Richard Feynman tangled regularly with military censors at Los Alamos. Playing one day with a computing machine, he discovered a pleasing little pattern:

1/243 = 0.004115226337448559670781893004115226337448559670781893004115226…

“It’s quite cute, and then it goes a little cockeyed when you’re carrying; confusion occurs for only about three numbers, and then you can see how the 10 10 13 is really equivalent to 114 again, or 115 again, and it keeps on going, and repeats itself nicely after a couple of cycles. I thought it was kind of amusing.”

Well, I put that in the mail, and it comes back to me. It doesn’t go through, and there’s a little note: ‘Look at Paragraph 17B.’ I look at Paragraph 17B. It says, ‘Letters are to be written only in English, Russian, Spanish, Portuguese, Latin, German, and so forth. Permission to use any other language must be obtained in writing.’ And then it said, ‘No codes.’

So I wrote back to the censor a little note included in my letter which said that I feel that of course this cannot be a code, because if you actually do divide 1 by 243 you do, in fact, get all that, and therefore there’s no more information in the number .004115226337… than there is in the number 243 — which is hardly any information at all. And so forth.

“I therefore asked for permission to use Arabic numerals in my letters. So, I got that through all right.”

(From his reminiscences.)

Here’s a surprise: A new geoglyph has been found in the soil of the Nazca Desert in southern Peru.

This one, evidently a cat, appears to be the oldest yet — it may have been engraved in the earth as early as 200 B.C. and has been waiting all this time to be discovered.

“The figure was barely visible and was about to disappear because it is situated on quite a steep slope that’s prone to the effects of natural erosion,” the culture ministry wrote.

“It’s quite striking that we’re still finding new figures,” said chief archaeologist Johny Isla, “but we also know that there are more to be found.”

Back in 2009 I worried that, if vampires are constantly converting humans, eventually we must all succumb.

Apparently this fear is not unfounded. In 2006 physicists Costas Efthimiou and Sohang Gandhi worked out that if the first vampires had turned up in 1600, if they’d needed to feed only once a month, and if the world population at that time had been 536,870,911 (as estimated), then the vampire population would have increased geometrically and the last human would have succumbed in June 1602, after a bloodbath of only two and half years.

Worse, in 1982 a team of Austrian mathematicians led by R. Haiti and A. Mehlmann found that intelligent vampires could calculate a bloodsucking frequency that would maximize total utility per vampire and keep the human race alive indefinitely — and solutions exist no matter whether they’re “asymptotically satiated vampires,” “blood-maximizing vampires,” or “unsatiable vampires.”

Later they expanded on this to show that cyclical bloodsucking patterns are optimal. That’s not very comforting.

(Dino Sejdinovic, “Mathematics of the Human-Vampire Conflict,” Math Horizons 16:2 [November 2008], 14-15.)

Shuffle a deck and deal three cards face down. A friend looks at the cards and turns up two that are the same color. What’s the probability that the remaining card is also of this color?

The answer is not 1/2 but 1/4. Three randomly selected cards might have any of eight equally possible arrangements of color. In only two of these (RRR and BBB) are all the colors the same. So the chance of this happening is 2/8 = 1/4.

(Martin Gardner, “Modeling Mathematics With Playing Cards,” College Mathematics Journal 31:3 [May 2000], 173-177.)

10/18/2020 UPDATE: A number of readers have pointed out that the probabilities here aren’t quite accurate. Gardner was trying to show how various mathematical problems can be illustrated using a deck of cards and contrived this example within that constraint, focusing on the “seeming paradox” of 1/4 versus 1/2. But because the cards are dealt from a finite deck without replacement, if the first card is red then the second card is more likely to be black, and so on. So the final answer here is actually slightly less than 1/4 — which, if anything, is even more surprising, I suppose! Thanks to everyone who wrote in about this.

In 2009, mathematician Jeff Chyatte and his colleagues at Maryland’s Montgomery College built a mathematical sculpture: An inclined rod is connected at its center to a horizontal arm, which is connected to a rotating vertical axis. As the axis rotates, the rod passes through a vertical plane.

What shape does the rod cut in the plane? Perhaps surprisingly, it’s a hyperbola. See the video above for an explanation. Chyatte’s sculpture was displayed at Washington’s Touchstone Gallery with the title “Theorem.”

(“Just Passing Through,” Math Horizons 16:4 [April 2009], 16.)

A footnote from T.W. Körner’s The Pleasures of Counting:

It may help to recall the bon mot I heard from a Russian physicist: ‘Proofs in physics follow the standards of British justice and hold the accused innocent until proved guilty. Proofs in mathematics follow the standards of Stalinist justice and hold the accused guilty until proved innocent.’

From Enrico Fermi’s eyewitness report on the first detonation of a nuclear device, July 16, 1945:

About 40 seconds after the explosion, the air blast reached me. I tried to estimate its strength by dropping from about six feet small pieces of paper before, during, and after the passage of the blast wave. Since, at the time, there was no wind I could observe very distinctly and actually measure the displacement of the pieces of paper that were in the process of falling while the blast was passing. The shift was about 2½ meters, which, at the time, I estimated to correspond to the blast that would be produced by ten thousand tons of T.N.T.

Radiochemical analysis of soil samples later indicated that the total yield had been around 18.6 kilotons of TNT.

10/09/2020 UPDATE: Here’s Fermi’s report. (Thanks, Sivaraam.)