## Posts tagged ‘beer’

### All Systems Go

I noticed the boys having an intense conversation in front of this sign at our local pizza shop:

When I asked what they were doing, they said, “We’re trying to figure out how much one slice and a beer would cost.”

As you read that, there were likely two thoughts that crossed your mind:

- Why can’t these poor boys look at a pizza menu without perceiving it as a system of equations?
- Why are eight-year-olds concerned with the price of beer?

The answer to both, of course, is that I’m a terrible father, and both beer and math are prominent in our daily lives.

But you have to admit that it’s pretty cool that my sons recognized, and then solved, the following system:

They didn’t use substitution or elimination because they didn’t have to — and, perhaps, because they don’t know either of those methods yet. But mental math was sufficient. If two slices and a soda cost $6.00, and one slice and a soda cost $3.50, then one slice must be 6.00 – 3.50 = $2.50. Consequently, two slices cost $5.00, so a beer must be 8.00 – 5.00 = $3.00. A beer and a slice will set you back $5.50.

I remember once visiting a classroom in Somerville, MA, and the teacher was reviewing the substitution method. My memory is a bit fuzzy, but the problem she solved on the chalkboard was something like this:

Mrs. Butterworth’s math test has 10 questions and is worth 100 points. The test has some true/false questions worth 8 points each and some multiple-choice questions worth 12 points each. How many multiple-choice questions are on the test?

The teacher then used elimination to solve the resulting system:

The math chairperson was standing next to me as I watched. “Why is she doing that?” I asked. “You don’t need elimination. It’s clear there have to be 8 or fewer multiple-choice questions (8 × 12 = 96), so why not just guess-and-check?”

“Because on the MCAS [Massachusetts Comprehensive Assessment System], if they tell you to use elimination but you solve the problem a different way, it’ll be marked wrong.”

So much for CCSS.Math.Practice.MP1. Although most of us would like students to “plan a solution pathway rather than simply jumping into a solution attempt,” apparently students in Massachusetts need to blindly follow algorithms and not think for themselves.

The following is my favorite system of equations problem:

I counted 34 legs after dropping some insects into my spider tank. How many spiders and how many insects?

Why is this my favorite system of equations problem? Because there is a unique solution, even though it results in just one equation with two unknowns. Traditional methods won’t work, and students have to think to solve it. Blind algorithms lead nowhere.

Other things that lead nowhere are spending your leisure hours reading a math jokes blog. But since you’re here…

Why did the student put his homework in a fish bowl?

He was trying to dissolve an equation.An engineer thinks that his equations are an approximation to reality. A physicist thinks reality is an approximation to his equations. A mathematician doesn’t care.

### Math for International Beer Day

I don’t need an excuse to do math. Nor do I need one to drink beer.

But if I did, today is IBD.

I’m most happy when I can pursue my two passions simultaneously…

That said, I never attempt calculus while imbibing. It’s not safe to drink and derive.

And like most of the American populace, I almost never attempt to think logically while drinking beer…

A bartender asks three logicians, “Would all of you like beer?”

The first answers, “I don’t know.”

The second answers, “I don’t know.”

The third answers, “Yes!”

### All Beer and Skittles

The winter has been unkind to my waist, so I joined a month-long fitness challenge at the gym. I asked one of the trainers what I should do to win. “Drink 25 beers on Saturday night,” he said.

“Why?”

“Because the weigh-in is Sunday morning, and you want to be heavy as possible.”

“Yeah, I get that,” I replied. “But there are 24 bottles in a case. Okay if I stop there?”

How many is too many? Hard to say…

Teacher: If I had 5 bottles in one hand and 6 bottles in the other hand, what would I have?

Student: A drinking problem?

With St. Patrick’s Day just around the corner, here are a few more beer jokes.

If you pour root beer in a square cup, will it become beer?

And who doesn’t like a joke that makes fun of professors?

A literature professor, a computer scientist, and a mathematician head to a pub. They each order a pint of beer, and when the drinks are brought to the table, each pint has a fly in it.

The literature professor pushes her beer away in disgust.

The computer scientist removes the fly and proceeds to drink his beer.

The mathematician picks the fly out of his drink, too, but then holds it out over the beer and yells, “Spit it out, you little bastard!”

### Rootin’ Around

The digits of today’s date can be concatenated to make the four-digit number 4913, and 4913 = 17^{3}. As it turns out, this is the only date in 2013 for which the concatenation of the digits forms a number that has a square, cube, fourth, fifth, or sixth root that is a whole number.

I’m sure there are more useless pieces of trivia, but I can’t think of one right now.

[**Update, 4/9/13:** Perhaps the following isn’t more useless, but it’s certainly not more useful, either. I failed to mention the trivial numerology contained within today’s date: 4 + 9 = 13.]

In any case, this fact about the cube root of 4913 got me to thinking about some of my favorite things.

My favorite drink:

My favorite highway:

My favorite LeVar Burton movie:

My favorite types of efforts:

My favorite idiom:

### Upside-Down Tooth Numbers

Alex and Eli know that 15 ÷ 3 = 5, that 63 ÷ 7 = 9, and, given a little time, could figure out that 104 ÷ 8 = 13. That’s not bad for five-year-olds.

As we were discussing sharing a treat the other day, we naturally happened upon a situation in which it would be good to know what 1 ÷ 2 is.

Alex suggested, “Two.”

I explained that while the order of the numbers in multiplication doesn’t matter — for example, 2 × 3 = 3 × 2 — order does matter with division. I used the word *commutative*, but I also tried to explain it with plainer language, too.

