Archive for December, 2013
6 Degrees of Bad Math Jokes
I once read an article that said, “To a greater or lesser degree, everything tastes like chicken.” Well, that’s true, but it’s also true that everything tastes like broccoli, to a greater or lesser degree. Carrots, to a greater degree; mint chocolate chip ice cream, to a lesser degree.
To a greater or lesser degree, some of the following jokes are funny.
What did the thermometer say to the graduated cylinder?
A scientist dropped a thermometer and a candle from the roof of a building. He observed that both objects reached the ground at the same time. Conclusion: A thermometer falls at the speed of light.
A doctor walks into a meeting, and a nurse asks why he has a rectal thermometer behind his ear. “Damn,” says the doctor, “some asshole has my pen!”
The star college football player was taking a math exam. The coach desperately needed him for the big game on Saturday, so the professor agreed to an oral exam.
“All right,” said the professor. “How many degrees are in a circle?”
“That depends,” said the boy. “How big is the circle?”
If you’re cold and there’s a right triangle nearby, stand in the corner opposite the hypotenuse. It’s always 90° over there.
The number you have dialed is imaginary. Please rotate your phone 90°, and try again.
Oreos, Ratios, and the Perfect Cookie
Okay, first things first. What do you call the following shape?
I call it a pill. My sons call it a racetrack. But is there a formal name for a shape formed by a rectangle with a semicircle attached to each end? If not, I feel like there should be. Place your suggestions in the Comments.
Until I hear a better suggestion, I’m gonna keep callin’ it a pill.
The following trivia question is the reason I ask.
How many pills appear around the circumference of the trademarked design on an Oreo^{®} cookie?
What’s that, you say? You didn’t know that there were little pills along the edge of each wafer on an Oreo cookie? Then you, my friend, need to pay a little more attention.
Because there aren’t just some pills around the circumference. There are 96 of those little buggers, and each of them has a rectangle with a lengthtowidth ratio of approximately 3:2 between two semicircles.
See for yourself.
Ironically, the ratio of 3:2 brings me to the main reason I’m writing today.
The original Oreo represented good design: a single layer of vanilla cream filling trapped between two crisp, chocolate wafers. But it always felt lacking to me. If only it had just a little more cream, then it would be perfect. A potential solution arrived in 1974, when Nabisco released the Double Stuf variety — two chocolate wafers with twice as much filling^{1} as its predecessor. Yet the Double Stuf teetered too far in the opposite direction. It was too sweet.
Which brings me to the delectable treat that I discovered today: the Triple Double Oreo, which is running a strong campaign for the title of World’s Best Cookie. My wife describes it as “the Big Mac of cookies.” Not two but three chocolate wafers with a thin layer of cream filling between each pair. And the pièce de résistance — one layer of vanilla cream filling, the other chocolate.
Now that’s what I call intelligent design.
It absolutely nails the ratio for wafer:filling.
Original 
Double Stuf 
Triple Double 

Wafers 
2 
2 
3 
Filling^{2} 
1 
1.86 
2 
Ratio of W:F 
2 
1.08 
1.5 
The chart above makes it all clear. The ratio is too high in the original, too low in the Double Stuf, and just right in the Triple Double. Indeed, the Triple Double Oreo is the Little Bear’s porridge of the cookie world.
This reminds me of Reese’s Peanut Butter Cups. While I haven’t quantitatively analyzed the peanut butter to chocolate ratio, qualitatively I would say that the original had a little too much peanut butter, the Big Cup was disgusting with far too much peanut butter, but nirvana was captured with the peanut butter to chocolate ratio in Miniature Reese’s Peanut Butter Cups. (Insert smacking lips sound here.)
So if you read this blog and wonder why I’m so hyper sometimes, now you know. I consume an unholy amount of refined sugar.
^{1} There is some debate about the actual amount of filling contained in a Double Stuf Oreo cookie. Although a spokesperson for Nabisco claimed that the cookies indeed contain twice as much filling as a regular Oreo, a math class in upstate New York experimentally found that Double Stuf cookies contain only 1.86 times as much cream filling as a regular Oreo. As I generally trust unpaid high school students more than moneygrubbing corporate types, I’m using 1.86.
^{2} The numbers for “filling” are relative to the amount of cream filling in a regular Oreo^{®}.
SudoClue for a Cold Winter’s Night
The holiday break is nigh, which means you need to be careful not to catch a cold.
For many people, the time preceding a holiday, vacation, or spring break is busy — finishing up a term paper, completing holiday shopping, or getting things off your desk so you can enjoy your trip to Tahiti. During that time, your immunity kicks into high gear. It helps to fend off germs while you’re pushing yourself to get stuff done. When your break finally comes, though, you relax, and your body thinks, “Oh, cool, the stress is over.” And BAM! No more immunity, and your body succumbs to infection. Sniffles, headache, and a cough ensue.
How can you prevent this?
Easy. Do puzzles.
That’s right. You can trick your body into thinking that you’re still stressed by doing crosswords, sudoku, nurikabe, battleship, nonogrids, or whatever you like. Your mind is working hard, so your body keeps your immunity up. Doing something you enjoy fends off disease. Winwin.
