The decimal expansion of 1/7 is
0.142857142857 …
Interestingly, if you split the repeating decimal period in half and add the two complements, you get a string of 9s:
142 + 857 = 999
It turns out this is true for every fraction with a prime denominator and a repeating decimal period of even length:
1/11 = 0.090909 …
0 + 9 = 9
1/13 = 076923 …
076 + 923 = 999
1/17 = 0.0588235294117647 …
05882352 + 94117647 = 99999999
1/19 = 0.052631578947368421 …
052631578 + 947368421 = 999999999
As to your method of work, I have a single bit of advice, which I give with the earnest conviction of its paramount influence in any success which may have attended my efforts in life — Take no thought for the morrow. Live neither in the past nor in the future, but let each day’s work absorb your entire energies, and satisfy your widest ambition. That was a singular but very wise answer which Cromwell gave to Bellevire — ‘No one rises so high as he who knows not whither he is going,’ and there is much truth in it. The student who is worrying about his future, anxious over the examinations, doubting his fitness for the profession, is certain not to do so well as the man who cares for nothing but the matter in hand, and who knows not whither he is going!
— William Osler, advice to students, McGill College, 1899
In 1818, English zoologist William Elford Leach named nine new genera of parasitic isopods: Anilocra, Canolira, Cirolana, Conilera, Lironeca, Nelocira, Nerocila, Olencira, and Rocinela.
Each of these is an anagram of the name Caroline (or its Latinized form Carolina). But Leach was not married and had no known relationship with any woman of that name.
The genera stand as a “tantalizing puzzle for posterity.” More here.
From Lee Sallows, a crossword grid that describes its own contents:
(Thanks, Lee!)
Twice a year, objects Hawaii lose their shadows as the sun passes directly overhead.
A “zero shadow day” occurs biannually between the Tropics of Cancer and Capricorn, arriving at each location when the sun’s declination equals its latitude.
From Lee Sallows:
(Thanks, Lee.)
What’s the funniest number? Yale physicist Emily Pottebaum proposed the Perceived Specificity Hypothesis, which states that “for nonnegative integers < 100, the funniness of a number increases with its apparent precision." She surveyed 68 acquaintances and found that:
The degree of specificity characterizes the distance between an integer and the nearest multiple of 5:
So 3, 7, 13, 17, etc. were judged to be funniest.
“I acknowledge my Ph.D. advisor, who I shall not name out of respect for her academic integrity, for her exasperation upon learning about this study. I thank her for putting up with my antics and plead that she continue to do so until I graduate.”
(E.G. Pottebaum, “What Is the Funniest Number? An Investigation of Numerical Humor,” arXiv preprint, arXiv:2503.24175 [2025].)
In the Spring 1957 issue of Pi Mu Epsilon Journal, C.W. Trigg points out that, by two continuous cuts, the surface of a cube can be divided into two pieces that can be unfolded and assembled into a hollow square:
The cuts divide the cube’s surface into two congruent pieces, each composed of six connected isosceles right triangles. Joining these two pieces forms a hollow square with exterior side 
10/10/2025 UPDATE: Reader Nick Hare made a much, much, much, much better diagram:
(Thanks, Nick.)
Two numbers are said to be betrothed if the sum of the proper divisors of each number is 1 more than the value of the other. For example:
The proper divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, and 24. 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 = 76 = 75 + 1.
The proper divisors of 75 are 1, 3, 5, 15, and 25. 1 + 3 + 5 + 15 + 25 = 49 = 48 + 1.
Interestingly, in all such pairs discovered so far, one number is odd and the other even. Is this always the case? That’s an open question.
