Archive for November, 2011
I’ve been thinking about a lot of things lately…
Instead of having “answers” on a math test, they should just call them “impressions,” and if you get a different impression, so what? Can’t we all just get along?
If you think that dogs can’t count — let him watch you put two biscuits in your pocket, and then only give him one.
If we stop teaching students about numbers less than zero, do you think there would be a positive impact on education?
A prime rib cannot be cut with a steak knife, because it is only divisible by itself and one.
A math professor is someone who talks in other people’s sleep.
A mathematician is someone who will begin a sentence with, “As everyone knows,” and then finish it with something he just learned.
And a famous quotation…
Never trust any quote you find on the Internet.
– Abraham Lincoln, Second Inaugural Address
Inspired by Planet Money’s Pick A Number contest, and buoyed by a story about how NCTM President Mike Shaughnessy recently used my favorite game with a group of students at Albuquerque Academy, I’ve decided to conduct an online experiment using a Google Docs form.
If you’ve got a minute and are willing to participate, read on.
The rules for my favorite game are as follows:
- On a piece of paper, everyone playing writes down a positive integer.
- Show your number to a neighbor (for verification purposes only).
- The winner is the person who wrote down the smallest integer not written by anyone else.
In order for this psychological math strategy game to be any fun, you need one important piece of information — how many people are playing. If played as a solitaire game, you should win every time. But if played with a group of 50, well, some real thought will need to go into your choice. Consequently, I’m going to limit the game to 100 players. (Well, sort of. What I’m actually gonna do is break the total number of responses into groups of 100, and I’ll consider each set as a separate game. So it’s not exactly the same, but this should allow you to play using the same strategy as if you were playing with just 99 other people.)
For this online version, the second step of the rules — show your number to a neighbor — is unnecessary. So all you need to do to play is enter your number. (I’ve also asked for your name and email address, too, just so I can give you proper credit and contact you if you win. But those are optional. If you do supply your email address, cross my heart, there will be no spam or third‑party solicitations.)
[Update] This game was originally run for one week, Nov 28 – Dec 5, 2011. The results of that initial trial (based on 1,042 entries) are available at the link given below. That said, I see no reason to prevent others from participating and, from time to time, I will update the results page to reflect new data.
If you have difficulty accessing the form below, click this link.
I recently read a conference proposal in which the potential presenter declared, “PEMDAS must die!” Upon reading this, I thought, “Hear, hear!” But then the potential presenter claimed, “We should use GEMDAS instead!” Really? Does this presenter honestly believe that changing P (parentheses) to G (grouping) is sufficient to eliminate all the problems students have with order of operations?
I have heard that some teachers use GEMS, where M stands for both multiplication and division and S stands for both subtraction and addition. That eliminates the problem some students have, thinking that multiplication has to happen before division or that addition has to happen before subtraction.
Whatever. From my experience, most of the trouble students have with PEMDAS, GEMDAS, or GEMS typically results from a failure to consider it at all when working with a complex expression. It isn’t the mnemonic.
Here’s a mnemonic for remembering what a mnemonic is: Think about a person with a terrible memory who previously suffered an inflammatory lung condition. Imagine that he often makes up catchy little phrases to help him remember things. Then you can make the association of pneumonic with mnemonic, and you won’t have any more trouble. There, now… isn’t that simple?
The following are some of my favorite mnemonics.
Feet in a Mile
Five Tomatoes → 5 2 M8 0′s → 5,280 feet per mile
Tough Multiplication Fact
5, 6, 7, 8 → 56 = 7 × 8
A Rat In The House May Eat The Ice Cream
Multiplying Signed Numbers
My friend’s friend is my friend (pos × pos = pos)
My friend’s enemy is my enemy (pos × neg = neg)
My enemy’s friend is my enemy (neg × pos = neg)
My enemy’s enemy is my friend (neg× neg = pos)
I am pretty → I = prt
DiRT → d = rt
King Henry Died By Drinking Chocolate Milk
Kilo, Hecto, Deca, Base, Deci, Centi, Milli
(sung to the tune of Yankee Doodle)
Oscar had a heap of apples, sine and cosine tangent
Angle Sum Formulas
Sine Cosine, Cosine Sine;
Cosine Cosine, Sign Sine Sine!
sin (a + b) = sin a cos b + cos a sin b
cos (a + b) = cos a cos b – sin a sin b
e (6 digits)
By omnibus I traveled to Brooklyn.
π (7 digits)
May I have a large container of coffee?