Well, MJ4MF is here to help. The following SudoClue puzzle will provide a halfhour of muchneeded stress. The idea is rather simple. Use the clues to fill in the corresponding squares of the 6 × 6 grid, then fill in the remaining squares like a sudoku puzzle.
The puzzle below, as well as an easier version, are available in PDF format.
SudoClue Puzzle – Easy SudoClue Puzzle – Hard
Enjoy!
 Number of unique tetrominoes
 Product of all singledigit divisors of 143
 Number of English words that end with –dous
 Half of π^{2}, approximately
 Number of tetrominoes that can be drawn without lifting your pencil from the paper
 0!
 Number in the title of the greatest math joke book ever
 Integer between e and π
 Circumference divided by radius, to the nearest whole number
 Smallest number of colors sufficient to color all planar maps
 V
 Side length of a square whose area (in square units) is equal to its perimeter (in units)
 A perfect number
 A hat trick
 For integer values of n, the smallest prime divisor of n^{2} + n
 Number of total handshakes when four people shake hands with each other
Don’t feel like thinking too much on holiday break? Fine, here’s a hint. And if you’ve already fully entered holiday break mode, here’s the solution.
Amazon Sales Rank, and What Math Geeks Do
Today, I asked my son’s if they would like to buy The Oatmeal’s Why Grizzly Bears Should Wear Underpants. They laughed uproariously at the title, and then Eli asked, “Is that the #1 book on Amazon?” In fact, it’s not. At the time of this writing, its ranking was #624. “That’s not #1,” Alex affirmed, then added, “but it’s a lot better than your book.”
Harumph.
“A lot better” is highly subjective. Sure enough, the #3,517 ranking of Math Jokes 4 Mathy Folks has an absolute difference of 2,893 compared to WGBSWU; or, if you’re into ratios, the rank of my book is five times as much as the rank of WGBSWU. But what does that really mean?
In practical terms, it means that the number of copies of WGBSWU that will sell on Amazon this week is approximately six times the number of copies of MJ4MF that will sell during the same period. If my calculations are correct, that is. No one is really sure how ranking translates to sales, but I estimate that approximately 250 copies of MJ4MF and 1,500 copies of WGBSWU will sell this week.
This is what math geeks do: We try to understand everything quantitatively.
I took weekly sales data for MJ4MF and compared that with the book’s average ranking for the week. I randomly chose 20 weeks in 201213 for this analysis, because while pulling weekly sales data is relatively easy — it’s provided at Amazon Author Central — determining weekly average ranking is more difficult, since data has to be pulled day by day. And it’s not as simple as just exporting the data to Excel or a CSV file… the data is provided in a graph, and if you want to manipulate that data in any way, you have to look at each point on the graph, determine its value, and then enter it manually. Ugh.
The graph below shows the relationship between average rank and weekly sales:
The regression equation S = 914.77 × R^{0.977} gives a reasonably good fit (r = 0.89). What’s interesting is that this formula is less accurate in November and December than during the rest of year. There are two reasons for that. First, sales increase dramatically during the holiday shopping season. Second, such a formula is bound to be less accurate with larger numbers.
The average rank for December 915 was #3,592, and using the formula above, approximately 253 copies of MJ4MF should have sold. (I suspect that estimate is a little low. For the same week last year, the average rank was #4,573 and 277 copies were sold.)
Amazon posts sales data for each week on the following Friday. Sales data for last week won’t post until December 20. I’ll update this post on Friday and let you know how well I did.
[Update, 12/20/13: A recordbreaking 335 copies of MJ4MF sold December 915. (Thank you!) But as predicted, the estimate was indeed low. As I gather more data, perhaps I will be able to create a better model.]
The Mathematics of Gift Wrapping
Has this ever happened to you?
You place a gift on the wrapping paper. You estimate how much you’ll need. You cut. You place the gift on the paper. You fold over both sides.
Crap.
That’s when you realize your estimation skills are on par with those of a government contractor.
But, no worries! Math is here!
The hypotenuse of a right triangle is longer than either leg. Consequently, turning the wrapping paper at an angle will allow the paper to cover the gift.
My wife hates it, but whatever! What initially appeared to be a terrible estimate yielded a 15.8% savings in wrapping paper.
Based on my calculations, if all gifts were wrapped this way, the country would save $147 million each year on wrappingpaper related expenses. (Where’s that statistic when politicians discuss the economy?)
Pigs in the Gutter
Finals are just around the corner, and another semester will soon be in the books. Here’s a poem to relieve the tension for all of you preparing for final exams — whether taking or administering them.
Late in the fall semester,
Dressed in suede and polyester,
I was thinking ‘bout a theorem I’d derived;
So drunk was I with mathy passion,
Into the gutter I went crashin’,
And a pig came up and lay down at my side.Yes, I lay there on my rear end
With my stinky, pinky new friend
When a woman passing by did softly say,
“You can tell a mathy creep
By the company he’ll keep” —
And the pig got up and slowly walked away.
I don’t want to, but I gotta…
We lay sidebyside in the gutter for quite some time — swine and coswine.