Pencils are infintely useful yet ridiculously simple — just a cylindrical piece of graphite surrounded by a hexagonal wooden sheath.
Pencils come in all shapes and sizes, actually. They often have hexagonal cross sections, though some are octagonal, rectangular, circular, and oval.
Heck, there are even pentagonal pencils…
Which has to make you wonder, do we really need pencils in such a wide variety of shapes?
The answer may be no, but there is a practical reason for the multitude of cross sections. Can you think of any possible benefits that a rectangular pencil would have over a circular one, or vice versa?
The following problem about a pencil comes from Peter Winkler’s Mathematical Mind-Benders:
A pencil with pentagonal cross-section has a maker’s logo imprinted on one of its five faces. If the pencil is rolled on the table, what is the probability that it stops with the logo facing up?
And here’s a good Fermi question:
How many pencils are there in the world?
I have no idea what the answer is, but one respondent to this question on www.answers.com said, “42,462,013,000,000,000 pencils about.” The amazing part is that 17 people found this useful!
Slightly less ambiguous is this question:
How many pencils were used to make this sculpture by George Hart?
Or maybe you prefer selected-response items…
Which of the following is the best estimate for the length of a continuous line that could be drawn using a standard pencil?
- 0.35 mile
- 3.50 miles
- 35.0 miles
- 350 miles
Or maybe you’re tired of all these questions. You didn’t come here for a quiz. You came here for some jokes. Fine.
Did you hear about the constipated mathematician?
He worked it out with a pencil.
What kind of pencil?
A #2 pencil, of course!
What’s the largest pencil in the world?
If you’d like to learn more about pencils and their history — and, let’s be honest, who wouldn’t — you can download a free copy of Every Pencil is a Sandwich. In return, you’ll be asked to sign up for the pencils.com newsletter. If you love pencils and use them as much as I do, receiving the newsletter will be a treat, not a burden!
I don’t know if problems like the following are famous, but there sure are a lot of them online — Cut the Knot, Stack Exchange, and Braingle, for example — and they’re typical for a high school classroom or middle school math competition:
There are 14 red, 6 orange, 10 yellow, 8 green, 4 blue, 12 indigo, and 2 violet socks in my sock drawer. How many socks must I randomly remove from the drawer to guarantee that I have two socks of the same color?
You may or may not know the answer, but the problem itself leads to a follow-up question:
Why the hell do I own socks in every color of the rainbow?
That’s just weird. But if you can get past that, here is a related problem:
If I randomly remove two socks from the drawer, what is the probability that they form a matching pair?
As it turns out, I’m something of a sock aficionado. (Yeah, it’s weird, but surely not surprising. I mean, I write a math jokes blog. You didn’t think I was normal, did you?) Although the context above is fictitious, I am indeed the owner of three pairs of identical socks that look like those shown in the picture. And yes, those are my feet and ankles. My mathematical sexy runs all the way down to my toes.
Here’s a close-up of one of them, in case you can’t see it in the larger picture:
That’s a letter R, because these socks are specially designed for each foot. The other sock has a letter L. (Duh.)
This leads to another mathematical question, more real-world than those above:
I just finished washing these three pairs of socks. While folding them, I selected two socks at random and rolled them together. What’s the probability that there’s one R and one L?
The answer, of course, is zero.
Yes, I know that theoretically the answer should be 3/5. But theory doesn’t match practice in this case. When I do my laundry, I sometimes forget to pay attention to the R and the L, and my sock drawer invariably results in one pair of two R’s, one pair of two L’s, and one correctly matched pair. And then when I wake up at 5:30 a.m. and put on my socks in the dark (so as not to rouse my wife from slumber), my feet feel all weird. The one with the wrong sock starts tingling, so I have to remove the socks and choose another pair entirely.
Similarly, here’s another real-world problem, based on my sock experience:
If there are 10 socks in a load of laundry that I place in the washer and then transfer to the dryer, how many socks will remain when the load is finished drying?
