From Graph Jam.
09.16.09
05.4.09
Good reasons for not doing your math homework
I accidentally divided by zero and my paper burst into flames.
I have the proof, but there isn’t room to write it in this margin.
I could only get arbitrarily close to my textbook. I couldn’t actually reach it.
I was watching the World Series and got tied up trying to prove that it converged.
I couldn’t figure out whether i am the square of negative one or i is the square root of negative one.
I locked the paper in my trunk but a four-dimensional dog got in and ate it.
I took time out to snack on a doughnut and a cup of coffee. I spent the rest of the night trying to figure which one to dunk.
I could have sworn I put the homework inside a Klein bottle, but this morning I couldn’t find it.
I’ve included a reference to the solutions manual, reducing this assignment to one previously solved.
I had too much π and got sick.
05.3.09
8 reasons π is better than e
- e is less challenging to spell than π.
- The character for e is so cheap that it can be found on a keyboard. But π is special (it’s under “special symbols” in word processor programs.)
- e has an easy limit definition and infinite series. The limit definition of π and the infinite series are much harder.
- You understand what e is even though you start learning it late when you’re in pre-calculus. But π, even after five or six years it’s still hard to know what it really is.
- People mistakenly confuse Euler’s Number (e) with Euler’s Constant (denoted by γ). There is no confusion with the one and only π.
- e is named after a person, but π stands for itself.
- π is much shorter and easier to say than “Euler’s Number”.
- To read π, you don’t have to know that Euler’s name is really pronounced Oiler.
05.2.09
9 reasons e is better than π
- e is easier to spell than pi.
- The character for e can be found on a keyboard, but π sure can’t.
- Everybody fights for their piece of the π.
- ln(π) is a really nasty number, but ln(e) = 1.
- e is used in calculus while π is used in baby geometry.
- ‘e‘ is the most commonly used letter in the English alphabet.
- e stands for Euler’s Number, π doesn’t stand for squat.
- You don’t need to know Greek to be able to use e.
- You can’t confuse e with a food product.
02.4.09
Evolution of mathematical teaching
Version 1: the potato problem
1960s:
A peasant sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price. What is his profit?
1970s:
A farmer sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price, that is, $8. What is his profit?
1970s (new math):
A farmer exchanges a set P of potatoes with set M of money. The cardinality of the set M is equal to 10, and each element of M is worth $1. Draw ten big dots representing the elements of M. The set C of production costs is composed of two big dots less than the set M. Represent C as a subset of M and give the answer to the question: What is the cardinality of the set of profits?
1980s:
A farmer sells a bag of potatoes for $10. His production costs are $8, and his profit is $2. Underline the word “potatoes” and discuss with your classmates.
1990s:
A farmer sells a bag of potatoes for $10. His or her production costs are 0.80 of his or her revenue. On your calculator, graph revenue versus costs. Run the POTATO program to determine the profit. Discuss the result with students in your group. Write a brief essay that analyzes this example in the real world of economics.
Adapted from The American Mathematical Monthly, Vol. 101, No. 5, May 1994.
Version 2: the logging problem
1960s:
A logger cuts and sells a truckload of lumber for $100. His cost of production is four-fifths of that amount. What is his profit?
1970s:
A logger cuts and sells a truckload of lumber for $100. His cost of production is four-fifths of that amount, i.e. $80. What is his profit?
1970s (new math):
A logger exchanges a set L of lumber for a set M of money. The cardinality of set M is 100. The set C of production costs contains 20 fewer points. What is the cardinality of Set P of profits?
1980s:
A logger cuts and sells a truckload of lumber for $100. Her cost is $80 and her profit is $20. Find and circle the number 20.
1990s:
An unenlightened logger cuts down a beautiful stand of 100 trees in order to make a $20 profit. Write an essay explaining how you feel about this as a way to make money. Topic for discussion: How did the forest birds and squirrels feel?
Adapted from Reader’s Digest, February 1996.
02.1.09
Mathematical anagrams
| a decimal point | – | I’m a dot in place |
| decimal point | – | I’m a pencil dot |
| logarithm | – | algorithm |
| a number line | – | innumerable |
| integral calculus | – | calculating rules |
| algebra | – | a garble |
| calculation | – | I call a count |
| higher mathematics | – | ahh! arithmetic gems |
| inconsistent | – | n is, n is not, etc. |
| negation | – | get a “no” in |
| pocket calculators | – | clack! total up score |
| the answer | – | wasn’t here |
| school master | – | the classroom |
| listen | – | silent |
| committees | – | cost me time |
| incomprehensible | – | problem in Chinese |
| eleven plus two | – | twelve plus one |
| math research | – | harms teacher |
01.27.09
Units
A team of engineers were required to measure the height of a flag pole. They only had a measuring tape, and were getting quite frustrated trying to keep the tape along the pole. They’d get it a bit up the pole, but then the tape would buckle and it would fal down.
A mathematician comes along and listens to their problem. After inspecting both the tape measure and the flag pole, he proceeds to remove the pole from its base in the ground. He lays it down flat, measures it easily with the tape measure, and then resets the pole in the ground.
When he leaves, one engineer says to the other and sighs. “Just like a mathematician! We need to know the height, and he gives us the length!”
01.24.09
Odd primes
Several people are asked to prove that all odd integers greater than 2 are prime.
- Tenured mathematician: 3 is prime, 5 is prime, 7 is prime, 9 is not prime. Ha! A counterexample.
- Untenured mathematician: 3 is prime, 5 is prime, 7 is prime… so by induction, all subsequent odd integers are prime.
- Statistician: Let’s verify this sone several randomly selected odd numbers, say, 23, 47, and 83.
- Computer scientist: 3 is prime, 5 is prime, 7 is prime, segmentation fault?
- Computer programmer: 3 is prime, 3 is prime, 3 is prime, 3 is prime…
- Physicist: 3 is prime, 5 is prime, 7 is prime, 9 is an experiemntal error, 11 is prime…
- Mechanical engineer: 3 is prime, 5 is prime, 7 is prime, 9 is approximately prime, 11 is prime…
- Civil engineer: 3 is prime, 5 is prime, 7 is prime, 9 is prime…
- Biologist: 3 is prime, 5 is prime, 7 is prime, 9 is… still awaiting results…
- Psychologist: 3 is prime, 5 is prime, 7 is prime, 9 is prime but suppresses it, 11 is prime…
- Economist: 2 is prime, 4 is prime, 6 is prime…
- Politician: Shouldn’t the goal really be to create a greater society where all numbers are prime?
- Sarah Palin: What’s a prime?
12.29.08
Texan mathematician
A mathematician, native Texan, once was asked in his class: “What is mathematics good for?”
He replied: “This question makes me sick. Like when you show somebody the Grand Canyon for the first time, and he asks you `What’s is good for?’ What would you do? Why, you would kick the guy off the cliff”.
12.28.08
Story about nothing
A man travelling through the Orient passed a small courtyard and heard voices murmuring. He went in and saw an altar with a large stone O in the middle. White-robed people were kneeling before the altar, softly chanting “Nil… nil… nil…” while ceremonial priests sang prayers to The Great Nullity and The Blessed Emptiness.
Eventually, the man turned to a white-robed observer beside him and asked “Is Nothing sacred?”