π (3,835 digits)
In 1995, Mike Keith wrote a poem called Poe, E., Near A Raven, which gave the first 740 digits of π (the number of letters in each word indicates the value for that digit of π). It was based on Edgar Allan Poe’s poem The Raven. But some people are never satisfied, so he later wrote the Cadaeic Cadenza, which gives the first 3,835 digits of π.
My life is pretty good. I mean, sure, I wish I were better at Scrabble®, or a little smarter, or a little faster, or a lot better looking. But don’t we all? Overall, I really can’t complain.
For instance, I get to write a blog about math jokes, I get to do math every day for a living, and I know that the proper amount of time t, in minutes, to cook a turkey is given by the formula t = 38 × w2/3, where w is the weight of the turkey in pounds. And all of that is pretty cool.
I’ve not been as happy lately as I probably should be. Thanksgiving seems like the right day to reverse that pattern and recount all the things in life for which a math geek like I should be grateful. Feel free to let me know what you’re grateful for, too.
- For twin sons who love math almost as much as their daddy
- For my sons getting so excited that they speak faster than I can possibly understand (especially when they’re excited about math)
- For a wife who’s willing to tolerate a schlub like me, and who makes it very easy to keep loving her
- For grocery store tiles of the perfect size, so that your natural stride length perfectly aligns with light and dark squares
- For the wonderful safety of numbers
- For getting lost in a challenging problem
- For going to bed with a challenging problem, and waking up with the solution
- For MathWorld
- For cheesy math jokes
- For people who appreciate cheesy math jokes
- For good health
- For Nurikabe
- For friends who know what a scoober, a thumber and a blade are
- For Excel®
- For all of the amazing people at Penn State who are not currently garnering headlines but are doing wonderful things for society
- For eyesight, to see the mathematical beauty in the world
- For teachers, and for anyone else who is willing to share their knowledge
- For disappointment, which reminds me to appreciate all the good things that I already have in my life
- For cell phones and free long distance
- For serendipitously changing the channel to a football game with five minutes left when Tim Tebow has the ball
- For zizzes, and for the word zizz
- For Scrabble® (and more recently Words with Friends)
- For finding a parking spot with time still left on the meter
- For placing the last piece of a puzzle
- For having a really great original idea
- For friends who save me six seconds by pulling a beer out of the cooler and tossing it to me rather than walking over and handing it to me; and, for friends who trust that I’ll catch it
- For clever food names, like the “Muddy Pig” (mini-donut with Nutella and bacon crumbles) at Union Jack Pub in Harrisonburg, VA, or “Devils on Horseback” (chutney-stuffed dates wrapped in bacon)
- For ordering a beer you’ve never heard of, and finding that it’s your new DOC (drink of choice)
- For usually making good decisions
- For having things happen that aren’t all that bad when I’ve made poor decisions
The following story was told to me by Judy White, one of the world’s greatest middle school teachers.
Using wooden cubes, Judy created a set of double stairs. As illustrated below, 2 cubes were required to create 1 step (green), 6 cubes were required to create 2 steps (green and red), and 12 cubes were required to create 3 steps (green, red, and blue).
Judy asked her students how many cubes would be required to create 4 steps, 5 steps, and 6 steps. With a little discussion, her students agreed that 20 cubes, 30 cubes, and 42 cubes would be needed, respectively.
She then asked them to generalize. “Do you see a pattern for how many cubes would be needed to create n steps?” she asked.
One boy responded, “No.”
“There isn’t a pattern?” Judy asked.
“No, Mrs. White,” the boy said, “the answer is no — n × o.”
Not well versed in algebraic notation, the boy used the letter o instead of n + 1.
How great is that?
Speaking of stairs, here’s a math joke involving stairs.
A statistician, a physicist, and an engineer die on the same day. At the Pearly Gates, they are greeted by St. Peter. “To enter Heaven,” he tells them, “you must climb these 1,000 stairs. But while you are climbing, I will read to you from Math Jokes 4 Mathy Folks. If you can make it to the top without laughing, you may enter.”
They start up the stairs. The statistician laughs when he reaches the 47th step. The physicist reaches the 125th step, but he then laughs, too. The engineer, however, makes it all the way to the top.
“Congratulations!” says St. Peter. “Welcome to Heaven!”
Upon hearing this, the engineer begins to laugh.
“What’s so funny?” asks St. Peter.
“I just got the first joke.”
