Flag Day Math

Tuesday, June 14. Flag Day. It’s nearly impossible for mathy folks to not tell this joke today.

Several engineers were attempting to measure the height of a flag pole. They only had a measuring tape, and they were getting quite frustrated trying to slide the tape up the pole. They could get the tape no more than a third of the way up the pole before it would bend and fall down.

A mathematician asks what they’re doing, and they explain. The mathematician offers to help. She removes the pole from the ground, sets it down, and measures it easily. She then returns the measuring tape to the engineers, and walks off.

When she leaves, one engineer says to the others, “That’s just like a mathematician! We need to know the height, and she gives us the length!”

Those who know it will also tell this one, or a variant.

How do statisticians determine which banner to hoist?
They take a flag poll.

And then there are jokes about specific flags.

I’m about as motivated as the guy who designed the Japanese flag.

Honestly, I want to stop. But I can’t. Just one more…

What’s the best thing about Switzerland?
I don’t know, but the flag’s a big plus.

Okay, seriously… I didn’t invite you here today to listen to bad jokes. (Well, that’s not the only reason, anyway.)

I invited you here today to have a little Flag Day fun with math. The projectionist Shahee Ilya has converted the flag of every country into a pie graph based on its colors. For example, the Austrian flag has two red stripes and one white stripe, so it is converted to a pie graph as follows:

Pretty cool, huh?

What follows are pie graphs for ten flags. Even if you are geographically challenged, I assure you that you’ve heard of all ten countries represented below. Can you name the country whose flag was used to create each pie graph?

 

Stumped by the challenge? Here’s a hint: The countries whose flags are represented above are the ten most populous countries on Earth. (Admittedly, had someone asked me to name the ten most populous countries prior to writing this post, I would have been lucky to identify half of them.)

And just to put some space between the pie graphs above and the countries whose flag they represent below (i.e., the answers), I include for your enjoyment one of the most hideous puns you’ll ever see, modified from an even worse version at Six Puns:

During a recent heat wave, a poll revealed that beads of sweat had amassed (mast) on the secretary’s forehead and a virus was rippling through the office staff. Although the boss knew that the secretary was very sick, he saw no reason to ban her from the office. Instead, he wrote a note with pennant (pen and) paper, and he flagged the issue to be addressed with the standard protocol.

If you tolerated that, you certainly deserve the answers…

Nigeria	Pakistan
Russia	United States
Indonesia	Japan
Bangladesh	Brazil
China	India

 

Click on over to shaheeilyas.com/flags to see the pie graph for every country in the world. Clicking on the pie graph will reveal the flag and country name.

I’m Playing Baaas-Ket-Baaall

Lego NBA Player

I recently had a meeting at the National Basketball Association (NBA) offices in New York City. I had gotten very excited about this meeting, thinking maybe I’d bump into Lebron or Kobe or Shaq or Dr. J or Jerry West or David Stern. (It could happen, ya know. Not so long ago, I bumped into Brooke Shields while attending a meeting for MoMath. All things are possible in NYC.)

But irony of ironies… when I arrived, I met no one famous; rather, one of the NBA staffers wanted to meet me because Math Jokes 4 Mathy Folks is his mom’s coffee table book. She’s a retired chemical-cum-mechanical engineer, so geeky jokes are her ilk.

Three engineers are arguing about God’s profession.

The first says, “God has to be a mechanical engineer. Look at the design of the joints and muscles.”

“No, no,” said the second. “Look at the central nervous system. All that wiring? Surely, God is an electrical engineer.”

“I think you’re both wrong,” said the third. “He’s got to be a civil engineer. Who else would put a waste management facility in the middle of a recreation area?”

Now, I know that this story likely sounds like an elaborate set-up.

Yo momma is so dorky, she reads Math Jokes 4 Mathy Folks.

Well, it’s not. All of this is true.

The wonderful young man who wanted to meet me was Daniel Feinberg. I asked about his mother’s favorite joke from Math Jokes 4 Mathy Folks, and he told me it was this one (which is sometimes known as the Pizza Theorem):

originally from Jay Fallon at Posterous Spaces,
which sadly no longer exists

Via email, Daniel told me:

It’s funny, because she [Daniel’s mom] hadn’t taken a look at the book in some time, and when I asked her for her favorite joke, she got sucked into reading the entire thing — again.

Now that’s a nice compliment.

