## Push-Up Percentages

Hands down, push-ups are my favorite exercise!

If you’re friends with me on Facebook, then you know I’m raising money for St. Jude Children’s Hospital by participating in the St. Jude Push-Up Challenge. And if not, then let me tell you: I’m challenging myself to do ~~3,000~~ 6,000 push-ups during the month of November. As of November 20, I was just 660 push-ups away from reaching my goal; you can see all of my progress on this Google sheet.

What’s been most fun about this challenge, though, is the math of it all. (Isn’t that always the case?)

**Arithmetic.** How many push-ups will I have to average each day to reach my goal? November has 30 days, and 6000 ÷ 30 = 200.

**Logistics.** How should I break up those 200 push‑ups each day? A regimented person might do 10 push‑ups a minute for 20 minutes, or maybe 25 push‑ups every hour for 8 hours. For the record, I’m not that routinized. Most days, I do anywhere from 8‑12 sets, with anywhere from 10 to 50 push‑ups per set. Though I did have one day — November 13 — where I set a timer and did 10 push‑ups every 45 seconds for 90 minutes; I completed 1,235 push‑ups that afternoon, a personal record for push‑ups in day.

**Physics.** When doing a push‑up, how much of your bodyweight are you actually moving? I know that I’m not pushing up all 200 pounds of my weight when doing a push‑up. And I’m sure the percentage decreases more as I elevate my hands. This is only a hypothesis, but incline push‑ups sure seem easier — I can do more of them before reaching failure — than regular push‑ups, and decline push‑ups seem harder. As it turns out, Jane Reaction explained exactly why this is in a Physics of Fitness Friday blog post, and her conclusions about the percent bodyweight supported by the hands when doing a push‑up were as follows:

- Regular Push-Up: 64%
- Incline Push-Up, Hands Raised 12″: 55%
- Decline Push-Up, Feet Raised 12″: 70%
- Decline Push-Up, Feet Raised 24″: 74%
- Handstand Push-Up: 100%

These, of course, are estimates, and Jane used her body for the calculations. The exact percentage will differ person to person, depending on your weight, the length of your arms, your body shape, the location of your center of mass, and other factors. For a reasonable estimate, Jane suggests placing your hands on a scale while in push‑up position, then dividing by your standing weight (i.e., your weight when standing on a scale). For instance, if your scale shows 128 pounds for your hands in push‑up position and 200 pounds when you stand on it — which is exactly what it showed for me — then your hands are supporting 128 ÷ 200 = 0.64, or 64%, of your bodyweight when doing a push‑up.

The following graph, from Zatsiorsky’s Science and Practice of Strength Training, shows the percent body weight based on the height that your feet or hands are elevated:

There were two reasons I was so curious about this estimate. First, math is cool. Second, I get bored easily, and I was wanting to substitute some bench presses for push-ups occasionally. Based on what’s above, I figured that if I did bench press with 125 pounds, then one rep would be equivalent to one push‑up. So on two of the days, I did a chest workout that included bench press, incline press, cable flyes… and *then* some push‑ups. And, yes, I was sore as hell the next day! But I was also rejuventated since I got to incorporate some activity other than just push‑ups.

I’m proud that, at 51 years of age, I’m going to complete this challenge. But I’m even more proud that I’m raising money for a good cause. If you’d like to contribute to St. Jude, **visit my Donate page on Facebook**. And if not, no worries; here’s one more joke for you before you go…

A man in a bar offers $100 to anyone who can do 100 push‑ups. Another patron leaves for a few minutes, then returns and says, “I’ll take that bet!” He drops to the ground and does 30 easily but then starts slowing down around 40 and collapses before he reaches 50. “I don’t understand,” he says. “I just did 150 outside!”

## IDK Puzzles

I like logic, and I like beer, so it’s no surprise that this is one of my favorite online comics:

Not sure why that’s funny? There’s an explanation at www.beingamathematician.org.

Logic puzzles in which a protagonist states, “I don’t know!” are ubiquitous. Borrowing from texting culture, I’ve taken to calling these IDK Puzzles.

Every math person remembers the first non-routine problem they solved and, more importantly, the *feeling* they experienced when solving it. The first time I had that feeling occurred after solving a logic puzzle about three children’s ages that I discovered in a Martin Gardner book; now many years later, I don’t remember the title of the book, and the following is my best recollection of the puzzle:

Two neighbors are speaking. One asks the other, “I know you have three children, but how old are they?”