What’s the best name ever? My vote goes to an Army Reservist whose name — and I’m not making this up; you can find documentation here — is
Staff Sergeant Max Fightmaster
If names truly imply destiny, then this guy was born to be a tough-as-nails sergeant.
A close second is Moxie Crimefighter Jillette, daughter of comedian Penn Jillette. One can only hope that she grows up to be a superhero.
These names got me to thinking: What are the best names in the math world? The math equivalent to Staff Sergeant Max Fightmaster would be Algebra von Calculus. Alas, no real person has ever borne the burden of that name. But with multiple thousands of mathematicians since the beginning of time, there have got to be a few gems in there, right? Indeed. Here’s my dirty baker’s dozen.
1. August Beer – Are you kidding me? My favorite month and my favorite libation? Honestly, this name could only be bested by Ultimate Frisbee Copulation, and no mathematician with that name has yet walked the Earth.
2. Weinan E – To my knowledge, the only mathematician with a single-letter last name.
3. Walcher of Malvern – If things didn’t work out with mathematics, he was ready to be a fearless knight.
4. Srinivasa Ramanujan – It just rolls off the tongue so effortlessly.
5. Jon Barwise – True to his name, his best work was done on beer-stained napkins.
6. Helmut Ulm – The letters in his last name are a subset of the letters in his first name. How cool is that?
7. John Viriamu Jones – The inclusion of Viriamu, which is the Erromangan translation of Williams, makes extraordinary this otherwise very ordinary Welsh name.
8. Ken Ono – Six letters total, and the last name is a palindrome that also means delicious (Hawaiian), is the alternative name for Wahoo (fish), and is an acronym for “Or Nearest Offer.”
9. Udny Yule – Why it’s cool defies description. It just is.
10. Brian Pink – Not many mathy folks can pull off this color, but the Australia Statistician wears his name without shame.
11. Nate Silver – A good name, but he gets bonus points for having a cool title: psephologist (elections analyst). And double bonus points for his statement, “It’s always more interesting to apply [numbers] to batting averages than algebra class.”
12. Chike Obi – First sub-Saharan African to hold a doctorate in mathematics.
13. Persi Diaconis – Just an unbelievably cool name, predestined for greatness.
Not worthy of the Top 13, the following are a few honorable mentions…
- Morris DeGroot – Sounds like a comic book character, and it has perfect cadence.
- W. B. R. Lickorish – Three initials, and his last name is a popular treat.
- Alicia Boole Stott – She got her middle name from her father George, who was no slacker in the math world. Then she married an actuary whose last name has a consonant repeated three times. But to ensure that her name didn’t overpower her brilliance, she coined the term polytope. Nicely done, Alicia.
- Jim Propp – The inventor of the SRAT has a name that is most propper.
- James Ax – If name really dictates destiny, shouldn’t little Jimmy Ax have grown up to be a serial killer? Kudos to him for rising above his nomenclatorial limitations.
- Lewis Carroll – Okay, perhaps this one should be disqualified since it’s a pseudonym — but it is a great name, no?
- Nathaniel Nye – Alliteration, anyone?
- Panini of Shalatula – A great mathematician and my favorite lunch-time snack. Win-win!
A warm-up question to prepare you for the jokes that follow:
Name four days that start with the letter T.
A joke for the Celsius crowd…
“It’s freezing outside!” she said.
“I know,” he replied, “and it’s supposed to be twice as cold tomorrow!”
A sentiment shared by too many students…
Mother: Did you learn a lot in school today?
Son: Apparently not! I have to go back tomorrow!
If only this didn’t seem so believable…
Teacher: Tomorrow, Dr. Feynman is giving a lecture on Saturn, and everyone must attend.
Student: Wow, can you get there in just one day?
Ever have a professor like this?
When the student went to his logic professor for help, she replied, “Come back tomorrow.” The student returned the next day and was given the same instructions. The student returned every day, and every day he was told, “Come back tomorrow.”
Finally, the professor lost her patience. “This is outrageous!” she said to the student. ”Don’t you understand simple language? I keep telling you to come tomorrow, yet you insist on coming today!”
And finally, a joke about yesterday…
“My math teacher is crazy,” Johnny told his mom. “Yesterday, she told us that 5 = 4 + 1. Today, she said that 5 = 3 + 2!”
Using Scrabble® tiles, my sons were making anagrams. One would select four tiles, and the other would have to rearrange them to form a word.
This struck me as interesting, so I posed the following question to them:
Take four consecutive letters from the alphabet, and rearrange them to form a common English word.
