A pastor, a doctor and a mathematician

A pastor, a doctor, and a mathematician were stuck behind a slow foursome while playing golf. The greenskeeper noticed their frustration and explained to them, “The slow group ahead of you is a bunch of blind firemen. They lost their sight saving our clubhouse from a fire last year, so we always let them play for free.”

The pastor responded, “That’s terrible! I’ll say a prayer for them.”

The doctor said, “I’ll contact my ophthalmologist friends and see if there isn’t something that can be done for them.”

And the mathematician asked, “Why can’t these guys play at night?”

Another Calculus Limerick

I love a good math limerick.  And, no, “Nantucket” is never a destination for some mathematician in a good math limerick.  Here’s a new one I discovered online:

$\displaystyle \int_{0}^{\frac{\pi}{6}} \sec y \, dy = \ln \sqrt{3} \ (i)^{64}$

For the laymen,

The integral sec y dy                         -> (read as “seek y dee y”)
From zero to one-sixth of pi
Is the log to base e
Of the square-root of three
Times the sixty fourth power of i.

This rivals my favorite limerick of all time. And I can’t talk about limericks without repeating it for you:

$\displaystyle \int_1^{\sqrt[3]{3}} z^2 \, dz \cdot \cos \left( \frac{3\pi}{9} \right) = \ln \sqrt[3]{e}$

Again, for the unconverted,

The integral z-squared dz
From one to the cube root of 3
Times the cosine
Of three pi over nine
Is the log of the cube root of e.

“It’s gold, Jerry! Gold!”

A new collection of math jokes

Ok, so I know that several of the readers of this blog will enjoy this, several others will groan as they read, and many others will just roll their eyes at the lack of humor below.  I’m posting anyways.

And for the record, at one time, I have laughed out loud at every one of these. There, I confessed.

—————–

Q: How does a mathematician induce good behavior in his children?
A: `I’ve told you n times, I’ve told you n+1 times…’

—————–

A mathematician and his best friend, an engineer, attend a public lecture on geometry in thirteen-dimensional space.
"How did you like it?" the mathematician wants to know after the talk.
"My head’s spinning", the engineer confesses. "How can you develop any intuition for thirteen-dimensional space?"
"Well, it’s not even difficult. All I do is visualize the situation in arbitrary N-dimensional space and then set N = 13."

——————

One day, Jesus said to his disciples: "The Kingdom of Heaven is like 3x squared plus 8x minus 9."
A man who had just joined the disciples looked very confused and asked Peter: "What, on Earth, does he mean by that?"
Peter replied: "Don’t worry – it’s just another one of his parabolas."

——————-

[I’ve heard the ones about the Abelian Grape and Zorn’s Lemon, but this one was new to me]

Q: What is normed, complete, and yellow?
A: A Bananach space…

——————-

A mathematician has spent years trying to prove the Riemann hypothesis – without success. Finally, he decides to sell his soul to the devil in exchange for a proof. The devil promises to deliver a proof within four weeks.
Four weeks pass, but nothing happens. Half a year later, the devil shows up again – in a rather gloomy mood.
"I’m sorry", he says. "I couldn’t prove the Riemann hypothesis either. But" – and his face lightens up – "I think I found a really interesting lemma…"

———————

That’s enough for now.  Are you smiling yet or just confused?

Common Terms from Your Math Professor

Following in the vein of my earlier post, here’s another oldie, but goodie:

[HT: SoftwareCraft]

CLEARLY: I don’t want to write down all the in-between steps.

TRIVIAL: If I have to show you how to do this, you’re in the wrong class.

OBVIOUSLY: I hope you weren’t sleeping when we discussed this earlier, because I refuse to repeat it.

RECALL: I shouldn’t have to tell you this, but for those of you who erase your memory tapes after every test, here it is again.

WITHOUT LOSS OF GENERALITY: I’m not about to do all the possible cases, so I’ll do one and let you figure out the rest.

ONE MAY SHOW: One did, his name was Gauss.

IT IS WELL KNOWN: See “Mathematische Zeitschrift”, vol XXXVI, 1892.

CHECK FOR YOURSELF: This is the boring part of the proof, so you can do it on your own time.

SKETCH OF A PROOF: I couldn’t verify the details, so I’ll break it down into parts I couldn’t prove.

HINT: The hardest of several possible ways to do a proof.

BRUTE FORCE: Four special cases, three counting arguments, two long inductions, and a partridge in a pair tree.

SOFT PROOF: One third less filling (of the page) than your regular proof, but it requires two extra years of course work just to understand the terms.

ELEGANT PROOF: Requires no previous knowledge of the subject, and is less than ten lines long.

SIMILARLY: At least one line of the proof of this case is the same as before.

CANONICAL FORM: 4 out of 5 mathematicians surveyed recommended this as the final form for the answer.

THE FOLLOWING ARE EQUIVALENT: If I say this it means that, and if I say that it means the other thing, and if I say the other thing…

BY A PREVIOUS THEOREM: I don’t remember how it goes (come to think of it, I’m not really sure we did this at all), but if I stated it right, then the rest of this follows.

TWO LINE PROOF: I’ll leave out everything but the conclusion.

BRIEFLY: I’m running out of time, so I’ll just write and talk faster.

LET’S TALK THROUGH IT: I don’t want to write it on the board because I’ll make a mistake.

PROCEED FORMALLY: Manipulate symbols by the rules without any hint of their true meaning.

QUANTIFY: I can’t find anything wrong with your proof except that it won’t work if x is 0.

FINALLY: Only ten more steps to go…

Q.E.D. : T.G.I.F.

PROOF OMITTED: Trust me, it’s true.