Nine. Yes, I know it’s a cliche. Everyone makes jokes about losing socks. It’s so overdone that the National Comedian’s Guild has declared a moratorium against them. But, I’m not joking. I can’t remember the last time I did a load of laundry and wasn’t missing a sock. I now have a drawer filled with unmatched socks, each like Tiger Woods longing for the return of its Lindsey Vonn.
Sadly, this post is going public just a little too late. Lost Socks Memorial Day was May 9, so we just missed that one. Likewise, we missed No Socks Day on May 8. But there are other holidays in the coming months when you can celebrate the amazing undergarments that protect our feet from our shoes:
- July (exact date TBD): Red Socks Day (commemorating Sir Peter Blake)
- October 4: Odd Socks Day (Australia)
- January (every Friday): Snow Sock Day
And though not an official holiday, there are unlimited Crazy Sock Days happening at elementary, middle, and high schools near you.
99% of socks are single, and you don’t see them crying about it.
How do engineers make a bold fashion statement?
They wear their dark grey socks instead of the light grey ones.
Somewhere, all of my socks, Tupperware lids, and ball point pens are hanging out together, just laughing at me.
Because I know you won’t be able to sleep tonight…
- I need to remove 8 socks from my sock drawer to guarantee a color match.
- I don’t actually own socks in every color of the rainbow. Just most colors.
- The probability of selecting two socks from my drawer and getting a matching pair is 23/140.
The FAQ at the Folger Shakespeare Library, referencing Martin Spevack, claims that Shakespeare’s complete works consist of 884,647 words. Open Source Shakespeare claims that his complete works consist of 884,421 words. Whatever. I’m not going to split hairs over one-twentieth of a percent.
What do you get if you add 1 rabbit + ½ rabbit + ¼ rabbit + … ?
Two rabbits, but that’s just splitting hares.
Those numbers got me thinking. Shakespeare — or whichever “secret author(s)” actually wrote all that stuff — is often considered to be one of the most prolific authors of all time.
Yet here’s my typical annual output over the last 5 years.
|Category||Number||Approximate Word Length|
|Email – Short||500||10|
|Email – Medium||1,500||100|
|Email – Long||50||1,000|
|Math Joke Book||1/5||12,000|
That translates to over 250,000 words a year, which means that I write the equivalent of Shakespeare’s 37 plays and 154 sonnets in about 42 months.
I mean, sure, Shakespeare’s typical lines are something like
For as the sun is daily new and old,
So is my love still telling what is told
whereas a line from my typical email is more like
I’d like to see the storyboard for the Featherless Birds interactive by the end of the week
but I’m not talking about quality here. I’m only referring to quantity.
And in that regard, Will, you got nothing.
Of course, he does deserve props for his occasional reference to math:
There is divinity in odd numbers, either in nativity, chance or death.
— The Merry Wives of Windsor, Act V, Scene 1
And whether deliberate or not, he had a penchant for 2 × 7:
So, sure, maybe William Shakespeare was not as prolific as I am. Or, for that matter, as prolific as most 21st century office workers who sit in a cubicle, stare at a screen, and bang on a keyboard all day. But he was pretty cool.
Better three hours too soon than a minute too late.
Elegant, isn’t it? After all, there’s nothing I enjoy more than hitting the “mute” button so I can microwave a Hot Pocket® while doing a conference call from home.
There are a few old jokes at the intersection of math and telephony:
I’m sorry. The number you dialed is imaginary. Please rotate your phone 90°, and try again.
When I dial into conference calls, I hope beyond hope that the dial-in number is imaginary. But no such luck.
Got math problems? Call 1 – 800 – (7 × 5 + 36) – (212).
Both of those jokes are terrible, and I apologize. But you came here for math jokes, and since I’m about to rant about something that isn’t math-related, I figured I should lead with something that connects the rant below with the reason for your visit. And those are the only jokes I know that even tangentially relate math to conference calls.
So, there ya go.