Daniel isn’t an engineer or even a math guy. He loves golf, though, and his favorite joke from Math Jokes 4 Mathy Folks is:

A pastor, a doctor, and a mathematician were stuck behind a slow foursome while playing golf. The greenskeeper noticed their frustration and explained to them, “The slow group ahead of you is a bunch of blind firemen. They lost their sight saving our clubhouse from a fire last year, so we always let them play for free.”

The pastor responded, “That’s terrible! I’ll say a prayer for them.”

The doctor said, “I’ll contact my ophthalmologist friends and see if there isn’t something that can be done.”

And the mathematician asked, “Why can’t these guys play at night?”

Incidentally, Joshua Ferris included this same joke in his book To Rise Again at a Decent Hour, though the main character tells it with a priest, a minister, and a rabbi. Go figure.

I’d like to thank Daniel and his mom for their continued support. Hearing that MJ4MF made even one person smile is enough to think that it was worth writing.

Before you go, here are some basketball-related math jokes. Or maybe they’re math-related basketball jokes. Whatever. Enjoy.

What do basketball players call the last occurrence of the function that gives the greatest integer less than or equal to x?
The Final Floor.

What do athletes playing basketball and students taking a math test have in common?
They both dribble.

What’s the difference between the Knicks and a dollar bill?
You can get four quarters from a dollar bill.

Okay, maybe that last one isn’t very mathy, so here’s a mathy quote from basketball commentator and former coach Doug Collins:

Any time Detroit scores more than 100 points and holds the other team below 100 points, they almost always win.

Almost?

Upside-Down Tooth Numbers

Alex and Eli know that 15 ÷ 3 = 5, that 63 ÷ 7 = 9, and, given a little time, could figure out that 104 ÷ 8 = 13. That’s not bad for five-year-olds.

As we were discussing sharing a treat the other day, we naturally happened upon a situation in which it would be good to know what 1 ÷ 2 is.

Alex suggested, “Two.”

I explained that while the order of the numbers in multiplication doesn’t matter — for example, 2 × 3 = 3 × 2 — order does matter with division. I used the word commutative, but I also tried to explain it with plainer language, too.

I took a rectangular piece of paper and ripped it in half. “How big is each piece?” I asked. The both knew it was one-half. “So there you have it: 1 ÷ 2 = 1/2.”

But why stop there? I divided one of the halves in half again, and I asked, “How big is this piece?” They both knew it was one-quarter. “So that shows that 1/2 ÷ 2 = 1/4.”

They saw that if we continued in this manner, we would get 1/8, 1/16, 1/32, and so on, a pattern they called the upside-down tooth numbers, because the numbers in the sequence are the reciprocals of the powers of two. (For them, tooth = 2^th.)

Looking at the pieces of paper on the table, I asked a more advance question. “What do you think we’d get if we added 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + …, and we kept adding half as much each time?”

Eli thought for a few seconds. “I think it would be one whole,” he offered.

I was surprised. “Why?” I asked.

“Well,” he said, “I’m thinking about a circle.”

I looked at the rectangular pieces of paper on the table, which had nothing to do with a circle. Sure, he got the right answer, but his reasoning is way off base, I thought.

He explained further. “If you fill half a circle, then a quarter more, then an eighth, and keep going, you’ll eventually fill the whole thing. That’s why I think it’s one.”

Visually, Eli’s argument would look something like this…

Holy sh*t, I thought. That’s pretty good for a five-year-old.

I don’t even care that he doesn’t understand this joke:

An infinite number of mathematicians walk into a bar. The first asks for half a beer. The second asks for a quarter of a beer. The third asks for an eighth of a beer. The bartender interrupts, pours one beer for them, and says, “You guys don’t know your limits.”

I think I was so impressed with Eli’s solution because infinite series can be difficult, even for mathy professionals:

A mathematician will call an infinite series convergent if its terms go to zero. An engineer will call it convergent if the first term is finite.