36 Methods of Mathematical Proof

If you ask an average person on the street what is the highest level of mathematics, the most common answer would probably be Calculus.  There might even be a few throwing College Algebra out there as fairly advance.  However, if you ask a math major or engineering student the question of what is the lowest level of mathematics, the foundation of the mathematics they use, the most common answer would likely be Calculus.   Why the disparity?

The mathematics that is taught from kindergarten through secondary is often limited to procedural techniques to solve specific problem types without recognizing that advanced mathematics is all about recognizing patterns and using axioms, definitions, and theorems to formalize those patterns thereby leading to new patterns.

So, of course, in upper level mathematics we spend a great deal of time moving from procedural mathematics, to proving theorems, to developing new theorems.  Unfortunately, the rigor is sometimes lost in the classroom for many reasons.  I’m sure I’ve used just about every one of the following invalid proof techniques.

• Proof by obviousness: "The proof is so clear that it need not be mentioned."
• Proof by general agreement: "All in favor?…"
• Proof by imagination: "Well, we’ll pretend it’s true…"
• Proof by convenience: "It would be very nice if it were true, so…"
• Proof by necessity: "It had better be true, or the entire structure of mathematics would crumble to the ground."
• Proof by plausibility: "It sounds good, so it must be true."
• Proof by intimidation: "Don’t be stupid; of course it’s true!"
• Proof by lack of sufficient time: "Because of the time constraint, I’ll leave the proof to you."
• Proof by postponement: "The proof for this is long and arduous, so it is given to you in the appendix."
• Proof by accident: "Hey, what have we here?!"
• Proof by insignificance: "Who really cares anyway?"
• Proof by mumbo-jumbo:
• Proof by profanity: (example omitted)
• Proof by definition: "We define it to be true."
• Proof by tautology: "It’s true because it’s true."
• Proof by plagiarism: "As we see on page 289,…"
• Proof by lost reference: "I know I saw it somewhere…."
• Proof by calculus: "This proof requires calculus, so we’ll skip it."
• Proof by terror: When intimidation fails…
• Proof by lack of interest: "Does anyone really want to see this?"
• Proof by illegibility:
• Proof by logic: "If it is on the problem sheet, it must be true!"
• Proof by majority rule: Only to be used if general agreement is impossible.
• Proof by clever variable choice: "Let A be the number such that this proof works…"
• Proof by tessellation: "This proof is the same as the last."
• Proof by divine word: "…And the Lord said, ‘Let it be true,’ and it was true."
• Proof by stubbornness: "I don’t care what you say- it is true."
• Proof by simplification: "This proof reduced to the statement 1 + 1 = 2."
• Proof by hasty generalization: "Well, it works for 17, so it works for all reals."
• Proof by deception: "Now everyone turn their backs…"
• Proof by supplication: "Oh please, let it be true."
• Proof by poor analogy: "Well, it’s just like…"
• Proof by avoidance: Limit of proof by postponement as it approaches infinity
• Proof by design: If it’s not true in today’s math, invent a new system in which it is.
• Proof by authority: "Well, Gauss says it’s true, so it must be!"
• Proof by intuition: "I have this gut feeling."

• Gauss, The Chuck Norris of Mathematics

I stumbled across the website of Chuck Norris Facts not long ago.  You know such treasured gems as

1. When Chuck Norris does a pushup, he isn’t lifting himself up, he’s pushing the Earth down.
2. There is no chin behind Chuck Norris’ beard. There is only another fist.
3. Chuck Norris can lead a horse to water AND make it drink.
and my personal favorite
4. Chuck Norris doesn’t eat honey, he chews bees.

Well, I was quite impressed when I came across a similar list of facts about one of the greatest (some would say THE greatest) mathematicians of all time, Carl Friedrich Gauss.

From Matt Heath:

• Gauss didn’t discover the normal distribution, nature conformed to his will.
• Gauss can construct transcendental numbers only using a compass.
• Parallel lines meet where Gauss tells them to.
• Some problems are NP because Gauss doesn’t like computers.
• Gauss never runs out of room in the margin.
• Gauss can write irrationals as the ratio of 2 integers.
• Gauss never needs the axiom of choice.
• Gauss can square the circle and then transform it into the hyper-sphere.
• The location and momentum of a particle are what Gauss say they are.
• An elegant proof is one line long. Gauss’ elegant proofs are one word long.
• Gauss doesn’t look for roots of equations, they come to him.
• There are no theorems, just a list of propositions Gauss allows to be true.
• When Gauss integrates he doesn’t need to add a constant.
• Hilbert put forward 23 unsolved problems because he hadn’t properly read Gauss’ notebooks.
• Gauss knows the topological difference between a doughnut and a coffee cup.
• Gauss can divide by zero.
• Gauss would never ever have a badbox error.
• Primes that aren’t Gaussian primes get teased.
• If Gauss had to walk 100 metres, and half the remaining distance, then half the remaining distance again, and so on, he’d get there.
• Erdos believed God had a book of all perfect mathematical proofs. God believes Gauss has such a book.
• Gauss has Hilbert hotels on Mayfair and Park Lane.
• God does not play dice, unless Gauss promises to let him win once in a while.

My favorite has to be "Gauss doesn’t look for roots of equations, they come to him."

Factoring Time

So don’t you think it would be a good idea to write a script that would factor every time throughout the day.  Just to make it interesting you might factor the time as a 6 digit number, including the seconds.  You could answer fascinating questions like what’s the most number of factors a time can have, how many times are prime, how many twin prime’s are there, etc…

Well, if you think it’s a good idea, too late.  It’s already been done and not by me.

Factor Clock

FYI:

What’s the largest number of factors a time can have?

6 factors, 57 matches

How many times are prime, and what are they?

7669

How many times form twin primes, and what are they?

859