The other says, “The product of their ages is 72.”

The first neighbor says, “I still don’t know their ages.”

“Well,” says the other, “the sum of their ages is equal to our street address.”

The first neighbor again replies, “I still don’t know their ages.”

“I’m sorry,” says the other, “I can’t talk anymore, because I have to take my oldest child to the dentist,” and then leaves.

While saying good-bye, the first neighbor thinks, “Ah, now I know their ages.”

This puzzle is typical of the genre, in that it appears there is insufficient information, but those who persist will be rewarded. Can you figure out the three children’s ages?

A slightly different IDK Puzzle involves geometric shapes.

Two people are shown the following five shapes:

They are told that a prize has been placed under one of the shapes. One of the people is told the color, and the other is told the shape, but they are not allowed to share their information with each other.

They are asked, “Do either of you know where the prize is hidden?”

Both of them reply, “I don’t know.”

They are asked a second time, “Do either of you know where the prize is hidden now?”

Again, they both reply, “I don’t know.”

They are asked a third time, “What about now?”

They both reply, “Yes!”

Under what shape has the prize been hidden?

Enjoy solving those puzzles. Staying with the theme, let’s end this post with a logic joke of sorts…

Sam comes home from the grocery store with twelve gallons of milk. Pam asks, “Why’d you buy so much milk?”

“Because before I left, you told me to buy a gallon of milk, and then you said, ‘If they have eggs, buy a dozen.’ And they had eggs.”

Pam shakes her head at Sam’s response. But then she notices he hasn’t bought anything else and asks, “Where are the rest of the things we needed?”

“Remember how you told me to put ketchup on the list?” replies Sam.

“Yeah. So?”

“So I put ketchup on the list, but then I couldn’t read the other items!” Sam says. “But I remembered the eggs!”

## They’re Moving Second Base

When I first heard that baseball is moving second base, my first thought was, “My, goodness! Isn’t it enough that we’re dealing with a global pandemic, a Russian tyrant invading a neighboring country, a humanitarian crisis in Nicaragua, food insecurity in Somalia, Haiti, and Madagascar, an ever-widening wealth gap, an uptick in calls from unknown numbers, paper cuts, and excessively long lines at the Starbucks drive-thru? I mean, when’s it gonna stop?”

But my second thought was, “This is going to wreak havoc on the secondary textbook publishing industry.” Just look at all the problems that exploit the baseball context:

- Location of the pitcher’s mound (Q2)
- Throw from catcher to second base
- Throw from catcher to second base
- Distance from first base to third base (Q4)
- Runner’s speed in relation to second base

All of those problems are predicated on a consistent distance between bases. Won’t the relocation of second base cause inconsistency?

Well, actually, it won’t.

According to the official rules of baseball, one vertex from first base, third base, and home plate are to be coincident with three vertices of the infield square; but, the *center* of second base is to be coincident with the fourth vertex. With the rule change, second base will be moved so that one of its vertices will be coincident with the fourth vertex of the infield square, finally bringing a state of geometric consistency to the game that I, for one, believe is long overdue. The image above shows the new (white) and old (gray) locations of second base.

The question all fans should be asking isn’t why are they changing the layout of the infield. The more pertinent question is, what took so damn long?

As it turns out, second base doesn’t get all the credit for the previous configuration issues. To the contrary, it was the movement of the other bases that resulted in a problem. In the 1860s, it was generally agreed that all four bases should be positioned with their centers at the vertices of the infield square. And by “generally agreed,” I mean that there was consensus about this, but it wasn’t officially stated in the rules until 1874. Then in 1877, the rules changed so that the back corner of home plate — at the time, home plate was still a square, not a pentagon like today — coincided with the vertex of the infield square, positioning all of home plate in fair territory. A decade later, first base and third base were moved to be entirely within fair territory, too; but most folks didn’t even notice, because that same year (1887) a number of other rules changes garnered more attention:

- Pitchers were limited to just one step when delivering a pitch; previously, they could take a running start
- Batters were prohibited from requesting a high or low ball from the pitcher, as they had been allowed in the past
- The pitcher’s mound was moved back five feet (from 50′ to 55′)
- Five balls were required for a walk, reduced from six
- Four strikes were required for a strikeout, increased from three

With so many drastic rules changes happening simultaneously, it’s hardly a surprise that first and third were repositioned in relative obscurity while second was left floundering in geometric misalignment.

