Archive for May, 2010
When I was an undergraduate at Penn State, I used to go to Pattee Library to do research or to study. Invariably, though, I’d find myself perusing the shelves corresponding to the 510’s of the Dewey Decimal system, locate a book with an intriguing title… and several hours later, I’d surface from the stacks. Nine out of 10 times, the book that would occupy my time would have been written by Martin Gardner.
It was through one of those books that I learned how to make a tetra-tetra-flexagon, and in another I read about the numerologist Dr. Irving Joshua Matrix. It was also in one of these books, Wheels, Life and Other Mathematical Amusements, that I learned my favorite problem, which became my favorite problem because it was the first true problem that I had ever solved entirely on my own. (By “true problem,” I mean that when I first looked at it, I had no idea how to proceed; it was not just an exercise, and it was going to take something beyond what I had learned in my math classes.) If you’re a math nut or a Martin Gardner fan, you’ve likely seen it before, but I offer it here for those who haven’t:
On Monday, Jonathan deposited x dollars in the bank. On Tuesday, he deposited y dollars. Each day thereafter, he deposited an amount equal to the sum of the previous two days’ deposits. On the following Thursday (that is, a week-and-a-half after his first deposit), he made a deposit of exactly $1,000. How much did he deposit each day?
(My apologies for paraphrasing. That may not be the exact wording that Gardner used, but you get the idea.)
I finished solving that problem at a very late hour. It was dark outside Pattee Library, and though I should have been tired, I was as awake and alive as I have ever been. I looked at the solution on my paper, and I remember thinking to myself, “Wow! That was fun!” And a second later, I was disheartened to realize that I was a sophomore in college, yet no one had previously shown me how much fun math could be.
That problem sparked my love affair with math, and it greatly influenced my philosophy about teaching.
Martin Gardner passed away on Sunday, May 22. My heart grew heavy when I heard the news, but my spirits were buoyed when I thought about his great life and the tremendous impact he had. It’s hard to estimate how many people he affected during his 25 years of writing the “Mathematical Games” column in Scientific American or with his 70 books.
But I know he affected at least one, and deeply.
Thank you, Mr. Gardner, and may you rest in peace.
This morning, my son Alex — who is only 3.03 years old — applied the transitive property. I asked, “How many feet are in our house?” He and his twin brother Eli counted their feet and my feet and correctly arrived at 6 feet.
“But you missed some feet,” I said. “Who else is in the house?” They realized that they had not included our dog, Remy, so they added four more and correctly concluded that there were 10 feet in our house. I said, “Great! So you just showed that 6 + 4 = 10.” (Yes, in fact, I really talk this way to my toddler sons.) I then asked, “If mommy were home, how many feet would there be?”
Eli noted that his mommy has 2 feet, and Alex said, “11, 12… 12!”
“Right,” I said. “And 10 + 2 = 12.”
That’s when Alex hit me with something I hadn’t quite expected. He said:
“So, 6 + 4 + 2 = 12.”
Holy mackerel! I was astounded. My 3‑year‑old son had just applied the transitive property!
In doing so, he reminded me of a transitive argument that comedian Richard Jeni displayed in one of his shows:
God is love.
Love is blind.
Therefore, Ray Charles is God.
And speaking of Ray Charles…
Some researchers say that the iPad and laptops may alter sleep cycles, fooling your brain into thinking it’s daytime. Alon Avidan of the Sleep Disorders Center at UCLA said that people should just take a boring, old-fashioned book and read by a lamp. I think that’s a good idea… and might I suggest that Math Jokes 4 Mathy Folks be your book of choice?
Okay, that was a shameless plug. Then again, I’ve never claimed to be above that.
For tolerating that shameless self-promotion, you’ve earned the right to read a few math jokes about books and sleeping…
Why was the math book sad? Because it had so many problems.
Some mathematicians have become so tense recently — many of them are no longer able to sleep during seminars.
A math professor is a person who talks in someone else’s sleep.
My apologies if that last one hits a little close to home…
Instead of giving a toast just before the meal, the best man at my wedding asked if he could give his toast just before we cut the cake. It was an odd request, and it didn’t really matter to me — but more importantly, it didn’t matter to my wife — so we agreed. This is how he ended his toast:
Today is May 16, and you know that today is a special day for Patrick and Nadine. But what you may not know is that today is an important day in history — Marie Antionette was beheaded on May 16. So as she said, “Let them eat cake!”
With that, all guests were directed to the wonderful cake prepared by my wife’s high school friend, Kate Zuckerman, who, at the time, was the pastry chef at Chanterelle, a five-star restaurant in New York City.
All this talk of decapitation reminds me of a joke…
A priest, a rabbi and a mathematician are in the queue to be decapitated.
The priest’s head is put in the slot and the executioner pulls the lever. The blade moves a few inches but then stops before reaching the priest’s neck. The executioner raises the blade again and releases it, but again, it stops short of its target. The priest declares that the hand of God had intervened, so the executioner lets him go.
