Let ε < 0.

04.27.09

The missing dollar

Filed under: Riddles — Travis @

This isn’t a joke; rather it’s an interesting problem.

Three mathematicians went to a convention. They needed a room, but all the hotels were full. They finally found a motel that had a vacancy. They told the Innkeeper they needed rooms. The Innkeeper said “I’ve only got one room left.”

The three mathematicians said “We’ll take it.”

“That’ll be $30.00.”

The mathematicians each pulled out 10 $1 bills; they handed to collected $30 to the Innkeeper and went to their room.

After a while, the Innkeeper thought to himself “I’ve overcharged those three men. I should give them a discount for having to share one room.” He called the bellboy over and told him: “Take this money to room 303 and tell the three men there I’m giving them a discount for having to share a room.” He handed the bellboy five one dollar bills.

The bellboy took off to the three men’s room. On the way, he thought, How are three men going to split $5? I can help them out by giving them just three dollars. So, in the spirit of altruism (obviously) the bellboy quietly pocketed two of the dollar bills. When he got to the room, he rang the bell and when one of the mathematicians answered, he said “The Innkeeper said to tell you he is sorry for the inconvenience, and offers this refund for your hardship.”

He then handed the man three one dollar bills and left. The mathematician gave a dollar to each of his companions, and the three went to sleep.

So what’s the problem?

Since each of the mathematicians received $1 back from the bellboy, each man paid only $9 apiece for the room. That is, they paid only $27 for the room. The bellboy has $2 in his pocket. This accounts for $29 of the original $30 paid.

What happened to the missing dollar?

03.22.09

Lotsa riddles 12: crossing jokes

Filed under: Riddles — Travis @

Q: What do you get when you cross an elephant with a banana?
A: Elephant banana sine(theta) in a direction mutually perpendicular to
the elephant and banana as determined by the right hand rule.

Q: What do you get when you cross an elephant with a mountain climber.
A: You can’t do that. A mountain climber is a scaler.

Q: What do you get when you cross a mosquito with a mountain climber?
A: You can’t cross a vector with a scaler.
[ Vector: an organism, such as an insect, that transmits a pathogen. ]1

Q: What do you get when you cross a mountain goat and a mountain climber?
A: Nothing. You can’t cross two scalars.

1. Told to me by Bill Wood.

The following two aren’t mathematical, but they fit the theme and are personal favorites.

Q: What do you get when you cross an elephant with a rhinoceros?
A: Elephino!

Q: What did Hannibal get when he crossed the Himalayas with elephants?
A: A mountain range that never forgets.

03.21.09

Lotsa riddles 11: light bulb jokes

Filed under: Academic humor, Riddles — Travis @

Q: How many mathematicians does it take to screw in a lightbulb?
A: 0.999…

Q: How many mathematicians does it take to screw in a light bulb?
A: None. It’s left to the reader as an exercise.

Q: How many mathematicians does it take to screw in a light bulb?
A: None. A mathematician can’t screw in a light bulb, but he can easily prove the work can be done.

Q: How many mathematicians does it take to screw in a light bulb?
A: Just one, once you’ve managed to present the problem in terms he is familiar with.

Q: How many mathematicians does it take to screw in a light bulb?
A: Three: one to screw it in, and two to figure out how to get rid of the remainder.

Q: How many Californians does it take to replace a lightbulb?
A: Six: one to replace the bulb and five to share in the life experience.

Q: How many mathematicians does it take to screw in a light bulb?
A: One, who gives it to six Californians, thereby reducing it to an earlier riddle.

Q: How many mathematicians does it take to screw in a light bulb?
A: In earlier work, Wiener [1] has shown that one mathematician can change a light bulb. Now, f k mathematicians can change a light bulb, and if one more simply watches them do it, then k+1 mathematicians will have changed the light bulb. Therefore, by induction, for all n in the positive integers, n mathematicians can change a light bulb.

Bibliography:
[1] Weiner, Matthew P,…

Q: How many analysts does it take to screw in a lightbulb?
A: Three. One to prove existence, one to prove uniqueness and one to derive a nonconstructive algorithm to do it.