Just so you know, the rules change will only occur in the minor leagues this year. If it pans out, you can bet you’ll see it in the MLB in a year or two.

But why stop there? Here are some other rules changes in sports that should probably be implemented.

**Scoring system in football.** I mean, you can score 1, 2, 3, 6, 7, or 8 points depending on what you do. Isn’t that a little excessive? While we’re at it, let’s change the width of the field, too — who the hell thought 53⅓ yards was an appropriate dimension?

**College basketball uniforms.** Bring back 6, 7, 8, and 9. You may not have known that those digits are not allowed, because each of them requires two hands. Referees indicate the player who committed a foul using their fingers — for instance, holding up two fingers on the right hand and three fingers on the left to indicate that an infraction was committed by number 23 — and the digits 6‑9 would require more than five fingers.

**Frames in bowling. **Two balls ain’t enough. Give everyone three attempts to knock down all ten pins.

**Cheerleader weigh-ins. **Really, folks? The 15th century called, and they want their misogyny back. One anonymous NFL cheerleader wrote that she was banned from performing because she weighed more than 122 pounds. While we’re at it, ban weigh-ins for jockeys, too. The Kentucky Derby — which apparently has one of the more liberal weight allowances — caps the weight at 126 pounds; that includes 7 pounds for the jockey’s gear, so the jockey can’t tip the scale at more than 119 pounds.

**Taunting.** Allow it everywhere. In college football, the rule is just stupid. Admittedly, one player shouldn’t be allowed to stand over another player while making insulting comments about their mother; but “taunting” according to the NCAA Rule Book includes spinning or spiking the ball, choreographed acts, and the player altering stride when approaching the end zone. C’mon! Further, I’d like to see taunting *encouraged* a bit more at some events, such as math competitions. Wouldn’t it be great if one participant walked up to another and said, “You can’t even spell Q.E.D.!”

## The Great Puzzle Hunt

A woman after my own heart, Millie Johnson loves both puzzles and jokes. She regularly posts to Facebook, and these two gems appeared recently in her feed:

- If all whole numbers between 1 and 1000 were spelled out and arranged in alphabetical order, which number would be next-to-last?

- Arrange the digits 0‑9 into a ten-digit number such that the leftmost
*n*digits comprise a number divisible by*n*. For example, if the number is ABCDEFGHJK, the three-digit number ABC must be divisible by 3, the five-digit number ABCDE must be divisible by 5, and so on.

The answers to both can be found with an online search, and the latter can be computed in milliseconds by writing some code, but you’ll have more fun if you find the answers using that big lump of gray matter in your skull.

She also recently shared this joke, which I just adore:

Millie is also the founder and puzzle creator for the **Great Puzzle Hunt**, a free, fun, full-day, team puzzle-solving event. While folks in and around Bellingham, WA, on April 9 will be lucky enough to participate in the face-to-face event on the Western Washington University campus, the rest of the world is invited to participate virtually. There are divisions for secondary (middle and high school), open (any age), WWU students, and WWU alumni. And in case you missed the subtle mention above, I’ll say it again: registration for a team of up to six participants is FREE!

Participants will engage with four puzzles; then, the answers to those puzzles will be used to form a fifth and final meta-puzzle. How hard are the puzzles? See for yourself; the puzzle below, **My Life Is In Ruins!**, is from the 2021 Great Puzzle Hunt:

The Great Puzzle Hunt is a full-day event, so pack a lunch! But my sons and I participated last year and had a phenomenal time. By the end, we were mentally exhausted but invigorated and intellectually satisfied. If you like to solve puzzles, head on over to https://www.greatpuzzlehunt.com/register and register today!

## What an Amazing Date!

There are lots of good dates — meeting at a bookstore coffee shop for, well, perusing books and sipping coffee; spending hours playing Super Mario Bros. and Pac-Man at a retro video game arcade; and, of course, going to an open-mic comedy show where one of the performers tells nothing but math jokes.

