I used to like to hear him admire the beauty of a flower; it was a kind of gratitude to the flower itself, and a personal love for its delicate form and colour. I seem to remember him gently touching a flower he delighted in; it was the same simple admiration that a child might have.
— Francis Darwin, of his father
From Lee Sallows:
(Thanks, Lee!)
The infinite series 1/4 + 1/16 + 1/64 + 1/256 + … was one of the first to be summed in the history of mathematics; Archimedes had found by 200 BC that it totals 1/3. There are two neat visual demonstrations that make this fact immediately apparent. In the unit square above, the largest black square has area 1/4, the next-largest black square has area 1/16, and so on. Regions of black, white, and gray make up equal areas in the total figure, so the black squares, taken together, must have area 1/3.
The same argument can be made using triangles (below). If the area of the largest triangle is 1, then the largest black triangle has area 1/4, the next-largest 1/16, and so on. Areas of black, white, and gray make up equal parts of the total figure, so the black regions must total 1/3.
“No general proposition is worth a damn.” — Oliver Wendell Holmes Jr. (a general proposition)
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.)
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