Now, my rant. I hate conference calls. I mean, a lot. We’re talking full-on despision here, like the kind Tartaglia had for Cardano. Conference calls are occasionally useful and productive, but typically they involve too many people and waste too much time. If I’m never invited to another conference call, I promise I won’t complain about feeling lonely.
Dave Barry said:
If there’s one word that describes why the human race never has and never will reach its full potential, that one word would be: meetings.
Replace “meetings” with “conference calls,” and it’s equally true.
I have 11 reasons for despising these unproductive time-sucks, but feel free to add additional reasons in the Comments section.
- People who dial in late. For God’s sake, please don’t dial in 10 minutes late and then expect the rest of us to catch you up on what’s been discussed so far. Show up on time.
- People who dial in late and announce themselves. As if it isn’t bad enough that you’re late, now the conversation is interrupted while the rest of us hear your name. If your conference call provider says, “After the tone, please state your name and then press the pound key,” just press the pound key; and if your provider says, “Please announce yourself,” don’t.
- Someone bumping the redial button. Now we all have to hear ten (or more) melodic beeps. Oh, for Pete’s sake, please put your finger back in your nose so this doesn’t happen again.
- People who coordinate activities for those in the main office. For instance, someone interrupts the conference call to sing “Happy Birthday” and deliver cupcakes to the 8 people who are gathered in a conference room. Meanwhile, the 14 of us in other locations have to imagine how good those cupcakes must taste, based on what sounds like giraffes chewing bubble gum on the other end of the line.
- Trying to focus for an hour on voices from a far-away land. I know I can’t do it, and I’m not alone. Dr. Mike Hollier from Dolby Communications explains,
…if we visualize our entire cognitive capability as the size of a football field, then our conscious intelligence — the portion of our intelligence that’s available in the moment — would be the size of a tiny grain of sand. In face-to-face meetings, we don’t need to strain our conscious intelligence to figure out who’s speaking… But conference call audio is so hard to decipher that we need to devote our entire conscious intelligence to analyzing audio information. With our conscious intelligence so taxed, paying attention to the subject of the conference call is exhausting.
- Multi-tasking douchepickles who continually ask, “I’m sorry, could you repeat the question?” Sorry, Biff, I cannot repeat the question. But I would like you to repeat after me: I will not play Evil Genius during conference calls.
- Calls being continually rescheduled because one person can’t attend. Perhaps this is reasonable if the one person is the Queen Mum or the Dalai Lama. Otherwise, accept that it’s impossible to find a time that will work for 27 people, and proceed with those who are available. Be a good employee, take notes, and send a follow-up to everyone after the call — including those who couldn’t be there. That’s progress, and you won’t have to wait till June 2054 to find a mutually agreeable time.
- Making 15 people wait while the organizer uses his cell phone to call the one jerk-off who hasn’t dialed in yet. If he doesn’t deem the call important enough to remember it, why does the organizer think he’s important enough to warrant a reminder? Why is his time more important than yours? Send him an IM, maybe, but proceed without him.
- The long-distance yeller who shouts, “Okay!” from the far side of his office to the speakerphone. Are you afraid of catching a communicable disease through the phone? Or is it just that your Justin Bieber bobblehead is on the other side of the room? Please, get a little closer to the phone so we can hear you.
- Bad mobile connections. If you cause static for more than 5 seconds, mute yourself. If you cause static for more than 10 seconds, hang up. Nothing you have to say is so important that we should have to tolerate this. And if your input is that important, then call from a landline.
- Conference calls that take place when you should be driving home. No calls starting later than 4 p.m. Period. And for goodness sake, no calls after noon on Friday!
Greg at www.ihateconferencecalls.com says, “You hate conference calls? I hate them more.” Here’s a pearl of his wisdom.
I really am doing my best. I have to remember:
- They aren’t doing this call because they hate me specifically, but rather…
- They are doing this call because they hate humanity, and this small amount of suffering that we all share will bring us together as humans.
- By suffering through the call, I become more human.
