The number 360 is centered across the 360th decimal place of π:
6998970 = 36 + 19 + 49 + 18 + 59 + 97 + 20
6998971 = 36 + 19 + 49 + 18 + 59 + 97 + 21
(Thanks, Pablo.)
The 22nd, 7th, 355th, 113th, and 52163rd digits of π (counting from the 3) are 2s.
The 16604th digit, alas, is a 1 — but it’s flanked by 2s.
At the end of your visit to an elderly, infirm relative who lives alone, the relative says, ‘I’m sorry but my arthritis won’t let me get up from this chair today. You’ll have to show yourself out.’ How can you show yourself out of someone’s house? If you know the way out, you can act as a guide to someone else. But how can you act as your own guide?
— T.S. Champlin, Reflexive Paradoxes, 1988
If three hula hoops cover a common point, then a fourth hoop of the same size will cover their remaining intersections.
Mathematician G.H. Hardy had an ongoing feud with God. Once, after spending a summer vacation in Denmark with Harald Bohr, he found he’d have to take a small boat across the tempestuous North Sea to return to England. Before boarding, he sent Bohr a postcard that said “I have proved the Riemann hypothesis. — G.H. Hardy.”
When Bohr excitedly asked about this later, “Oh, that!” Hardy said. “That was just insurance. God would never let me drown if it meant I’d get undue credit.”
From Samuel Isaac Jones, Mathematical Wrinkles (1929), a magic square with a twist:
“It will be observed that this square when turned upside down is still magic.”
Discovered by J.A.H. Hunter.
A line that bisects the right angle in a right triangle also bisects a square erected on the hypotenuse.
Proof:
If a second is defined by reference to the rotation of the earth on its axis, i.e. as 1/60 of 1/60 of 1/24 of the time between 2 identical positions of the Greenwich meridian relatively to the fixed stars, then, if the earth rotated 10 times more slowly than it does now, it would be possible to run 10 yds. in a second, instead of only a yard as now, and a second would be 10 times longer than it is now; but if cinema machines still moved as fast as they do now, it would still be quite impossible for any one to see a succession of static pictures instead of a moving one. Don’t we mean by a second the length of time which is now 1/60 of 1/60 of 1/24 of the time between etc.?
— G.E. Moore, Commonplace Book, 1962
On Jan. 18, 1897, California farmer George Jones bought a quantity of livestock feed from Henry B. Stuart of San Jose. As security he signed a $100 promissory note that bore 10 percent interest per month, compounded monthly.
They had agreed that Jones would pay the debt in three months, but the note had run for almost 25 years when Stuart got tired of waiting and told his lawyer to sue. Judge J.R. Welch of the Superior Court of Santa Clara entered this judgment on March 6, 1922:
“Wherefore, by virtue of the law and the facts, it is Ordered, Adjudged and Decreed that said Plaintiff have and recover from said Defendant the sum of $304,840,332,912,685.16 with interest thereon at the rate of 7% per annum until paid, together with the further sum of $50.00 Plaintiff’s attorney’s fees herein with interest thereon at the rate of 7% per annum until paid.”
That’s $304 trillion, “more money than there is in the world, outside of Russia,” the New York Tribune reported drily. Jones paid $19.69 and filed for bankruptcy.