Maths
|A shoeseller meets a mathematician and complains that he does not know what size shoes to buy. "No problem," says the mathematician, "there is a simple equation for that," and he shows him the Gaussian normal distribution. The shoeseller stares some time at het equation and asks, "What is that symbol?" "That is the Greek letter pi." "What is pi?" "That is the ratio between the circumference and the diameter of a circle." Upon this the shoeseller cries out: "What does a circle have to do with shoes?!"
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November 11, 2009
|It is often cited that there are half as many divorces as marriages in the US, so one concludes that average marriages have a 50% chance of ending by divorce. While I was a graduate student, among my peers there were twice as many divorces as marriages, leading us to conclude that average marriages would end twice...
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November 11, 2009
|Analysis:1. Differentiate it and put into the refrig. Then integrate it in the refrig.2. Redefine the measure on the referigerator (or the elephant).3. Apply the Banach-Tarsky theorem.Number theory:1. First factorize, second multiply.2. Use induction. You can always squeeze a bit more in.Algebra:1. Step 1. Show that the parts of it can be put into the refrig. Step 2. Show that the refrig. is closed under the addition.2. Take the appropriate universal refrigerator and get a surjection from refrigerator to elephant.Topology:1. Have it swallow the refrig. and turn inside out.2. Make a refrig. with the Klein bottle.3. The elephant is homeomorphic to a smaller elephant.4. The elephant is compact, so it can be put into a finite collection of refrigerators. That's usually good enough.5. The property of being inside the referigerator is hereditary. So, take the elephant's mother, cremate it, and show that the ashes fit inside the refrigerator.6. For those who object to method 3 because it's cruel to animals. Put the elephant's BABY in the refrigerator.Algebraic topology:Replace the interior of the refrigerator by its universal cover, R^3.Linear algebra:1. Put just its basis and span it in the refrig.2. Show that 1% of the elephant will fit inside the refrigerator. By linearity, x% will fit for any x.Affine geometry:There is an affine transformation putting the elephant into the refrigerator.Set theory:1. It's very easy! Refrigerator = { elephant } 2) The elephant and the interior of the refrigerator both have cardinality c.Geometry:Declare the following:Axiom 1. An elephant can be put into a refrigerator.Complex analysis:Put the refrig. at the origin and the elephant outside the unit circle. Then get the image under the inversion.Numerical analysis:1. Put just its trunk and refer the rest to the error term.2. Work it out using the Pentium.Statistics:1. Bright statistician. Put its tail as a sample and say "Done."2. Dull statistician. Repeat the experiment pushing the elephant to the refrig.3. Our NEW study shows that you CAN'T put the elephant in the refrigerator.
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November 11, 2009
|"First and above all he was a logician. At least thirty-five years of the half-century or so of his existence had been devoted exclusively to proving that two and two always equal four, except in unusual cases, where they equal three or five, as the case may be." -- Jacques Futrelle, "The Problem of Cell 13"Most mathematicians are familiar with -- or have at least seen references in the literature to -- the equation 2 + 2 = 4. However, the less well known equation 2 + 2 = 5 also has a rich, complex history behind it. Like any other complex quantitiy, this history has a real part and an imaginary part; we shall deal exclusively with the latter here.Many cultures, in their early mathematical development, discovered the equation 2 + 2 = 5. For example, consider the Bolb tribe, descended from the Incas of South America. The Bolbs counted by tying knots in ropes. They quickly realized that when a 2-knot rope is put together with another 2-knot rope, a 5-knot rope results.Recent findings indicate that the Pythagorean Brotherhood discovered a proof that 2 + 2 = 5, but the proof never got written up. Contrary to what one might expect, the proof's nonappearance was not caused by a cover-up such as the Pythagoreans attempted with the irrationality of the square root of two. Rather, they simply could not pay for the necessary scribe service. They had lost their grant money due to the protests of an oxen-rights activist who objected to the Brotherhood's method of celebrating the discovery of theorems. Thus it was that only the equation 2 + 2 = 4 was used in Euclid's "Elements," and nothing more was heard of 2 + 2 = 5 for several centuries.Around A.D. 1200 Leonardo of Pisa (Fibonacci) discovered that a few weeks after putting 2 male rabbits plus 2 female rabbits in the same cage, he ended up with considerably more than 4 rabbits. Fearing that too strong a challenge to the value 4 given in Euclid would meet with opposition, Leonardo conservatively stated, "2 + 2 is more like 5 than 4." Even this cautious rendition of his data was roundly condemned and earned Leonardo the nickname "Blockhead." By the way, his practice of underestimating the number of rabbits persisted; his celebrated model of rabbit populations had each birth consisting of only two babies, a gross underestimate if ever there was one.Some 400 years later, the thread was picked up once more, this time by the French mathematicians. Descartes announced, "I think 2 + 2 = 5; therefore it does." However, others objected that his argument was somewhat less than totally rigorous. Apparently, Fermat had a more rigorous proof which was to appear as part of a book, but it and other material were cut by the editor so that the book could be