But great dates? Well, those are pretty rare. My first date with my wife — where I took her to a hotel and “whispered” to her from the couch across the lobby — is an example, though the stimulating conversation and her perfect laugh may have contributed more than the elliptical ceiling. (Maybe.)

Few dates, however, can compare to today’s date:

**12/3/21**

Look at that beautiful symmetry! Marvel at its palindromic magnificence! The way it rises then falls, like a Shostakovich melody.

But wait… there’s more! Consider the following pattern:

1 × 1 = 1

11 × 11 = 121

111 × 111 = ?

That’s right! The number 12,321 is a perfect square! And not only that, its square root contains only 1s.

Moreover, check this out:

1 + 2 + 3 + 2 + 1 = 9

That’s right! It’s a square number, and the sum of its digits is also a square number!

Finally, here’s a KenKen puzzle that makes use of the number, though it’s not unique unless one of the digits is already filled in:

No matter how you choose to celebrate, here’s hoping your day is as great as the date!

## Better Multiple-Choice

If I were a K-12 student right now, I’d want to live in San Diego. In 2020, San Diego Unified School District introduced a new district-wide math test that contained **no multiple-choice questions**. The district was allowed to use their own internal test instead of the state test last year, due to the pandemic, and they’re apparently allowed to use it again this year. Supposedly, the test moves away from a reliance on computational ability and instead measures three dimensions: students’ knowledge of mathematics (concepts and formulas); their application of that knowledge; and, their ability to communicate mathematically.

The optimist in me says, “It’s about time!” But the pessimist in me thinks, “Don’t they know that it’s a lot more expensive, and harder to ensure reliable and replicable results, when using humans to do the scoring instead of machines?” I’m old enough to remember the controversy and eventual dissolution of the Maryland State Performance Assessment Program (MSPAP) exams, which required extended answers and contained no multiple-choice questions. FairTest called the MSPAP test “perhaps the single best state exam,” but it was criticized for providing school-level but not individual student scores. Though generally agreed to have been a catalyst for improved teaching, it was replaced by an entirely multiple-choice test to meet the requirements of the Elementary and Secondary Education Act (ESEA).

Ah, the good old days. Reminiscing sure ain’t what it used to be. But, I digress.

To determine if multiple-choice questions are valid tools, I made a list of pros and cons regarding their use in educational assessment.

Pros | Cons |

They can be scored quickly. | The correct answer can be guessed. |

They can be scored objectively and without bias. | The correct answer can be found by process of elimination. |

They encourage students to think like the test creators instead of like themselves. | |

They provide no information about the student’s solution strategy. | |

They are required to have only one answer. | |

They exacerbate test anxiety. | |

They don’t prepare students for college or the work force. | |

Incorrect answer choices expose students to misinformation, which can influence future recall and thinking. |

Seems a bit lopsided.

In recent years, multiple-choice questions have gotten a bit of a makeover. Those in the educational assessment industry now call them “selected-response items” because, well, students get to select a response.

But this is just semantics. Referring to a pig as a mud wrestler may sound nicer, but the pig won’t be any less dirty.

It’s the advertising trope of…

New look, same great taste!

Or as a pretentious coffee brand said when they changed the label…

Innovative presentation, but consistent quality.

Truth is, selected-response items look like they’ve always looked, typically with a really boring prompt and even more boring answer choices. As one example, the following item is from a PACE (Packet of Accelerated Christian Education), which “integrate Godly character-building lessons into the academic content.”

**Mr. Louis Pasteur did experiments with milk.** Mr. Louis Pasteur was…

- a glass bottle
- an airplane
- a scientist

Despite your religious beliefs, you have to admit that this question is rather absurd. Would any student ever think that a glass bottle or an airplane would be referred to as “mister”? To be fair, this question appeared in a PACE packet in 2013, so it’s quite possible that it’s since been updated. Still, 2013 wasn’t that long ago, and there’s no time in history when those answer choices wouldn’t have been ridiculous.

And here’s one that was presented during a session at an NCTM regional conference:

To **convert to radians**, multiply by…

- π/180
- 180/π
- 225π/180
- π/40,500

Ignoring the fact that this question attempts to assess something that your calculator knows so you don’t have to, this question is fine. But in the reading passage directly above the question, it stated, “To convert an angle from degrees to radians, multiply by π/180.”

Well, that will just never do.

