Folks** from NCTM today! Not only will your purchase support a great organization (and my sons’ college fund), you’ll also receive a 20% discount for being an NCTM member.

Following the lead of Dwayne Reed, here are jokes that begin, “There are *n* kinds…,” all of which appear in *More Jokes 4 Mathy Folks*:

- There are only 2 kinds of math books: those you cannot read beyond the first sentence, and those you cannot read beyond the first page. (C. N. Yang, Nobel Prize in Physics, 1957)
- There are 2 kinds of people in the world: those who don’t do math, and those who take care of them.
- There are 3 kinds of people in the world: positive, negative, and relative.
- There are 2 kinds of people in the world: those who are wise, and those who are otherwise.
- There are 2 kinds of statistics: the kind you look up, and the kind you make up.
- There are 2 kinds of experienced actuaries: those who say they have made significant forecasting errors, and liars.
- There are 10 kinds of people in the world: those who understand binary, and those who don’t.
- There are 10 kinds of people in the world: those who understand binary, and 9 others.
- There are 10 kinds of people in the world: those who understand ternary; those who don’t understand ternary; and, those who mistake it for binary.
- There are 11 kinds of people: those who understand binary, and those who don’t.
- There are 8 – 3 × 2 kinds of people in the world: those who correctly apply the order of operations, and those who don’t think that 6 ÷ 2 × (1 + 2) = 9.
- There are 2 kinds of people in the world: logicians and ~logicians.
- There are 2 kinds of people in the world: those who can extrapolate from incomplete data…

The Phillies scored 4 runs in the top of the 5th to take a 6‑2 lead. When the Nationals failed to score in the bottom of the 5th, I asked my friends, “What are the chances that the Nationals come back?” With only grunts in response and 10:43 glowing from the scoreboard, we decided to leave.

On the drive home, we listened as the Nationals scored 3 runs to bring it to 6‑5. That’s where the score stood in the middle of the 8th inning when I arrived home, and with the Nats only down by 1, I thought it might be worth tuning in.

The Nats then scored 3 runs in the bottom of the 8th to take an 8-6 lead. And that’s when an awesome stat flashed on the television screen:

Nats Win Probability

- Down 6-2 in the 6th: 6%
- Up 8-6 in the 8th: 93%

Seeing that statistic reminded me of a Dilbert cartoon from a quarter-century ago:

I often share Dogbert’s reaction to statistics that I read in the newspaper or hear on TV or — *egad!* — are sent to me via email.

I had this kind of reaction to the stat about the Nationals win probability.

For a weather forecast, a 20% chance of rain means it will rain on 20% of the days with exactly the same atmospheric conditions. Does the Nats 6% win probability mean that *any team* has a 6% chance of winning when they trail 6-2 in the 6th inning?

Or does it more specifically mean that the Nationals trailing 6-2 in the 6th inning to the Phillies would only win 1 out of 17 times?

Or is it far more specific still, meaning that this particular lineup of Nationals players playing against this particular lineup of Phillies players, late on a Sunday night at Nationals Stadium, during the last week of June, with 29,314 fans in attendance, with a 38-minute rain delay in the 4th inning during which I consumed a soft pretzel and a beer… are **those** the right “atmospheric conditions” such that the Nats have a 6% chance of winning?

As it turns out, the win probability actually includes lots of factors: whether a team is home or away, inning, number of outs, which bases are occupied, and the score difference. It does not, however, take into account the cost or caloric content of my mid-game snack.

A few other stupid statistics I’ve heard:

- Fifty percent of all people are below average.
- Everyone who has ever died has breathed oxygen.
- Of all car accidents in Canada, 0.3% involve a moose.
- Any time Detroit scores more than 100 points and holds the other team below 100 points, they almost always win.

**Have you heard a dumb stat recently?** Let us know in the comments.