Fun and Sun at 2013 MathCounts National Competition
On May 10, I attended the MathCounts National Competition.
From my perspective, the most important part of the event was the world-record attempt to place 244 middle school students, 61 coaches, and 20 advisors into an arrangement of the first 25 rows of Pascal’s Triangle. (As the chair of the MathCounts Question Writing Committee, I was counted among the advisors.) This may sound easy — after all, each term of Pascal’s Triangle is the sum of the two numbers above it, and the triangle is vertically symmetric, so how hard could it be to arrange people holding the numbers?
Well, there were two pieces to this attempt that increased the difficulty level. First, no one knew what number they would get ahead of time. Each of us received a sealed manila envelope, and inside was a number from Pascal’s Triangle printed on a piece of 8.5″ × 11″ cardstock. We weren’t allowed to open our envelopes until given the signal to begin.
Second, the folks from Guinness required that we accomplish this feat in under 10 minutes. (Unbeknownst to me, if you want to set a benchmark for a Guinness World Record, you can’t just call the folks at Guinness and tell them that you were able to remove all the hairs from your chihuahua using only a pair of tweezers in 3 days, 16 hours, and 34 minutes, for example, and expect that they’ll include you in the book. Instead, you have to call Guinness ahead of time, tell them what you’re planning to do, and then they’ll tell you how fast you’ll have to do it for them to consider it worthy of inclusion.)
An adjudicator from Guinness was there to officiate and ensure that there was no funny business. He confirmed that all 25 rows were assembled correctly, and because we were able to complete the triangle in an astounding 6 minutes, 16.5 seconds, we set a Guinness World Record. This is what we looked like upon completion:
I’m along the right side of the triangle, holding a 9. You may not know what I look like, but I’m still fairly easy to spot — even sitting down, I’m quite a bit taller than the middle school students who surrounded me.
The Countdown Round — a Jeopardy-like event where twelve kids, arranged in a tournament bracket format, compete head-to-head to answer questions before their opponent — is the culmination of the event. The winning question from this year’s Countdown Round was:
What is the greatest integer that must be a factor of the sum of any four consecutive positive odd integers?
Alec Sun was crowned national champion when he gave the correct answer to this question. (Which he did in less than 20 seconds, by the way. You can have more time than that, but you won’t find the answer on this page.)
When Akshaj Kadaveru, a seventh-grader from Virginia, took the stage for the Countdown Round, Lou asked him, “You’re a local. What is one place in Washington, DC, that you’d recommend your fellow competitors see during their visit to the nation’s capital?”
Akshaj suggested the Air & Space Museum.
“Oh, I’m sorry,” said Lou. “The answer we were looking for is the zoo.” And he held up a piece of paper with the word ZOO.
A little while later, another competitor from Virginia, seventh-grader Franklyn Wang, took the stage. Lou asked him the same question about which place out-of-town competitors should visit.
“This hotel!” Franklyn giggled into his microphone.
“Actually,” said Lou, “the correct answer is the zoo.” Again, Lou held up a piece of paper with the word ZOO.
When Alec Sun took the stage, Lou explained to the crowd that Alec was the only competitor in the history of MathCounts to make it to the Countdown Round three straight years. “But,” Lou said to the audience, “I was talking to Alec yesterday, and he told me that he was nervous. In his two previous appearances, he hadn’t answered a single question. I’d really hate for him to leave the stage today without having answered at least one question correctly. So, Alec,” he said, turning to the young man, “I’m going to give you a non-math question to answer. It’s not a softball — you’re really gonna have to think about this one. But I’m confident you can do it.” And then Lou asked him, “Alec, what is one place you’d recommend that folks visit while they’re in town this weekend?”
“Uh… the zoo?” Alec asked.
“Correct!” yelled Lou. “The zoo!” And the entire room burst into applause.
Who said that math people can’t be funny?
Is It Phi Day Yet?
There are several pressing matters that needs to be resolved.
Let’s use the following poll to resolve the first…
Don’t be swayed by the giant.
The second matter concerns the date of Phi Day.