Q: How many Bourbakists does it take to replace a lightbulb?
A: Changing a lightbulb is a special case of a more general theorem concerning the maintain and repair of an electrical system. To establish upper and lower bounds for the number of personnel required, we must determine whether the sufficient conditions of Lemma 2.1 (Availability of personnel) and those of Corollary 2.3.55 (Motivation of personnel) apply. If these conditions are met, we derive the result by an application of the theorems in Section 3.11.23. The resulting upper bound is, of course, a result in an abstract measure space, in the weak-* topology.

Q: How many classical geometers does it take to replace a lightbulb?
A: None. You can’t do it with a straight edge and a compass.

Q: How many constructivist mathematicians does it take to replace a lightbulb?
A: None. They do not believe in infinitesimal rotations.

Q: How many light bulbs does it take to change a light bulb?
A: One, if it knows its own Godel number.

Q: How many mathematical logicians does it take to replace a lightbulb?
A: None. They can’t do it, but they can prove that it can be done.

Q: How many number theorists does it take to change a light bulb?
A: I don’t know the exact number, but I am sure it must be some rather elegant prime.

Q: How many numerical analysts does it take to replace a lightbulb?
A: 0.9967, after six iterations.

Q: How many simulationists does it take to replace a lightbulb?
A: Infinitly many. Each one builds a fully validated model, but the light actually never goes on.

Q: How many topologists does it take to change a light bulb?
A: It really doesn’t matter, since they’d rather knot.

Q: How many topologists does it take to screw in a lightbulb?
A: Just one. But what will you do with the doughnut?

Q: How many professors does it take to replace a lightbulb?
A: One. With eight research students, two programmers, three post-docs and a secretary to help him.

Q: How many university lecturers does it take to replace a lightbulb?
A: Four. One to do it and three to co-author the paper.

Q: How many graduate students does it take to replace a lightbulb?
A: Only one. But it takes nine years.

Q: How many math department administrators does it take to replace a lightbulb?
A: None. What was wrong with the old one?

Q: How many UC Berkeley students does it take to change a lightbulb?
A: Seventy-six. One to change the lightbulb, fifty to protest the lightbulb’s right not to change, and twenty-five to hold a counter-protest.

Q: How many UC Davis students does it take to change a lightbulb?
A: None. Davis doesn’t have electricity.

Q: How many UC Irvine students does it take to change a lightbulb?
A: None. Irvine looks better in the dark.

Q: How many UC Riverside students does it take to change a lightbulb?
A: None. See UC Irvine.

Q: How many UCLA students does it take to change a lightbulb?
A: One. He just holds the bulb and lets the world revolve around him.

Q: How many UC San Francisco students does it take to change a lightbulb?
A: Two. One to change the lightbulb and one to crack under the pressure.

Q: How many UC San Diego students does it take to change a lightbulb?
A: Two. One to mix the margaritas and one to call the electrician.

Q: How many UC Santa Barbara students does it take to change a lightbulb?
A: Only one, but he gets six credits for it.

Q: How many UC Santa Cruz students does it take to change a lightbulb?
A: Eleven. One to change the lightbulb and ten to share the experience.

03.20.09

Lotsa riddles 10: purple and commutes

Filed under: Riddles — Travis @

Q: What’s purple and commutes?
A: An abelian grape.

Continuing the theme:

Q: What is purple, commutes, and is worshipped occasionally?
A: A finitely venerated abelian grape.

Q: What’s purple, commutes, and all of its offspring have been committed to institutions?
A: A simple grape… it has no normal subgrapes.

Q: What’s lavender and commutes?
A: An Abelian semigrape

Q: What has gills and commutes?
A: An abelian grouper.

Q: What’s black and white and fills space?
A: A piano curve.

Q: What’s green and uncountable?
A: The real lime.

Q: What’s grey and huge and has integer coefficients?
A: An elephantine equation.

Q: What’s grey and proves the uncountability of the reals?
A: Cantor’s Diagonal Elephant.

Q: What’s hallucinogenic and exists for every group with order divisible by p^k?
A: A psilocybin p-subgroup.

Q: What’s old, plows, and obeys the fundamental theorem of arithmetic?
A: An antique tractorisation domain.

Q: What’s non-orientable and lives in the sea?
A: Moebius Dick.

Q: What’s polite and works for the phone company?
A: A deferential operator.

Q: What’s tasty, denim, and detects uniform convergence?
A: The Weiner-Strauss M-Test.

