12 = 3 × 4; 56 = 7 × 8
Science & Math
Words and Numbers
In English, the name of each integer shares a letter with each of its neighbors. ONE shares an O with TWO, TWO shares a T with THREE … and so on to infinity.
Huth’s Moving Star
In late 1801, Johann Bode, director of the Berlin Observatory, received a curious series of letters from astronomer Hofrath Huth in Frankfort-on-the-Oder. On Dec. 2 Huth had seen something new in the sky, “a star with faint reddish light, round, and admitting of being magnified.” But it wasn’t a star: On subsequent nights he watched it drift slowly to the southwest, growing gradually fainter, and by Jan. 6 it had disappeared. Huth concluded that he was watching an object recede from Earth.
Unfortunately, Bode was busy with other things, and the weather was too cloudy for him to confirm Huth’s observations. Also, the positional data that Huth had provided were somewhat poor.
Huth wasn’t a nut: Among other things, he co-discovered Comet Encke in 1805. And Nature noted later that he had alerted Bode to the object in time for the director to witness it himself if the skies had been clear. But as it happened, Huth was the only one to witness the curious object, whatever it was. And, whatever it was, it has not returned.
Still Waters
Gauss’ scientific diary was a great boon to mathematical historians, but his notes could be frustratingly cryptic. On July 10, 1796, he made this entry:
ΕΥΡΗΚΑ! num = Δ + Δ + Δ
He had discovered that every positive integer is the sum of at most three triangular numbers.
Among the 146 entries, two remain completely opaque. On Oct. 11, 1796, Gauss had written:
Vicimus GEGAN.
And on April 8, 1799:
No one knows what either of these means — if they had mathematical significance, it was lost with Gauss.
So it goes. Dirichlet was famously uncommunicative, not even informing his family that his wife had given birth. His father-in-law later complained that he “should at least have been able to write 2 + 1 = 3.”
Fitting
In the Dewey decimal system, books on number theory are labeled 512.81.
512 = 29 and 81 = 92.
Misc
- Jimmy Carter was the first U.S. president born in a hospital.
- Hamlet has 1506 lines, fully 39 percent of the play.
- 736 = 7 + 36
- NOOK combines two antonyms.
- “Everything that deceives may be said to enchant.” — Plato
Symmetric Milestones
What’s unusual about these numbers?
Each series is spaced evenly on the number line:
Each number is a palindrome.
And each is prime.
Education Reconsidered
Reflect, Socrates; you may have to deny your words.
I have reflected, I said; and I shall never deny my words.
Well, said he, and so you say that you wish Cleinias to become wise?
Undoubtedly.
And he is not wise as yet?
At least his modesty will not allow him to say that he is.
You wish him, he said, to become wise, and not to be ignorant?
That we do.
You wish him to be what he is not, and no longer to be what he is?
I was thrown into consternation at this.
Taking advantage of my consternation he added: You wish him no longer to be what he is, which can only mean that you wish him to perish. Pretty lovers and friends they must be who want their favourite not to be, or to perish!
— Plato, Euthydemus
Math Notes
9 + 9 = 18; 9 × 9 = 81
24 + 3 = 27; 24 × 3 = 72
47 + 2 = 49; 47 × 2 = 94
497 + 2 = 499; 497 × 2 = 994
Two Milestones
The date 11/19/1999 contained only odd digits. Less than three months later, 2/2/2000 contained only even.
That’s a rare coincidence. It had been 1111 years since the last all-even date … and it’ll be 1111 more before the next all-odd one.