As if it weren’t enought that the contrivance known as Pi Day is celebrated on 3/14, simply because the three digits of that date agree with the first three digits of π. Now the folks at www.phiday.org say that Phi Day should be celebrated on June 18, since 6/18 are the first three digits after the decimal point of φ, the golden ratio. What’s next? Are we gonna say that e Day should be celebrated on 7/18, since e = 2.718? Please.
But wait, there’s more. The folks (or should I say folk, since I think it’s just one guy) at www.goldenratio.org have proposed that Phi Day should be celebrated on October 31 in the Northern Hemisphere and May 6 in the Southern Hemisphere. The convoluted calculations for these dates can be found in this white paper.
Let’s settle this once and for all. The Golden Ratio divides a line into mean and extreme ratio, so Phi Day ought to divide the year into mean and extreme ratio, too.
The golden ratio divides a line segment into two parts, a and b, such that
For a non-leap year, then, we are looking for the date that divides a 365-day year into the golden ratio.
This formula yields
For leap years, which contain 366 days, the result is
In non-leap years, the 139th day of the year is May 19; in non-leap years, the 140th day is May 19. Consequently, a rather satisfying result occurs: the same date can be used for Phi Day in leap and non-leap years.
Further, it’s nice that the date occurs during the school year. One last chance to have a math party before summer break. And while a standard cake pan measures 9″ × 13″, you are strongly encouraged to use an 8″ × 13″ cake pan to concoct a treat for this special day.
So there you have it. An official MJ4MF declaration:
Whereas, phi represents the golden ratio, which divides a length into the ratio 1:1.618; and,
Whereas, the 19th day of May divides the year into the golden ratio; therefore, be it
RESOLVED, that Phi Day henceforth shall be celebrated on May 19; and be it further
RESOLVED, that there shall be no further discussion of this matter.
We’ll use the results of the poll above to determine whether it should be pronounced National Fee Day or National Fie Day.
Interview: Matt Parker, Stand-Up Maths
Matt Parker is a funny dude — and a bit warped.
He created a show called Your Days are Numbered which, as the name implies, is about the statistics of death. The tagline reads, “You’ve got a 0.000043% chance of dying during this show.”
He claims that his favorite number is 3,435, because 33 + 44 + 33 + 55 = 3,435.
And he took two diametrically opposed careers — math teaching and stand‑up comedy — and morphed them into one.
What do you get when you cross a mathematician and a stand-up comic?
Matt Parker.
But Matt Parker is not only funny and warped. He’s also wicked smart. Check this out…
Being a math guy and wanna-be funny guy, I interviewed Matt with the hope that maybe I could learn a little.
Popular belief holds that both Brits and mathematicians are notoriously unfunny. How do you explain your phenomenon?
I am one of many counterexamples.
Your show Your Days Are Numbered: the Maths of Death deals with the probability of dying in various ways. What’s your favorite statistic about death?
You are more likely to die from falling out of bed than falling off a ladder or cliff.
You’re clearly not dead, but have you ever had a near-death experience?
I once nearly died trying to find the integer crossing point of two lines of latitude and longitude in the Australian desert. But I made it to the ‘confluence’ and back.
As far as I know, you’re the first mathematician ever to do a national comedy tour. Tell us how this came to be. What was the trajectory?
I was working as a stand-up comic in regular comedy clubs as well as being a maths teacher. Slowly, the two careers started to merge. In stand-up comedy, you cannot help but talk about what you are interested in, so I would talk about maths. I wouldn’t do maths jokes — they are notoriously unfunny — but I would use maths and being a maths teacher as the basis for my jokes.
Eventually I got a following for talking about maths and so my material could gradually get more and more nerdy. My maths tour show Matt Parker: Number Ninja contains a lot of maths, but it’s still a comedy show in its own right. You don’t need to be a mathematician to enjoy it — just like I enjoy political comedians without having a big interest in politics — but there is an extra layer of jokes for the extra-nerdy.