I’m not convinced that a great multiple-choice question actually exists. That said, some are better than others, so I offer you the following seven multiple-choice — or selected-response, or objective-response, or whatever-you-want-to-call-them — items.

What is the probability that you will **randomly choose the correct answer** to this question?

- 25%
- 50%
- 0%
- 25%

At any given time, **the number of people in the air** — that is, those who are flying in motorized aircraft, and not counting those who were recently launched by catapults or who have bounced on a trampoline — is closest to the population of…

- Flint, Michigan
- Seattle, Washington
- New York, New York

The approximate **volume of an average chicken egg** is…

- 7 cm
^{3} - 70 cm
^{3} - 700 cm
^{3} - 7,000 cm
^{3}

The **polar (north-to-south) diameter of the Earth** is about…

- 1,000,000 inches
- 20,000,000 inches
- 500,000,000 inches
- 1,000,000,000 inches

**One million one-dollar bills** weigh about as much as…

- a three-toed sloth
- a giant panda
- Chris Christie
- a grizzly bear
- a black rhinoceros

The total number of **calories in all the hot dogs consumed at Yankee Stadium** during one season of Major League Baseball is closest to…

- the number of five-card poker hands
- the number of possible license plates in Indiana
- the number of combinations in the Powerball lottery
- the number of humans on Earth
- the number of stars in the Milky Way

If **the residents of New Mexico joined hands and stood in a straight line**, they could reach from one side to the other of…

- New Mexico
- Rhode Island
- Texas
- Alaska

The answers to these questions will not be provided, though each question absolutely has a best answer among the choices. In lieu of an answer key, enjoy the following joke:

How do you keep a fool in suspense?

## Interview: Kerry Schultz, Saucon Valley High School

It sounds like the start of a math joke: Did you hear about the mathematical economist who became a teacher? The punch line is, “Her name is Kerry Schultz,” which, admittedly, isn’t very funny, but it’s absolutely true. Kerry used to work as an analyst for JPMorgan Chase but now teaches calculus and computer science at Saucon Valley High School in Hellertown, PA.

Seniors selected Kerry to be the faculty speaker at the 2021 SVHS commencement. During her speech, Kerry gave the graduates some sage advice. “When you get the choice to sit it out or dance, I hope you dance,” she told them, drawing from Lee Ann Womack’s 2000 hit. She also referenced one of my favorite publications:

After a difficult last two years, I promised to avoid the pandemic topic, and I wanted to be sure to keep this on the lighter side. So I brought my favorite book,

Math Jokes 4 Mathy Folks. I’m pretty sure this book is the reason I was chosen to speak tonight.

As it turns out, Kerry and I have more in common than just our love of math jokes. We both have twins. (In fact, she has twin 10-year-old daughters and a 9-year-old son. I’ve never been good with numbers, but I’m pretty sure that means that, at one point, she had three kids under age two in her house. My goodness!) Like my wife and me, Kerry and her husband both love math jokes, math memes, and all things numeric. The two of them used to play The Game of 24 on long car rides; my wife and I played Dollar Nim with our kids.

The comparison ends when it comes to exercise, though. I’m active, but Kerry runs at 4:30 a.m. most mornings, because she spends her afternoons taking kids to their various activities (soccer, baseball, football, swimming, cross country, and golf). She’s finished 10 marathons and hopes to run the Chicago Marathon in 2022. (I’ve also never been asked to speak at a graduation. Yet.) In her limited downtime, Kerry enjoys traveling or reading a good book on the beach.

I caught up with Kerry when a friend forwarded her picture from the Lehigh Valley Press. As it turns out, Kerry has a fascinating story about her path to education.

**Can you tell us how you got to Saucon Valley?**

I went to college with the hopes of becoming a math teacher, but others convinced me that I was “too smart” for that. So I graduated from Colgate University in 2000 with a degree in mathematical economics, and I went to work as an analyst at JPMorgan Chase in midtown Manhattan. Some might say it was glamorous, with lots of fancy meals and car service home every night — but I hated pretty much everything about it.

I was working in midtown on September 11, 2001, and my brother was working on the 90th floor of the South Tower. He was extremely lucky to escape the attack on the World Trade Center, but many of his co-workers did not. This was a pivotal day for me. I realized life was way too short to spend it doing something I hated. In the following weeks, I began looking for graduate programs in mathematics education. In 2002, I enrolled at Lehigh University, and in 2004, I began teaching middle school math in the Saucon Valley School District.