How many solutions do you think there are? Before you solve the problem, take a guess. Can five words be formed from four consecutive letters? Maybe ten words? Or fifteen?
Okay, now solve the problem. Take your time. We’ll wait for you.
There are 23 ways to select four consecutive letters, and each set of four letters can be arranged in 4! = 24 ways. With 23 × 24 = 552 possibilities, it seems like there ought to be several solutions.
Were you as surprised as I was to find that there was only one?
But maybe I shouldn’t be too surprised. Lots of things in life are unique…
Always remember that you’re unique, just like everybody else.
Student: Do you believe in God?
Professor: Yes — up to isomorphism!
Then again, lots of things aren’t unique…
Don’t think you’re special. Even if you’re 1 in a million, there are still 7,000 people in the world just like you.
Here are two unique, non-math jokes…
How do you catch a unique rabbit?
Unique up on it.
How do you catch a tame rabbit?
The tame way!
Today is a special day indeed. You may have already noticed that today’s date is the repetitive 11/11/11, but did you know that today is the only date this century that can be written in the form mm/dd/yy with one digit repeated six times?
Some people celebrate 3/14 as Pi Day, and to ensure complete precision for their celebration, the moment at which they celebrate is 1:59:26 p.m. In a similar vein, I suggest that we all celebrate “100/9 Day” at 11:11.11 a.m. today. Too bad 100/9 doesn’t have a Greek letter nickname for which it is better known…
Not too long ago, I was forwarded an email that contained several pieces of numerical trivia. The first was this:
This year we’re going to experience four unusual dates: 1/1/11, 1/11/11, 11/1/11, and 11/11/11.
Today is one of those dates, and it is certainly unusual for a date to contain only one repeated digit. The only other dates with just one repeated digit during this century are 2/2/22, 2/22/22, 3/3/33, 4/4/44, 5/5/55, 6/6/66, 7/7/77, 8/8/88 and 9/9/99. Since there are only 13 dates that contain just one repeated digit, it could also be said that 2011 is an unusual year for hosting four of them.
The email also contained the following:
Take the last two digits of the year in which you were born. Now add the age you will be this year. The result will be 111 for everyone in the whole world.
Blanket mathematical statements like this one are frustrating, especially when they are untrue. My friend’s grandfather was born in 1899, so he will turn 112 this year. For him, the result is 99 + 112 = 211. And my sons were born in 2007 and turned 4 this year. For them, the result is 7 + 4 = 11. In fact, based on data about age distribution, the result will not be 111 for approximately 15% of the U.S. population. The yellow bars in the graph below indicate the ages for which this trick does not work.
A better statement of this “trick” might be…
Take the year in which you were born. Now add the age that you will be this year. The result will be 2011 for everyone in the whole, wide world.
Wow! Can you believe it? But it’s not much of a trick anymore, is it?
Happy 100/9 Day, everybody!
[Update] This post originally appeared as “Happy 10/9 Day,” but that was in error. I blame sleep deprivation. It has been updated to “100/9 Day” in all places.
I was presented with an interesting Fermi question today:
How many pounds of food will you eat in your lifetime?
My first estimate: About 20 tons — approximately 1.5 pounds per day (roughly 500 pounds a year) for 80 years.
My second estimate: Unless by pounds you mean British currency, and by food you mean caviar, in which case my estimate would be closer to 21 million.
This made me think of several math and food jokes.
At a restaurant…
“What can I get for you?” asked the waiter.
The mathematician replied, “I’ll have the seven‑layer dip as an appetizer. For my entree, prime rib, dim sum, and the three‑bean salad. To drink, a root beer, and pi for dessert.”
Meanwhile at the cannibals’ house…
The cannibal family was eating dinner. One son says, “I really hate my math teacher.” The other son says, “I know. He’s so tough!” The mother tells them, “Quit complaining. If you don’t like the meat, just eat the noodles.”
And at the university…
What do you call a smiling, sober, courteous person at a math department social event?
One of my favorite pieces about math and food comes from Dave Barry:
Algebra is a vital tool for our young people to learn. The traditional method for teaching it, of course, is to require students to solve problems developed in 1928 by the American Association of Mathematics Teachers Obsessed With Fruit. For example: “If Billy has twice as many apples as Bobby, and Sally has seven more apples than Chester, who has one apple in each hand plus one concealed in his knickers, then how many apples does Ned have, assuming that his train leaves Chicago at noon?”