And let us not forget the Eilenburg swindle, which proves that 1 = 0 since:

1 − 1 + 1 − 1 + … = 1 + (−1 + 1) + (−1 + 1) + … = 1

and

1 − 1 + 1 − 1 + … = (1 − 1) + (1 − 1) + … = 0

Related to all this, there is a perhaps apocyphal story in which it is rumored that a student once posed the following problem to John von Neumann:

Two trains begin a mile apart and head towards each other at 60 miles an hour. A fly on one train flies at 120 mph to the other train, and when it touches the other train, it immediately turns around and flies back to the first train, and so on, flying back and forth between the two trains until it gets squashed in the middle. How far does the fly travel?

von Neumann thought about it a moment and said, “One mile.” The student said to von Neumann that most people don’t realize that the problem can be figured out easily: the trains meet in 30 seconds, and the fly can travel one mile in half a minute; yet most people think they have to add up the infinite series to figure out how far the fly travels. As the story goes, von Neumann replied, “But that’s how I did it.”

A Busy Week — Fun at NCTM and USASEF

The 2012 Annual Meeting of the National Council of Teachers of Mathematics (NCTM) is happening next week, April 25‑28, in Philadelphia, PA. As it winds down, the USA Science and Engineering Festival starts in Washington, DC, and will occur April 28‑29. It will be a busy week for me — I am performing twice at each event! If you happen to be attending either event, please stop by and say hello.

At the NCTM Annual Meeting…

• To 10 and Beyond Using Free Illuminations Resources
  Friday, April 27, 8:30-10:00 a.m.
  Salon A/B (Philadelphia Marriott Downtown)
• Using Free NCTM Resources to Promote an Understanding of Proportion
  Friday, April 27, 1:00-2:30 p.m.
  Salon A/B (Philadelphia Marriott Downtown)

At the USA Science and Engineering Festival, Washington, DC…

• Puns and Puzzles
  Saturday, April 28, 2:00-2:30 p.m.
  Franklin Stage (Washington Convention Center)
• Puns and Puzzles
  Sunday, April 29, 3:00-3:30 p.m.
  Franklin Stage (Washington Convention Center)

I am expecting an engaged crowd at each event, and I am hopeful that my presentations are received better than this…

A mathematician and an engineer attend a physics lecture. The topic is Kulza-Klein theories involving physical processes that occur in 9-dimensional space. The mathematician is enjoying the lecture, but the engineer is confused and frustrated. At the end, the mathematician comments about how wonderful he thought the lecture was. The engineer asks, “How do you understand this stuff?”

The mathematician replies, “I just visualize the process.”

“But how can you possibly visualize something that occurs in 9-dimensional space?”

“Easy,” says the mathematician. “First, I visualize it in n-dimensional space, and then I let n = 9.”

Look Before You Leap

Too predictable?

Why do frogs, kangaroos, lords and leopards like 2012?
Because it’s a leap year!
(Did you know that a group of leopards is called a “leap”?)

Speaking of leaps, a friend and I were recently discussing the following problem:

A flea can jump up to 350 times its own length. If the same were true of humans, how far would a person whose height is 5′ 6″ be able to jump?

Though the intent is clear, the problem assumes that the length of a flea is analogous to the height of a human. A would-be solver who overthinks this problem might reason that a flea’s length is approximately twice its height, in which case it could jump 350 × length = 350 × (2 × height) = 700 times its own height. Solving the proportion required by the problem, a 5′ 6″ human would be able to jump 3,850 feet, which is twice the intended answer.

Not that it matters. Even long jumper Mike Powell, who holds the world record with a jump of 29′ 4″, was not able to leap even five times his height.

But the problem reminded me of this joke…

A team of engineers was required to measure the height of a flag pole. They only had a measuring tape, and they were frustrated that they couldn’t slide the tape up the pole. After a while, a mathematician happens by, hears about their problem, removes the pole from the ground, and proceeds to measure it easily.

When he leaves, one engineer says, “That is just like a mathematician! We need to know the height, and he gives us the length!”

Love Thy Dilbert!

Why do I make fun of engineers so often? Well, mainly because they deserve it, but also because it’s so damn easy.

Today is the first day of National Engineers Week, an annual celebration to honor those who ensure that things don’t fall over, blow up, or go flying off the rails unexpectedly, as well as to honor those who make sure that things do fall over, blow up, and go flying off the rails when they’re supposed to.

Engineers receive an inordinate amount of abuse. Well, inordinate might not be the right word. Perhaps a better word would be, um, appropriate. But most of it is in good fun, and it is widely acknowledged that there are lots of reasons to love engineers…

• They can handle stress and strain in a relationship.
• They understand that it’s not the length of the vector, it’s how you apply the force.
• They understand the motion of rigid bodies.
• They can teach you what those other “buttons” on your “calculator” do.
• They understand fluid flow and heat transfer.
• They excel at erections.
• The world revolves around them, literally — they chose the coordinate system.
• Just like beams, they elongate when they get loaded.
• They understand projectile motion.
• They do it right the first time.
• They can go all night with no sign of fatigue.
• They know the right-hand rule.
• They have significant figures.