Q: What’s yellow and equivalent to the Axiom of Choice?
A: Zorn’s Lemmon.

Q: What’s yellow and has a power series expansion about each point?
A: A bananalytic function.

Q: What’s yellow, linear, normed and complete?
A: A Bananach space.

03.19.09

Lotsa riddles 9: mathematicians, et al.

Filed under: Riddles, Science humor — Travis @

Q: Why can’t mathematicians tell jokes timing?

Q: How can you tell that a mathematician is extroverted?
A: When talking to you, he looks at your shoes instead of at his.

Q: How do you tell that you are in the hands of the Mathematical Mafia?
A: They make you an offer that you can’t understand.1

Q: How does a French mathematician try to pick up chicks?
A: He asks “Voulez vous Cauchy avec moi?”

Q: What do a mathematician and an engineer have in common?
A: They are both stupid, except for the mathematician.

Q: What do you do when a civil engineer throws a grenade at you?
A: Pull the pin and throw it back.

Q: What does a mathematician do when he’s constipated?
A: He works it out with a pencil.

Q: What is the difference between a PhD in mathematics and a large pizza?
A: The pizza can feed a family of four.2

Q: What would you hear at a mathematicians dance party?
A: I draw the sine, by Ace of Log-base.

Q: Why are mathematicians so negative?
A: Because they are nonplussed.

Q: Why did the computer scientist die in the shower?
A: Because he read the instructions on the shampoo bottle, “Lather, rinse, repeat.”

Q: Why did the cat fall of the roof when he lost his voice?
A: He lost his mu.
[ To help explain: "mew" is the sound a cat makes, while "mu" is the coefficient of static friction. ]

1. This is attributed to Cambridge mathematician Tom Korner.

2. Sent in by Ian Garduna and Mike Cowan.

03.18.09

Lotsa riddles 8: pure and applied

Filed under: Riddles — Travis @

Definitions

Q: What is a dilemma?
A: A lemma that proves two results.

Q: What is a proof?
A: One-half percent of alcohol.

Q: What is the difference between a lemma and a proposition?
A: You’ll never hear a lemma at a bar.

Number and set theory

Q: What does an analytic number theorist say when he is drowning?
A: Log-log, log-log, log-log, . . .

Q: Why isn’t the pope is the greatest cardinal?
A: Because every pope has a successor.

Q: Why did the Pythagoran movement end when they discovered the square root of 2?
A: They couldn’t find a rational explanation for it.

Statistics and numerical analysis

Q: Did you hear the one about the statistician?
A: Probably….

Q. How did the analytic number theorist finish his email?
A. He log-logged out!

Q: What goes “Pieces of seven! Pieces of seven!”?
A: A parroty error!!

Q: Why is it that the more accuracy you demand from an interpolation function, the more expensive it becomes to compute?
A: It’s the Law of Spline Demand.

03.17.09

Lotsa riddles 7: algebra

Filed under: Riddles — Travis @

Q: How do you expand (a+b)n?
A: Easily:

         (a+b)^n
      ( a + b ) ^ n
   (  a  +  b  )  ^  n
(   a   +   b   )   ^   n

…and so on…

Q: Does there exist a politician who does nothing at all?
A: Yes, because politians form a Lie group.

Q: How does an algebraist express appreciation?
A: Thanks. Thanks abelian.

Q: What is an ‘ugh’?
A: The dual of a cough.

Q: Why can’t you grow wheat in Z/6Z?
A: Because it’s not a field.

Q: Why didn’t Newton discover group theory?
A: Because he wasn’t Abel.

Q: What do you call a young eigensheep?
A: A lamb. Duh.

Q: How does an engineer define a vector space?
A: A set V satisfying the axiom that for any x in V, x has a little arrow drawn over it.

Q: How did the linear algebraist defeat the Chicago Bulls in the playoffs?
A: He used Krause-Jordan elimination.
[ Bulls GM: Jerry Krause; star player: Michael Jordan ]

03.16.09

Lotsa riddles 6: analysis

Filed under: Riddles — Travis @

Q: Why did the mathematician name his dog Cauchy?
A: Because it left a residue around every pole.

Q: By what process to two mathematicians determine the timbre of a musical instrument?
A: Four-ear analysis.

