Science & Math

Math Notes

28 + 48 + 68 + 78 + 88 + 08 + 58 + 08 = 24678050

Presto

Pick a three-digit number (example: 412).

Double it to create a six-digit number (412412).

Divide the result successively by 7, by 11, and by 13. There will be no remainders.

The result is the original number.

Where’s the Fallacy?

square-mile fallacy

“In Event of Moon Disaster”

http://commons.wikimedia.org/wiki/Image:Buzz_salutes_the_U.S._Flag.jpg

On July 18, 1969, two days before the first lunar landing, presidential speechwriter William Safire composed the following text to be read by President Nixon if astronauts Neil Armstrong and Edwin Aldrin were stranded on the moon:

Fate has ordained that the men who went to the moon to explore in peace will stay on the moon to rest in peace.

These brave men, Neil Armstrong and Edwin Aldrin, know that there is no hope for their recovery. But they also know that there is hope for mankind in their sacrifice.

These two men are laying down their lives in mankind’s most noble goal: the search for truth and understanding.

They will be mourned by their families and friends; they will be mourned by the nation; they will be mourned by the people of the world; they will be mourned by a Mother Earth that dared send two of her sons into the unknown.

In their exploration, they stirred the people of the world to feel as one; in their sacrifice, they bind more tightly the brotherhood of man.

In ancient days, men looked at the stars and saw their heroes in the constellations. In modern times, we do much the same, but our heroes are epic men of flesh and blood.

Others will follow, and surely find their way home. Man’s search will not be denied. But these men were the first, and they will remain the foremost in our hearts.

For every human being who looks up at the moon in the nights to come will know that there is some corner of another world that is forever mankind.

Safire also suggested that Nixon call the “widows-to-be” before the speech, and that a clergyman should commend the astronauts’ souls to the “deepest of the deep” when communications ended.

Math Notes

17 + 77 + 47 + 17 + 77 + 27 + 57 = 1741725

Subtraction Pangram

Each term in this equation contains each of the nine digits once:

subtraction pangram

Proof That 2 Does Not Exist

2 is the only even prime.

But the total number of primes is infinite.

Therefore the probability that a given prime number is even is 1 over infinity, or zero.

Hence it’s impossible for a prime number to be even — and 2 does not exist.

Math Notes

55 + 45 + 75 + 45 + 85 = 54748

The Barber’s Dictum

Let’s say that the densest human head of hair contains 200,000 strands, and that the human population is 6 billion. That means there’s a group of at least 30,000 people today who have precisely the same number of hairs on their heads.

Do you see why?

Where’s the Fallacy?

fallacy

Waistline

Suppose the earth were a perfect sphere and you fitted a belt around its equator.

The belt would be 40 million meters long. If you now increased its length by a mere 5 meters, how high would it ride above the earth’s surface?

The answer, surprisingly, is 0.8 meters — well above the current limbo record.

Square Deal

Look! Canceling exponents works even in algebra:

canceling exponents in algebra

Math Notes

1634 = 14 + 64 + 34 + 44

The Declining Dollar

declining dollar

Numerical Pangrams

A pangram is a sentence that uses each letter of the alphabet exactly once:

CWM FJORD BANK GLYPHS VEXT QUIZ.

“Carved symbols in a mountain hollow and on the bank of a fjord irritated an eccentric person.” They’re a bit awkward in English, so here’s the same idea using numbers. Each of these (valid) equations uses the digits 1-9 exactly once:

42 × 138 = 5796
27 × 198 = 5346
39 × 186 = 7254
48 × 159 = 7632
28 × 157 = 4396
4 × 1738 = 6952
4 × 1963 = 7852

Even better: The numbers 3 and 51249876, between them, use all 9 digits — and so does their product, 153749628.

Torn Up

Imagine a large sheet of rice paper one-thousandth of an inch thick. Tear it in half and stack the pieces, then tear the stack in half and stack those, and so on. If you could do this 50 times in succession, how tall would the final stack be?

A. 0.6 inches
B. 22.84 feet
C. 17 million miles

Surprisingly, the answer is 17 million miles:

250 ply × 0.001 inches/ply
= 1.12589991 × 1012 inches
= 17,769,884.9 miles

Math Notes

equations

Science Fiction

In Gulliver’s Travels, Jonathan Swift describes two fictional moons of Mars:

They [the Laputan astronomers] have likewise discovered two lesser stars, or ‘satellites,’ which revolve about Mars, whereof the innermost is distant from the centre of the primary planet exactly three of his diameters, and the outermost five; the former revolves in the space of ten hours, and the latter in twenty-one and a half; so that the squares of their periodical times are very near in the same proportion with the cubes of their distance from the centre of Mars, which evidently shows them to be governed by the same law of gravitation, that influences the other heavenly bodies …

That was in 1726. A century and a half later, two Martian moons were discovered. Phobos and Deimos were in fact about 1.4 and 3.5 diameters from Mars’ center, and they revolved in 7.7 and 30.3 hours, respectively. Voltaire had made a similarly prescient guess in his romance Micromegas of 1752.

Fittingly, two craters on Deimos have been named Swift and Voltaire.

Math Notes

122 = 144
212 = 441

132 = 169
312 = 961

Say It With Constants

MIT mails its acceptance letters on 3/14 — “Pi Day.”

The Life on Mars Paradox

http://commons.wikimedia.org/wiki/Image:Mars_atmosphere.jpg

What’s the probability that there are horses on Mars? Let’s be extremely generous and say it’s 1/2. And let’s also say there’s a probability of 1/2 that there are parrots, and aardwolves, and each of 17 other species.

Then the probability that none of these 20 species exists is (1/2)20. And the probability that at least one of them exists is 1 – (1/2)20, or 0.999999046.

Thus it’s nearly certain that there’s life on Mars.

Witchcraft

Mersenne once wrote to Fermat asking whether 100895598169 were a prime number.

Fermat replied immediately that it’s the product of 898423 and 112303, both of which are prime.

To this day, no one knows how he knew this. Has a powerful factoring technique been lost?

Math Notes

93 + 13 + 93 = 1459
13 + 43 + 53 + 93 = 919

How to Win Six Million Dollars

http://www.sxc.hu/photo/276465

Summon six millionaires and invite them to stake their fortunes on a single hand of poker. They will eagerly agree. Open a new deck of cards, discard the jokers, and ask the millionaires to cut (but not shuffle!) the deck as many times as they like. Then deal seven hands, ostentatiously dealing your own second and fourth cards from the bottom of the deck.

The millionaires may be reluctant to object to this, as all six of them will be holding full houses. (This works — try it.) But “See here,” they will finally say. “What was that business with the bottom-dealing? You’re up to something. We insist that you discard that hand.” Look hurt, then deal yourself a new hand.

You’ll likely be holding a straight flush.