Of course, there are lots of reasons not to, as well…

• They won’t buy anything without a cost-benefit analysis.
• They file for divorce if you call while they’re debugging.
• Pocket protectors, slide rules, and Star Trek.
• They talk in acronyms.
• They touch their cars more often than they touch their spouses.
• They only listen to classic rock, and they generally hate everything from Bach to Prince.
• No matter how hard you cry and how loud you yell, they’ll just calmly discuss your emotions in terms of mathematical logic.
• They work from 6:30am to 7:30pm daily; there are no morning kisses and no evening walks.
• The only social life they know consists of posting and “talking” on the Internet.
• T-shirts and jeans are their formal dress.
• A hot dog and a six-pack is their seven-course meal.

Though most of us harbor a high level of disdain toward engineers, the following synopsis explains why most humans respect them. This explanation is borrowed from The Dilbert Principle by Scott Adams:

Engineers are widely recognized as superior marriage material: intelligent, dependable, employed, honest, and handy around the house. While it’s true that many normal people would prefer not to “date” an engineer, most normal people harbor an intense desire to “mate” with them, thus producing engineer-like children who will have high-paying jobs long before losing their virginity.

Finally, I leave you with the funniest thing that I ever heard uttered by an engineer…

4 Jokes, Just For Fun

A random compilation of four unrelated jokes, just for fun…

Two math professors are exiting the subway when a panhandler asks them for some change. The first prof refuses in disgust. The second prof, however, opens his wallet and gives him a $5 bill. “What’d you do that for?” asks the first. “You know he’s just going to use it for booze.”

“And we weren’t?” says the second.

What do statisticians use for birth control?
Their personalities.

Three engineers on a desert island find a magic lamp. They rub it, and a genie pops out. “I’ll grant you each a wish,” says the genie.

The first engineer says, “I wish I had 25% more intelligence. Then I’d be smart enough to get off of this island.” The genie turns her into an accountant, and she swims off the island.

The second engineer watches this and says, “I wish I had 50% more intellignce. Then I’d be smart enough to get off this island.” The genie turns her into a statistician, and she makes a raft from trees and sails off.

Finally, the third engineer says, “I wish I had 100% more intelligence. Then I’d be smart enough to get off this island.” The genie turns her into a mathematician, and she walks across the bridge.

What’s the difference between a dead skunk in the road and a dead economist in the road?
There are skid marks before the skunk.

Twice the Sum of Its Digits

As my sons and I were doing a 6 × 6 KenKen puzzle today, we needed two numbers with a product of 18. “What two numbers multiply together to give 18?” I asked the boys.

Eli answered, “4 and 4½.”

“Um, yeah,” I responded. “How do you know that?”

“Well,” he said exuberantly, “4 × 4 is 16, and 4 × 5 is 20, so 4 × 4½ is 18.”

By the look on my wife’s face, I could tell that she was as shocked as I was. “Holy sh*t,” I said. “He just did linear interpolation!”

Why is it that the more accuracy you demand from an interpolation function, the more expensive it becomes to compute?

That’s the Law of Spline Demand.

As it turns out, our paths crossed the number 18 several times today. While brushing their teeth, Eli explained that he had to floss 18 times. “There are 4 spaces between my fingers, so there are 9 spaces between my teeth. So I have to floss 18 spaces on the top and bottom.”

The number 18 walks into a bar. “I’d like a beer,” he says.

“Sorry, I can’t serve you,” says the bartender.

“Why not?” asks 18.

“Because you’re under 21.”

After each night’s bedtime story, either my wife or I count to the boys before they go to sleep. Tonight, Eli asked mommy to count to 198 by the Phibby (pronounced fee‘-bee) numbers, which is Eli’s word for the multiples of 11. Nadine said, “That seems like a lot of counting,” to which Eli responded, “Not really — 198 is only the 18th Phibby number.”