[Ed. note: The opinions expressed by Matt Parker about math jokes being “notoriously unfunny” do not necessarily reflect the views and opinions of the MJ4MF blog.]
Why do you call yourself “the number ninja”?
A mathematician is not someone who does lots of boring sums, like what most people remember from school maths. A mathematician is someone who plays with numbers and maths and tries to solve puzzles. The phrase “Number Ninja” helps to get this sense of playfulness across.
What’s the funniest thing you’ve ever said during a lecture?
I was once showing a spreadsheet which was an RGB digital photo of myself, turned into a series of conditionally formatted cells. I couldn’t help but say, “I’ve really exceled myself.”
Who’s the funniest mathematician or professor you know? What’s the funniest thing that he or she ever said?
A surprising number of stand-up comedians were once mathematicians. The fantastic Dave Gorman is always worth looking up. [Ed. note: You might like Dave Gorman's bit about perfect numbers.]
Where is it harder to be funny — on stage, or at the front of a classroom?
The stage is far easier because you’re expected to be funny. The classroom is a place to communicate maths. There is a lot you can learn from performing comedy when you are in the classroom, but jokes are the very last thing. The real transferable skills from comedy to teaching are things like structuring a lesson and knowing how to pace a talk.
What’s your favorite blog post that you’ve written for The Guardian?
I am rather proud of Mobile Phone Masts Linked to Mysterious Spikes in Births.
Matt Parker will be performing in the Festival of the Spoken Nerd in London through July 12.
Mathiest Week of 2013
Can you hear it? That’s the sound of the awesomeness approaching.
It starts this Wednesday.
5/8/13
The month, date and year are consecutive terms in the Fibonacci sequence.
It continues on Thursday.
5/9/13
The numbers form an arithmetic sequence.
And then there’s Sunday.
5/12/13
That’s a Pythagorean triple.
Arithmetic sequence dates are a dime a dozen. In fact, there are six of them in 2013 alone. Pythagorean dates and Fibonacci dates are far more rare. There are only eight Pythagorean dates and six Fibonacci dates in the entire 21st century. To have all of them occur within a six-day span is incredible.
How will you celebrate?
How Many Share Your Birthday?
This afternoon, we celebrated Alex and Eli’s sixth birthday with a Disney-themed Cinco de Mayo party. The kids all wore Mickey Mouse ears, while the parents drank lots of margaritas. Tonight’s “bedtime math” question for my sons was the following:
You celebrated your birthday on May 2. How many other people in the world do you think celebrated their birthday on May 2?
It’s a simple estimation problem for most of us, but ratio is a tough concept for six-year-olds. I wasn’t sure they’d make much progress… especially since the good folks at about.com make this claim:
You currently share your birthday with about 859,178 people who reside in the United States.
This estimate appears to have used 313,600,000 as the U.S. population, which is reasonable, and then divided by 365. My frustration is that they then display the result to six significant figures. That’s problematic for two reasons — first, because their population estimate has only four significant figures, but also because it’s not the case that exactly 1/365 of the population celebrates their birthday on a given day.
But I digress. Sure, I’m frustrated with about.com’s negligence, but I started this post to tell you about our bedtime math problem, and it highlighted why I hate traditional textbook problems even more than I hate bad math in the media.
Alex first suggested that maybe the number of people who have the same birthday could be found by calculating 1/14 of 7 billion. When I asked why he wanted to divide by 14, his response was, “Because it’s a multiple of 7.” When I asked a few more questions to probe his thinking, he changed his mind. “No, wait, maybe it’s 1/35.” This time, he said he wanted to divide by 35 because it was a multiple of 7 and a multiple of 5, and he knew that 7 billion was also a multiple of both 7 and 5.
Then it hit me. He wasn’t trying to solve the problem. He was just trying to make sure the answer was a “nice number,” that is, an integer that preferably would end in a couple of zeroes.
A few more questions, and he finally admitted he knew an estimate could be found by dividing 7 billion by 365. “But that doesn’t work when you divide,” he told me.
Arrgh.