**What is your current role?**

I taught middle school math for five years while obtaining my principal certification from Lehigh. I then became a Coordinator of Academic Services and later an Instructional Coach for Math, all in Saucon Valley. In 2015, I requested a return to the classroom and was thrilled to be asked to teach high school math. I have been in the high school for five years now, teaching Algebra 2, Pre-Calculus, Calculus, and AP Computer Science Principles. I absolutely love my job!

**And if you weren’t teaching math?**

I’d love to be a professional athlete or work in an athletic setting — maybe a statistician for the NY Mets!

**What’s your favorite thing about teaching?**

The kids! It’s important to get to know each and every one of my students as best I can. Nothing is better than knowing I have made a difference in the life of a student. Sometimes it’s by helping them solve a difficult problem, sometimes by building their confidence, sometimes by showing up to their lacrosse game, and sometimes it’s simply by being there when they’ve had a rough day. The relationships I’ve built with students over the years are by far the most important thing to me.

**What is your favorite math joke(s)?**

My oldest favorite has to be, “What did 0 say to 8?” Now that I teach computer science, I really like, “There are 10 kinds of people: those who understand binary, and those who don’t.”

**Which math joke(s) do your students like best?**

The jokes that poke fun at mathematicians tend to be class favorites. “What do you call a beautiful woman on the arm of a math graduate student? A tattoo.” And, “What’s the difference between a large pizza and a mathematician? A pizza can feed a family of four.”

**What’s the funniest thing you’ve ever said during class? Or maybe, what’s the funniest thing that’s ever happened in class?**

This is definitely a case of “you had to be there,” but one year I had an Honors Calculus student convince me, with the help of her classmates, that after high school she was going into the family business of designing chairs. I was skeptical at first, but they were so believable and had so many details, they had me convinced for days. They told me that her family designed chairs for Nicki Minaj, and to this day I can’t hear that name without dying of laughter.

**What is your favorite area of mathematics? Is that also your favorite thing to teach?**

I don’t have a personal favorite, but I definitely love teaching calculus. Calculus is a great challenge for many students, but most of them are willing and able to put forth the effort to succeed. I enjoy helping students work through the difficulties, and I’m just as excited as they are when it all starts to make sense. It is fantastic when you see the light bulb go on!

## A Great Day for a Pattern

When I first saw today’s date in mm/dd/yy format — 11/12/21 — I thought, “Well, that’s pretty cool. It’s all 1s and 2s.” And then I thought, as I’m sure you did, “In ternary, that’d be 376,” because everyone thinks in ternary, right?

But then I looked at the number again, and I thought, “Ah, hello, old friend. Good to see you again.”

Those six digits form the fifth term of a famous pattern:

1

11

21

1211

111221

So your first question is, what’s the next term?

If you’ve never seen this pattern before, it’s worth a little of your time to try to figure it out before reading more about it at MathWorld.

Your second question — if you’re still reading — is, what’s the greatest digit that will ever appear in this sequence? As you can see above, the first five terms only contain 1s and 2s. What digits are in the sixth term? What digits will appear beyond the sixth term? How do you know?

## There Are Two Types of People…

It’s estimated that there are 7.9 billion people in the world, and counting. But in many ways, it’s fairly easy to divide us all into two types.

There are two types of people:

- Those who think the world can be divided into two types of people.
- Those who don’t.

The earliest known usage of the two-types format was by Mark Twain:

There are basically two types of people: people who accomplish things, and people who claim to have accomplished things. The first group is less crowded.

The potential origin of the two-types meme, as we know it today, may have been this ubiquitous math and computer science joke:

There are 10 types of people in the world: those who understand binary, and those who don’t.

A modification of that joke has appeared more recently for the uber-geeks:

There are 10 types of people in the world: those who understand ternary, those who don’t, and those who mistake it for binary.

Physicist C. N. Yang, who won the Nobel Prize in 1957, is credited with this version:

There are two types of math books: those you cannot read beyond the first sentence, and those you cannot read beyond the first page.

Two of my favorites were included in **More Jokes 4 Mathy Folks**:

There are three types of people: positive, negative, and relative.

