Futility Closet

We’re told that, in any right triangle, a² + b² = c². But consider:

In the figure above, the total length of the red line is 2(a/2) + 2(b/2), or a + b. And again:

Here the red line’s length is 4(a/4) + 4(b/4), which is still a + b.

With each iteration, the red line more closely approximates c, but its length remains a + b. At the limit, then, it seems, a + b = c. Was Pythagoras mistaken?

In 1952, a stray cat wandered into Elysian Heights Elementary School in Echo Park, Calif. He seemed to be about 7 years old, skinny but healthy, and he was apparently determined to live at the school. The students quickly adopted him, feeding him from their sandwiches, and he made a home in classroom 8, disappearing each night but turning up again in the morning.

The sandwiches must have been pretty good, because “Room 8″ stayed at the school for 15 years, reappearing mysteriously at the end of each summer vacation. Thanks to widespread media coverage, including features in Time and Look, he’s said to have received 10,000 letters in that time, which the children dutifully answered. And every year his picture was taken with the graduating class of sixth graders.

Wherever he came from, it seems he’d found what he wanted. He died in August 1968, and his pawprints grace the sidewalk in front of the school.

On Friday morning of the week before last, early risers in Baton Rouge, Louisiana, witnessed a peculiar sight in the shape of a shower of birds that fell from a clear sky, literally cluttering the streets of the city. There were wild ducks, catbirds, woodpeckers, and many birds of strange plumage, some of them resembling canaries, but all dead, falling in heaps along the thoroughfares, the singular phenomenon attracting many spectators and causing much comment.

The most plausible theory as to the strange windfall is that the birds were driven inland by the late storm on the Florida coast, the force of the current of air and the sudden change of temperature causing the death of many of the little feathered creatures when they reached Baton Rouge. Some idea of the extent of the shower may be gathered from the estimate that out on National Avenue alone the children of the neighborhood collected as many as 200 birds.

– St. Louis newspaper, quoted in The Osprey, December 1896

Well, maybe you’ll need one someday.

Seroun Kesh’s 1964 invention has a bonus application: You can attach a hair dryer to tube 21 “so that the same may be used to dry the dog after a bath.”

Solution to Two by Two:

Essentially the technique converts the first factor into binary, multiplies each of its constituents by the second factor, and sums the results.

Imagine that each line is associated with a power of 2: the first line with 2⁰, the second with 2¹,and so on.

The business in the first column, halving the first factor successively and crossing out those lines with even numbers, effectively reduces the first factor to its binary constituents — here, the lines that remain are those associated with 2⁰, 2⁵, and 2⁶, and, sure enough, 2⁰ + 2⁵ + 2⁶ = 97.

Now we need to multiply each of those constituents by the second factor, 23. In other words, we want to find:

(23 × 2⁰) + (23 × 2⁵) + (23 × 2⁶)

That’s what’s accomplished in the second column. Doubling the second factor successively, as we’ve done there, is equivalent to multiplying it by 2⁰ in the first line, by 2¹ in the second, and so on. That is, 23 = 23 × 2⁰, 46 = 23 × 2¹, etc. And the lines that haven’t been crossed out are precisely the ones we want:

23 (= 23 × 2⁰)
736 (= 23 × 2⁵)
1472 (= 23 × 2⁶)

So if we add those values, we’ll get the product of the original two numbers, which is what we sought: 23 + 736 + 1472 = 2231.

Here’s essentially what we’ve done, from the top:

97 × 23
= (2⁰ + 2⁵ + 2⁶) × 23
= (23 × 2⁰) + (23 × 2⁵) + (23 × 2⁶)
= 23 + 736 + 1472
= 2231

It works with any pair of numbers.

DEAD-ENDEDNESSES contains one A, two Ns, three Ss, four Ds, and five Es.

TEMPERAMENTALLY can be separated into a single letter followed by words of 2, 3, 4, and 5 letters: T, EM, PER, AMEN, TALLY.

British statesman Charles James Fox (1749-1806) managed to have two aunts who died 171 years apart:

Fox’s grandfather married twice — once at 27 and once at 76. A baby produced by the first marriage died in 1655, and a son produced by the second marriage married a woman whose sister died in 1826.

Fox himself died in 1806, but his widow survived until 1842 — nearly 200 years after the death of her aunt-by-marriage.

See also Proof That a Man Can Be His Own Grandfather.

Here’s a curious way to multiply two numbers. Suppose we want to multiply 97 by 23. Write each at the head of a column. Now halve the first number successively, discarding remainders, until you reach 1, and double the second number correspondingly in its own column:

Cross out each row that has an even number in the left column, and add the numbers that remain in the second column:

That gives the right answer (97 × 23 = 2231). Why does it work?

(Answer)

Malta is criss-crossed with ruts like these. No one knows who made them, when, or why. If they’re cart ruts, why are some 60 centimeters deep? If it’s an irrigation system or some kind of astronomical undertaking, what was its purpose?

The most popular theory is that ancient sledges hauled limestone to build local temples. But why then do some ruts lead straight into the sea?

(Image: Wikimedia Commons)

Solution to Paradox, by a Lady:

“The lady walked 200 yards backward.”