What do you hate about conference calls?
Let’s get this party started with a classic word puzzle.
What English word contains four consecutive letters that appear consecutively in the alphabet?
In Mathematical Mind-Benders (AK Peters, 2007), Peter Winkler describes how the puzzle above served as inspiration for a word game.
I and three other high-school juniors at a 1963 National Science Foundation summer program began to fire letter combinations at one another, asking for a word containing that combination… the most deadly combinations were three or four letters, as in GNT, PTC, THAC and HEMU. We named the game after one of our favorite combinations, HIPE.
This seemed like a good game to play with my sons. I explained the game, and then I gave them a simple example to be sure they understood.
They quickly generated a long list of solutions, including:
Since that introduction a few weeks ago, the boys and I have played quite a few games. It’s a good activity to pass the time on a long car ride. The following are some of my favorites:
(these two are fun in tandem)
(the game’s namesake is a worthy adversary)
The practice with my sons has made me a better-than-average HIPE player, so when I recently found myself needing to keep my sons busy while I prepared dinner, I offered the following challenge:
Create a HIPE for me that you think is difficult, and I’ll give you a nickel for every second it takes me to solve it.
Never one to shy away from a challenge, Eli attacked the problem with gusto. Fifteen minutes later, he announced, “Daddy, I have a HIPE for you,” and presented me with this:
That was three days ago. Sure, I could use More Words or some other website to find the answer, but that’s cheating. Winkler wrote, “Of course, you can find solutions for any of them easily on your computer… But I suggest trying out your brain first.”
The downside to relying on my brain? This is gonna cost me a fortune.
For your reading enjoyment, I’ve created the following HIPEs. They are roughly in order from easy to hard, and as a hint, I’ll tell you that there is a common theme among the words that I used to create them.
- TRAH (bonus points for finding more than one)
Winkler tells the story of how HIPE got him into Harvard. He wrote “The HIPE Story” as the essay on his admissions application, and four years later, he overheard a tutor who served on the admissions committee torturing a colleague with HIPEs and calling them HIPEs.
I can’t promise that HIPEs will get you into college, but hopefully you’ll have a little fun.
Her name is Tara, but she should expect her friends to call her by a different name from now on.
Not knowing all seven dwarfs is forgivable. Not knowing that sneaky isn’t spelled with two e‘s is less excusable. That she committed both errors simultaneously all but guarantees that her friends will call her Sneaky for the rest of her life.
Or maybe it’s only a guy thing to give nicknames to their friends for colossal fails?
If a guy had made this mistake, his best friend would have texted him before the show was over:
Nice guess, Sneaky.
I got a nickname in a most inglorious fashion. After an Ultimate Frisbee tournament in Fort Devens, MA, we headed to the local bar and ordered a round of Irish car bombs.
The problem was, the Guinness arrived in a 16-ounce plastic cup, and the shot of Bailey’s and Jameson’s arrived in a 10-ounce plastic cup. When we tried to drop the smaller cup into the larger cup, it floated. We spent a good half-hour debating how we’d get the shot to the bottom of the larger cup, and I seemed to offer more ideas than most. The bartendress, finally tired of my yammering, looked at me and said, “Okay, cupcake, you gonna talk about it all night, or you gonna drink it?”
All I could think was, “Dear Lord, I pray that my friends didn’t hear that.”
When I turned around, they sang in unison, “Cuuuup-caaaaaake.”
It stuck. That was 15 years ago, but there are those who still call me Cupcake on the Ultimate field. And sadly, there are those who still call me Cupcake when they run into me at the grocery store. Nothing like your seven-year-old, father-worshiping son asking, “Daddy, why did that man call you ‘Cupcake’?”
Sadly, famous mathematicians don’t have nicknames. At least not cool ones, not generally. Sure, Euclid may be the “Father of Geometry,” but his friends didn’t call him that when they were drinking mead around a campfire. And while textbooks may refer to Leibnitz as the “Aristotle of the 17th Century,” none of his peeps did.