I believe this is what happens when kids see too many traditional textbook problems where the answers are neat and clean. They get conditioned to thinking that math is never messy.
[Update: 5/8/13] Just read this on the About page at the Let’s Play Math blog and thought it was worth including here: “Math is like ice cream, with more flavors than you can imagine — and if all your children ever do is textbook math, that’s like feeding them broccoli-flavored ice cream.”
And that couldn’t be further from the truth. Math is unbelievably messy. At least, real math is. Solving real-world problems often means getting a little dirty. You’ll have to roll around in fractions, dig through some decimals, and — Heaven help us! — occasionally tangle with some irrational numbers and extraneous results.
Eli then offered, “If you divide 7 billion by 365, you won’t get an integer.” (He smiled, proud of himself for using the term integer.) “That’s the answer, but I don’t know how to do that.” What he meant is that he couldn’t compute the result in his head; nor would I expect him to. We then found an estimate by building on Alex’s idea — instead of dividing by 35, we divided by 350 to approximate the number of people who celebrated a birthday on May 2, since 350 is close to 365 but gives a much nicer answer.
Wow. There are roughly 20 million people who will celebrate their birthday on the same date as you. Crazy, huh?
All of this reminds me of a few jokes.
Recent research shows that those who celebrate more birthdays live longer.
And all the time, I tell my wife:
Honey, you’re one in a million. Which means that there are 7,000 people on Earth exactly like you, so just remember that it wouldn’t be that hard to replace you.
The Math of Disney
Just returned from a week in the Magic Kingdom, where I learned a lot. Like this tidbit:
A recent government study just confirmed that six of seven dwarves is not Happy.
That’s so good, it deserves a graphic:
I also learned that relativity is a novel concept for kids who are 6 years old. When asked how fast we were traveling on The Barnstormer junior roller coaster, one of my sons replied, “It felt like we were going 100 mph!” The other said it only felt like 50 mph. When asked how fast we were traveling in the airplane on our ride back to Virginia, one son suggested 10 mph, the other suggested 20 mph.
Depressingly, the ratio of bottles of Coke to bottles of water consumed at Disney is almost 6 to 1. According to a Walt Disney World fact sheet, tourists to Disney consume 75 million bottles of Coke and 13 million bottles of water annually. My sincere hope is that most folks use refillable water bottles, which would explain the discrepancy in sales.
And finally a math question.
The fact sheet states that the Earffel Tower, which is the water tower at Disney’s Hollywood Studios, would wear a hat size of 342-3/4, although another reference says that the hat size would be 342-3/8. What is the approximate radius of the Earffel Tower?
Prime Twins
When my wife gave birth to our sons, Alex and Eli, I was so excited that I called the minister immediately. “Reverend,” I said, “Nadine just gave birth to twin boys!”
“That’s fantastic!” he replied. “Why don’t you bring ‘em down to the church on Sunday, and we’ll baptize ‘em.”
“How ’bout we just baptize one,” I said. “Let’s keep the other as a control.”
It can be difficult to tell that my sons are identical twins. The picture below, for instance, is a red herring — though they’re identical, Alex is using a TI Math Explorer purely for computation, while Eli clearly prefers the graphing capabilities of a TI‑73.
Prior to their birth, I tried to imagine mathematical names. There are, of course, many pedantic possibilities…
- Area and Perimeter (Ari and Peri, for short)
- Max and Min
- Vector and Scalar
- Radius and Diameter
- Abscissa and Ordinate
- Sine and Cosine
But I’m not one to settle for low-hanging fruit. I pushed myself to find better options.
- If and Only If
- Radius and Apothem
- Vector and Sector
- Perp and Dicular
- Johann and Jakob
- Catenary and Parabola (Cat and Perry, for short)
- Lucas Cameron Maximilian and Gregory Caliban Farquhar (aka, LCM and GCF)
Today, my perfect sons turn the perfect age — six! And though I wasn’t able to convince my wife that Epsilon and Delta would have been perfect names, I have to admit that Alex and Eli suit them just fine.
What are your suggestions for mathy twin names?