I took a rectangular piece of paper and ripped it in half. “How big is each piece?” I asked. The both knew it was one-half. “So there you have it: 1 ÷ 2 = 1/2.”

But why stop there? I divided one of the halves in half again, and I asked, “How big is this piece?” They both knew it was one-quarter. “So that shows that 1/2 ÷ 2 = 1/4.”

They saw that if we continued in this manner, we would get 1/8, 1/16, 1/32, and so on, a pattern they called the *upside-down tooth numbers*, because the numbers in the sequence are the reciprocals of the powers of two. (For them, *tooth* = 2^{th}.)

Looking at the pieces of paper on the table, I asked a more advance question. “What do you think we’d get if we added 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + …, and we kept adding half as much each time?”

Eli thought for a few seconds. “I think it would be one whole,” he offered.

I was surprised. “Why?” I asked.

“Well,” he said, “I’m thinking about a circle.”

I looked at the rectangular pieces of paper on the table, which had nothing to do with a circle. *Sure, he got the right answer, but his reasoning is way off base*, I thought.

He explained further. “If you fill half a circle, then a quarter more, then an eighth, and keep going, you’ll eventually fill the whole thing. That’s why I think it’s one.”

Visually, Eli’s argument would look something like this…

*Holy sh*t*, I thought. *That’s pretty good for a five-year-old.*

I don’t even care that he doesn’t understand this joke:

An infinite number of mathematicians walk into a bar. The first asks for half a beer. The second asks for a quarter of a beer. The third asks for an eighth of a beer. The bartender interrupts, pours one beer for them, and says, “You guys don’t know your limits.”

I think I was so impressed with Eli’s solution because infinite series can be difficult, even for mathy professionals:

A mathematician will call an infinite series convergent if its terms go to zero. An engineer will call it convergent if the first term is finite.

And let us not forget the Eilenburg swindle, which proves that 1 = 0 since:

1 − 1 + 1 − 1 + … = 1 + (−1 + 1) + (−1 + 1) + … =

1

and

1 − 1 + 1 − 1 + … = (1 − 1) + (1 − 1) + … =

0

Related to all this, there is a perhaps apocyphal story in which it is rumored that a student once posed the following problem to John von Neumann:

Two trains begin a mile apart and head towards each other at 60 miles an hour. A fly on one train flies at 120 mph to the other train, and when it touches the other train, it immediately turns around and flies back to the first train, and so on, flying back and forth between the two trains until it gets squashed in the middle. How far does the fly travel?

von Neumann thought about it a moment and said, “One mile.” The student said to von Neumann that most people don’t realize that the problem can be figured out easily: the trains meet in 30 seconds, and the fly can travel one mile in half a minute; yet most people think they have to add up the infinite series to figure out how far the fly travels. As the story goes, von Neumann replied, “But that’s how I did it.”

### Beer and Calculus Don’t Mix — Don’t Drink and Derive!

After Franklin Delano Roosevelt signed the Cullen-Harrison Act to end prohibition, sales of beer in the U.S. became legal on April 7, 1933. (Not a moment too soon, I might add. My father was born on April 12, 1933, and he surely gave my grandmother plenty of reasons to imbibe!) Consequently, April 7 is now known as National Beer Day, and April 6 is unofficially New Beer’s Eve.

A definite integral walks into a bar and orders five pints of Guinness. The bartender pours them, and the definite integral finishes them one after the other. “Can I have five more?” he asks.

The bartender says, “Don’t you think you’ve had enough?”

“Don’t worry about me,” says the integral. “I know my limits.”

Someday, I hope to meet the guy who invented beer — and buy that man a beer!

Finally, a logic puzzle with a solution that seems appropriate…

You come to a fork in the road. One branch leads to the City of Truth, and the other leads to the City of Deceit. You can ask the person stationed at the fork in the road one simple question to help you determine the correct path to the City of Truth. If the person is from the City of Truth, he will answer your question honestly; if he is from the City of Deceit, he will answer your question dishonestly. What question should you ask?

“Did you know they’re serving free beer in the City of Truth?”

The truth‑teller will say, “No!” and run to get a beer. The liar will say, “Yes!” and run to get a beer. Either way, follow him.

### Drink It Green!

Today is St. Patrick’s Day, of course, but at 9:33am, my mother’s baby boy celebrated the 40th anniversary of his birth. (Yes, I’m a cliche. I was born on St. Patrick’s Day, and my parents named me Patrick. But it was for the best, really — before my exact birthdate was known, the leading name candidate was George William, Jr. *Yecch.*)

Here’s an appropriate math joke for a beer-filled holiday:

An infinite number of mathy folks walk into a bar. The first one goes up to the bar and orders a pint. The second one goes up and orders half a pint. The third orders 1/4 pint. The fourth orders 1/8 pint, and so forth. A little overwhelmed, the bartneder asks them, “Hey, are you guys sure you want to do this? Isn’t that a bit much?”

The mathy folks reply, “Don’t worry. We know our limits.”

And some other jokes for a day dedicated to drinking…

Charles Dickens walks into a bar and orders a martini. The bartender asks, “Olive or twist?”

René Descartes is sitting in a bar. The bartender asks if he’d like another. “I think not,” says Descartes, and he promptly disappears.

An absent-minded math professor walks up to an attractive woman at the bar. “So, tell me,” he says, “do I come here often?”

A guy walks into a bar with a lizard on his shoulder. “What do you call that?” asks the bartender. “Tiny,” says the guy, “because he’s my newt.”

Okay, enough of that nonsense. Happy St. Patrick’s Day! Have a pint or two for me.