The only two cool mathematician nicknames I could find — and by “cool,” I mean that they didn’t start with “Father of” — were “The Passionate Skeptic” for Bertrand Russell and “The Samian Sage” for Pythagoras. Granted, it’s not like “The Italian Stallion” for Rocky or “The Master of Disaster” for Apollo Creed, but mathematicians aren’t generally nickname-acquiring types.
But I think mathematicians deserve nicknames, so here are some suggestions for your consideration.
- Leonardo “No Questionacci, No” Fibonacci
- Pierre “Not Fer Pa” de Fermat
- Leonhard “If She’s Squeaky” Euler
- Carl Friedrich “Anyone’s” Gauss
- Blaise “Little” Pascal
- John “Cock-a-Doodle-Do” Napier
- Benoit B. “Benoit B. Mandelbrot” Mandelbrot
- “Chortlin'” Lewis Carroll
- Maria “Which Witch” Agnesi
- George Bernard “Dirty” Dantzig
- Emmy “I Barely” Noether
- Girolamo “I’m Sick” Cardano
- William “Off the Charts” Playfair
- Alan “Fac” Turing
- Charles “Too Much” Babbage
To be sure, the best thing you could do right now would be to leave a comment in which you refer to me as “cupcake.”
While most nicknames above are silly, like the nicknames given to football by players by Chris Berman, some of them may require an explanation.
- John Napier once covered a black rooster with lamp soot to catch a thief.
- Benoit B. Mandelbrot is the “Father of Fractals,” which are self-repeating.
- Lewis Carroll coined many words, including chortle.
- The Witch of Agnesi is a famous curve.
- Girolamo Cardano was an infamous hypochondriac who predicted his own death.
- William Playfair invented line graphs, bar charts, pie charts, and circle graphs.
My favorite question is, “Why?” (And my favorite answer is, “Because.”) But not far behind is the question, “What if?”
What if a baseball player swings a bat with the proper speed, but starts swinging 0.01 seconds too late? What if I could earn 6.3% on a real estate investment instead of 1.4% in a Roth IRA, but had to pay capital gains taxes? What if I tried to walk through a revolving door with a pair of skis on my shoulder?
“What if…?” questions don’t always have to be mathy, ya know.
The beauty of Excel is that you can repeatedly ask “What if…?” questions and then explore to your heart’s content.
Overheard in math class:
“It’s not that I don’t want to do all those math problems,” Julia said to her teacher. “I’m just saying, if we put them into a spreadsheet and let Excel do its thing, we can have an extra 20 minutes for recess.”
Sure, one of the powers of Excel is reducing the tedium associated with calculations, but a much greater power is its ability to allow for deep exploration of math topics in a short period of time.
Art Bardige and Peter Mili agree. That’s why they’re giving away spreadsheets that allow students to explore mathematics.
Their What If Labs allow students to investigate questions like:
- What if you used Excel to design a house?
- Is the world population growing at a faster or slower rate than 50 years ago?
- Instead of wood, nails, and string, what if you used a graph and coordinates to create string art?
The spreadsheets are useful, fun, educational and — dare I say — beautiful. Not to mention, free.
Art believes that teaching math with Excel has two benefits. First, it fosters business skills by having students learn the basics of the most ubiquitous business application on the planet. Second, it empowers students by giving them complete control to explore on their own.
I concur with Art’s philosophy.
Excel is one of my best friends. I use it to test conjectures, especially for probability problems about which I don’t have any intuition — or, more often, when my intuition is wrong!
One of my favorite problems, which was discussed in the post Fair and Square in 2011, is the following:
Three points are randomly chosen along the perimeter of a square. What is the probability that the center of the square will be contained within the triangle formed by these three points?
Would I have solved that problem without Excel? Maybe. Probably. But without Excel, it would have taken longer, and I might not have had the same deep understanding of the underlying structure.
Kudos to Art and Peter for providing a free resource that will let other students benefit from that same type of insight.