The rabbi’s head is then put in the slot. The executioner pulls the lever, the blade drops, but again it stops before reaching the rabbi’s neck. The executioner lets the rabbi go, assuming that God had intervened again.
The mathematician’s head is put in the slot. He looks upward and smiles.
“What are you so happy about?” the executioner asks.
“I figured out the problem,” says the mathematician. “A small pebble is blocking the path of the blade. If you remove the pebble, it should work just fine!”
My kids are three years old — yes, both of them are three years old; they’re twins — and they already know how to read and spell. I’ve always enjoyed watching kids’ intellectual development, but it’s all the more exciting when they’re your own children.
They’re pretty good with numbers, puzzles, and patterns, too, but yesterday they reminded me that they’re still just three years old. Alex, Eli, and our golden retriever Remy were riding in the car on the way to a local park. From the backseat, Eli asked, “How do you spell park, daddy?”
This is a word that Eli knows how to spell, so I said, “I don’t know. Can you help me spell it? What’s the first letter?”
That was all the prompting he needed. He spelled it easily: “P-A-R-K.”
“Great!” I said. “Let’s spell some other words. What’s the opposite of light?”
Alex said excitedly , “Dark!” and then spelled it correctly: “D-A-R-K.”
“Excellent!” I said. “And you have a cousin…”
“Mark!” Eli screamed. “M-A-R-K!”
“Hmm… park, dark, Mark… and what would Remy do if he saw a cat?” I asked, thinking that they’d see the pattern of rhyming words.
“He’d chase it,” Alex said.
I chuckled. “Well, yeah, he probably would. But what else might he do?”
“He’d eat it!”
Like I said, they’re only three. “I suppose he might,” I said.
I have to admit, I’ve never been a huge fan of the books of Theoni Pappas. They don’t excite me in the same way that a collection of Martin Gardner’s problems or Ian Stewart’s math essays do. But I greatly respect the huge impact she’s had in making mathematics palatable to so many people. She’s written over 40 books, many for kids, and they’ve been very well received.
A brief biography of Theoni Pappas appears on the NCTM website, because the Theoni Pappas fund sponsors an award through NCTM’s Mathematics Education Trust. Teachers in grades 9‑12 can apply for awards up to $4,000 to develop materials under the Connecting Mathematics to Other Subject Areas grant.
So, what made me think about Theoni Pappas? It turns out that some folks on Amazon who bought my book, Math Jokes 4 Mathy Folks, also bought her book, Math Talk. And though I’m not a fan of most of her books, I do love this one. It’s a collection of “mathematical poems for two voices,” and it contains quite a few gems. One reviewer at Amazon said, “This is a delightful, engaging introduction to the world of mathematics, giving children and adults alike a glimpse of the wonderful adventures that lie beyond simple (and boring) drills.”
A review in the NCTM journal Mathematics Teacher said, “Math Talk, in its novel approach, would make an interesting addition to the mathematics library for any age group.”
Below is a poem from the book. I’m surely violating copyright laws by posting this, but you can see this same poem by choosing the “Look Inside” link at Amazon, so whatever.
I applaud her attempt to mix math and language, and I’m honored that my book gets to share a page with hers.
I hope you enjoy her poems as much as I do.
Tonight, my twin three-year-old sons were taking a bath, and they were playing with these floating letters. One of my sons held up the letters M and U and said, “Moo!” I explained that what he had actually spelled was mu, which is pronounced myoo. He could have cared less, but it reminded me of this joke…
What does a Greek cow say? Mu.
You may have seen that one coming, so the next one is a little less predictable. (Thanks to Paul Rustenberg, who sent this to me after reading Math Jokes 4 Mathy Folks.)
A farmer was showing his fields to a mathematician and his wife. The mathematician made continual attempts to impress with his intellect, referencing arcane formulas and then doing computations mentally. Frustrated by this, the farmer decided to teach him a lesson. He took them to a field packed with hundreds of cows and said to the mathematician, “If you can guess the exact number of cows in this field, you can have all of them! But if you get it wrong, I get to sleep with your wife!”
The mathematician thought for a moment, his eyes quickly scanning the entire field. Finally he said, “228.”
The farmer was stunned. “How on Earth did you do that?” he asked. “There’s no way you could have counted all those cows so quickly!”
“You’re right,” the mathematician replied. “‘I counted their legs and then divided by 4.”
And finally, speaking of cerebral capacity, here’s a non-math joke that you may need to think about for a second…
Two pigs are leaving a restaurant, talking about the wonderful meal they had and the wonderful service they received from their waiter, a very polite cow. The wife says, “And it was so reasonable, too!”
“Oh, my gosh,” says the husband. “I forgot to tip the waiter!”
If you don’t get that last one, drop me a line at email@example.com.