Q: How do you insult an analyst?
A: “Your IQ < ε.”

Q: What did the mathematician say about his dog Epsilon to the vet?
A: Let Epsilon be fixed.

Q: What do you call the irrational fear of convergent series?
A: Zenophobia.

Q: What did the mathematician say when he let epsilon go to zero?
A: Whoops! There goes the neighborhood!

Q: What did the mathematician say when he soaked a convergent sequence in brine?
A: A Cauchy pickle.

Q: What is the contour integral around Western Europe?
A: Zero, because all the Poles are in Eastern Europe!
Addendum: Actually, there ARE some Poles in Western Europe, but they are removable!

Q1: What is the fundamental computing principle of analysis?
A: Many functions can be approximated by their Taylor series to a high degree of accuracy.
Q2: What is the fundamental computing principle of physics?
A: Every function has a Taylor series that converges to it.
Q3: What is the fundamental computing principle of engineering mathematics?
A: Every function has a Taylor series that converges to the function and stops after the linear term.

Q: What is the shortest mathematical joke?
A: “Let ε < 0.”

Q: What is this?

  1. EA + EA + EA + EA + …,
  2. EA + EA + EA + EA + …,
  3. EA + EA + EA + EA + …,
  4. EA + EA + EA + EA + …,

A: Fourier Series.

Q: Where do the complex numbers take drinks?
A: Z, of course. [ Pronounced "zee-bar." ]

Q: Why was Cauchy convicted in the USA for violating its constitution?
A: Because he conspired with Schwarz in advocating ineqality.

Q: Why was Cauchy committed to an insane asylum?
A: Because he was an extreme non-normal deviate.

Q: Why was Cauchy convicted for being a vagrant?
A: Because he can show no means of support.

Q: Why was the analyst afraid to drive on the interstate?
A: The width of the road was neglible compared to its length.

03.15.09

Lotsa riddles 5: calculus

Filed under: Riddles — Travis @

Q: Why do MacLaurin series fit their functions so well?
A: They’re Taylor made for them.

Q: How does a Californian solve differential equations?
A: He uses the Perrier transform.

Q: How does a Canadian solve a differential equation?
A: He uses the Lacrosse transform.

Q: How do you find the unique solution to a differential equation?
A: Unique up on it.

Q: How do you pick up chicks in a Calculus II class?
A: “If you were f(x), then I’d like to be the integral from a to b of f(x) dx, just so I could be the area under your curves.”

Q: How does a Rabbi compute an improper integral?
A: He takes the kosher principal value.

Q: How is a Ph.D. student in Theology like the Laplacian operator?
A: They’re both a div grad.

Q: What do you get if you differentiate a cow?
A: Prime rib.

Q: Who knows everything there is to be known about vector calculus?
A: The Oracle of Del-phi.

Q: Why do pirates like calculus in polar coordinates?
A: They can integrate with respect to “Arrr.”

Q: Why did the calculus student have so much trouble making Kool-Aid?
A: Because he couldn’t figure out how to get a quart of water into the little package.

03.13.09

Lotsa riddles 4: geometry and trig

Filed under: Riddles — Travis @

Q: What is the difference between the diameter and the radius?
A: The radius.

Q: How many sides does a hexagon have?
A: Two. The inside and the outside.

Q: What are the trigonometric functions for farmers?
A.1: Swine and coswine, or
A.2: Swine and cow-sine.

Q: What did the little circle say to the tangent line?
A: Quit touching me! Quit touching me!

Q: What do you call a one-sided nudie bar?
A: A Moebius strip club.

Q: What keeps a plant from moving out of a math class?
A: Its square roots, of course.
Q: How many square roots does such a plant have?
A: Two. Obviously.

Q: What is a polar bear?
A: A rectangular bear after a coordinate transform.

Q: Why did the chicken cross the Moebius strip?
A: To get to the other … er, um …

Q: Why did the identity sin(2r) = 2sin(r) get turned down for a loan?
A: Because it needed a cos(r). [ Get it? A cosigner? ]

Q: Why did the mathematician-dentist name his son Pi?
A: Beacuse everyone knows pi is transcendental.1

Q: Why didn’t the Moebius strip enroll at the school?
A: They required an orientation.

1. Proposed by Carin Smith.

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