There are two types of people: those who are wise, and those who are otherwise.

The number of modifications to the format are nearly infinite. To create your own, choose the number of things you wish to compare; choose the type of things you wish to compare; describe that number of things, making sure that two of them are diametrically opposed, as to cause an incongruous and humorous result; if possible, be self-deprecating in one of the descriptions; and finally, determine if you want it in paragraph form or as a bulleted list. For instance,

There are two types of math jokes:

- Those that are funny.
- Those that have appeared on this blog.

See? It’s not hard. Now you try. The following mathy examples can serve as inspiration.

There are three things I hate:

- People who can’t do simple math.
- Irony.

There are three things I hate:

- Bulleted lists.
- Lazy people.

There are two kinds of statistics:

- Those you look up.
- Those you make up.

There are three kinds of lies:

- Lies.
- Damned lies.
- Statistics.

There are two kinds of people. Avoid both of them.

There are two kinds of people:

- Those you want to drink with.
- Those who make you want to drink.

On the web, you’ll find all manner of visual adaptations of the meme.

There are two types of people:

There are two types of people:

And finally, there are two types of bloggers:

- Those who would write a blog post about the world containing two types of people.
- Those who would Google it first to see that there about 24,000,000 results for “there are two types of people.”

## A Funny Thing Happened at the Periodontist

People in Portland are nice. Like, really nice. *Nice to a fault*, some would say. It’s the reason the term “Portland nice” exists, and it’s the impetus for the following scene from Portlandia in which two drivers at an intersection insist — politely, but with increasing determination — that the other one go first.

Ashley, one of the assistants at my periodontist’s office, is Portland nice. So at an appointment a while back, when I settled into the chair, it wasn’t surprising that her opening question was, “Got any plans for the weekend?”

As it turns out, I did. The Museum of Mathematics had invited me to host a webinar as part of their Family Fridays series, and I offered to deliver Punz and Puzzles, an hour or so of, well, math puns and math puzzles. I told Ashley about this, and there was a long pause before she responded. Finally, she said, “Do you know a lot of math jokes?” Before I could assure her that, indeed, I knew at least two volumes’ worth, Dr. Thanik entered the room, and our conversation was temporarily paused.

Dr. Thanik then did what periodontists do: he told me about the procedure that he was going to perform, and he injected several gallons of novocain into my gums. While it took effect, Ashley said, “Tell me a joke.”

“What?” asked Dr. Thanik.

“Not you,” she said, waving a hand at me. “Mr. Vennebush. Before you came in, he was telling me that he’s doing a webinar tonight that involves math jokes.”

“Do you know a lot of math jokes?” Dr. Thanik asked.

I explained that I had literally written the book on them.

“Well, then… let’s hear one!” he demanded.

Neither of them seemed to care that my mouth was numb and any joke would be delivered through an excessive amount of drool. Fortunately, I have very little self-respect or regard for etiquette, so I didn’t care, either. I launched in.

“Well, you probably know the world’s most ubiquitous math joke,” I began. “Why is 6 afraid of 7?”

They responded in unison. “Because **7 8 9**!”

“Yes!” I said. “But there’s a follow-up. Why is epsilon afraid of zeta?”

Raised eyebrows. Blank looks. Silence.

“Because **zeta eta theta**!” I exclaimed.

“Oh, I should’ve gotten that!” Dr. Thanik said, with the knowing look of someone bearing a Greek surname.

He then performed the procedure. As he finished the last suture, he said, “Okay, I don’t quite have the wording right, but what about this? Why couldn’t the **tangent** get a loan? Because his parents wouldn’t **cosine**.”

“Did you just make that up?” I asked.

“You seem surprised,” he said.

“I just didn’t expect my periodontist to make references to trigonometry,” I replied.

“Well,” he said, “I know a lot of things. After all, I spent 20 years in school.”

I continued, “Well, I guess I’m also a little surprised that you were trying to formulate a math joke while performing gum surgery.”

“Fair,” he said.

And then it occurred to me. “Oh, of course!” I said. “I’ve got the *perfect* joke for you. Did you hear about the middle school math teacher who became a dentist?” I asked.

“No,” they said.

“Her specialty is **square root canals**!”

They both laughed politely. Like I said, Portland nice.