[Footnote] As I was doing “research” for this post, I did a Google search for “joke interpolation.” I was directed to Joke Retrieval: Recognizing the Same Joke Told Differently, an academic paper that codifies jokes independent of context, characters, and location; instead, jokes are compared by punch line, and professions/countries are viewed as interchangeable. The result is a model that attempts to identify two different versions as the same joke. Several variations of the following joke appeared within that paper:

An engineer driving westbound collides with a mathematician driving eastbound on the same highway. Their cars are completely demolished, yet neither driver has even a scratch. They each crawl from the wreckage, and they begin to marvel at what just transpired. “This is a miracle!” says the engineer. “Can you believe that neither of us got hurt?”

“I know!” says the mathematician. “And look! This bottle of whiskey in my back seat is still intact. Such an amazing occurrence calls for a celebration,” he says, as he unscrews the cap and hands the bottle to the engineer.

The engineer swigs half the bottle, then hands it back to the mathematician. The mathematician puts the cap back on and sets the bottle on the ground.

“Aren’t you having any?” asks the engineer.

“Nah,” says the mathematician. “I think I’ll wait till after the police arrive.”

Working at NCTM

I am the Online Projects Manager at the National Council of Teachers of Mathematics. I love my job — I’ve been here for 6 years, and I’ll stay here another 60, if they’ll let me; I love my organization — I’m not yet 40 years old, but I’ve been a member almost half my life; and I love my colleagues. But working at NCTM has its share of, um, challenges.

Take the equipment we have in the building, for instance. Today, I selected “single‑sided” on the photocopier, and all of my copies were printed on Möbius strips.

Of course, my mathy colleagues cause problems, too. There are three types of people who work at NCTM: those who can count, and those who can’t.

About a year ago, a small fire started in one of the hallways. An engineer, a scientist, and a statistician — who were at NCTM headquarters attending a summit about the merits of always including three related professions in the set-up of a joke — began debating the best way to extinguish the blaze.

“Dump some water on it!” the engineer suggested.

“No! Remove the oxygen!” said the scientist.

The statistician, however, started running around the building, starting fires in other locations. “What the heck are you doing?” the other two asked.

“Trying to create a decent sample size,” he said.

To put out the fires, a mathematician on staff brought them several buckets of water. The fires were extinguished one by one, but when they finished, there was an unused bucket of water. The statistician said to the mathematician, “Can you please get rid of that water?”

The mathematician proceeded to start another fire, and then he dumped the bucket of water on it.

“What’d you do that for?” the statistician asked.

“I reduced it to a previously solved problem,” said the mathematician.

More seriously, the following is a true story about NCTM.

The James D. Gates Building in Reston, VA, serves as the national headquarters for NCTM. In 1993, an addition to the building nearly doubled its size. In the area between the original structure and the addition, a courtyard was created, and a geometric design of circles and triangles was constructed on the floor of the courtyard with bricks and drainage pipes:

Long‑time members of NCTM might recognize the old NCTM logo:

Shortly after the building was expanded, however, it was learned that a number of publishing companies, eager to align themselves with NCTM after the release of Principles and Standards for School Mathematics, began placing the NCTM logo directly on their products. Cease‑and‑desist letters were sent to the publishers asking them to kindly remove the logo from their materials — and NCTM was shocked when they said, “No!” As it turns out, the publishers’ lawyers had done their homework, and they learned that the NCTM logo had never been trademarked. As a result, there was nothing that NCTM could do to prevent them from using it. 

Consequently, the NCTM logo was revised to the version we have today:

In the courtyard, we have a constant reminder of a bureaucratic blunder. As you’ll notice, the current logo has the ® symbol — and no one’s taken this one away from us, baby! Personally, I think the new one is better, anyway, with allusions to the infinity symbol; the letter x, as an algebraic variable; and a small child, which is a constant reminder that our profession is not just about numbers and shapes but about the lives we touch.

Behind Closed Doors

No profession is safe…

A physicist, an engineer, and a mathematician are using a public restroom.

The physicist finishes at the urinal, washes his hands very well using lots of soap and water, and says, “Physicists are very clean.”

The engineer finishes, then washes his hands with a very small amount of soap and water. He says, “Engineers are able to make maximum use of scarce resources.”

The mathematician finishes and walks out the door without washing his hands. On his way out, he says, “Mathematicians know enough to not piss on our hands.”

After the other three have finished, a minister walks in, washes his hands first and then goes to the urinal. He says to the others, “At seminary, they taught us to wash our hands before handling sacred objects.”