printed with wider margins.Between the fact that no definitive proof of 2 + 2 = 5 was available and the excitement of the development of calculus, by 1700 mathematicians had again lost interest in the equation. In fact, the only known 18th-century reference to 2 + 2 = 5 is due to the philosopher Bishop Berkeley who, upon discovering it in an old manuscript, wryly commented, "Well, now I know where all the departed quantities went to -- the right-hand side of this equation." That witticism so impressed California intellectuals that they named a university town after him.But in the early to middle 1800's, 2 + 2 began to take on great significance. Riemann developed an arithmetic in which 2 + 2 = 5, paralleling the Euclidean 2 + 2 = 4 arithmetic. Moreover, during this period Gauss produced an arithmetic in which 2 + 2 = 3. Naturally, there ensued decades of great confusion as to the actual value of 2 + 2. Because of changing opinions on this topic, Kempe's proof in 1880 of the 4-color theorem was deemed 11 years later to yield, instead, the 5-color theorem. Dedekind entered the debate with an article entitled "Was ist und was soll 2 + 2?"Frege thought he had settled the question while preparing a condensed version of his "Begriffsschrift." This condensation, entitled "Die Kleine Begriffsschrift (The Short Schrift)," contained what he considered to be a definitive proof of 2 + 2 = 5. But then Frege received a letter from Bertrand Russell, reminding him that in "Grundbeefen der Mathematik" Frege had proved that 2 + 2 = 4. This contradiction so discouraged Frege that he abandoned mathematics altogether and went into university administration.Faced with this profound and bewildering foundational question of the value of 2 + 2, mathematicians followed the reasonable course of action: they just ignored the whole thing. And so everyone reverted to 2 + 2 = 4 with nothing being done with its rival equation during the 20th century. There had been rumors that Bourbaki was planning to devote a volume to 2 + 2 = 5 (the first forty pages taken up by the symbolic expression for the number five), but those rumor remained unconfirmed. Recently, though, there have been reported computer-assisted proofs that 2 + 2 = 5, typically involving computers belonging to utility companies. Perhaps the 21st century will see yet another revival of this historic equation.The above was written by Houston Euler.
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November 11, 2009
|An engineer, a physicist, and a mathematician are trying to set up a fenced-in area for some sheep, but they have a limited amount of building material. The engineer gets up first and makes a square fence with the material, reasoning that it's a pretty good working solution. "No no," says the physicist, "there's a better way." He takes the fence and makes a circular pen, showing how it encompasses the maximum possible space with the given material.Then the mathematician speaks up: "No, no, there's an even better way." To the others' amusement he proceeds to construct a little tiny fence around himself, then declares:"I define myself to be on the outside."
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November 11, 2009
|A very large mathematical convention was held in Las Vegas. The conventioneers filled two hotels, each with an infinite number of rooms. The hotels were across the street from each other and were owned by brothers. One evening, while everyone was out at a bar-b-que, one of the hotels burned to the ground. The brothers got together and worked out a plan. In the remaining hotel, they moved all guests to twice their room number -- room 101 moved to 202, room 1234 moved to room 2468, etc. Then all the odd number rooms were empty, and there were an infinite number of odd rooms. So the guests from the other hotel moved into them
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November 11, 2009
|Math problems? Call 1-800-[(10x)(13i)^2]-[sin(xy)/2.362x]. If parallel lines meet at infinity - infinity must be a very noisy place with all those lines crashing together!Maths Teacher: Now suppose the number of sheep is x...Student: Yes sir, but what happens if the number of sheep is not x?Zenophobia: the irrational fear of convergent sequences.Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives.If I had only one day left to live, I would live it in my statistics class: it would seem so much longer.
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November 11, 2009
|It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest. -- S. den Hartog, Ph D. Thesis Universtity of Groningen.
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November 11, 2009
|Hello, this is probably 438-9012, yes, the house of the famous statistician. I'm probably not at home, or not wanting to answer the phone, most probably the latter, according to my latest calculations. Supposing that the universe doesn't end in the next 30 seconds, the odds of which I'm still trying to calculate, you can leave your name, phone number, and message, and I'll probably phone you back. So far the probability of that is about 0.645. Have a nice day.
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November 11, 2009
|. Ten percent of all car thieves are left-handed2. All polar bears are left-handed3. If your car is stolen, there's a 10 percent chance it was taken by a Polar bear1. 39 percent of unemployed men wear spectacles2. 80 percent of employed men wear spectacles3. Work stuffs up your eyesight1. All dogs are animals2. All cats are animals3. Therefore, all dogs are cats1. A total of 4000 cans are opened around the world every second2. Ten babies are conceived around the world every second3. Each time you open a can, you stand a 1 in 400 chance of becoming pregnant
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November 11, 2009
