The horizontal lines are parallel.
“Note How Your Friend Laughs”
It is a well known and easily demonstrated scientific fact that different people sound different vowels when laughing, from which fact a close observer has drawn the following conclusions: People who laugh in A (pronounced as ah) are frank, honest, and fond of noise and excitement, though they are often of a versatile and fickle disposition. Laughter in E (pronounced as ay) is peculiar to phlegmatic and melancholy persons. Those who laugh in I (pronounced as ee) are children or simple-minded, obliging, affectionate, timid, and undecided people. To laugh in O indicates generosity and daring. Avoid if possible all those who laugh in U, as they are wholly devoid of principle.
— Henry Williams, A Book of Curious Facts, 1903
A Novel Proof
We’ve had some pretty smart presidents. James Garfield devised this proof of the Pythagorean theorem in 1876, while serving in the House of Representatives:
The area of the trapezoid above is
The area of each green triangle is
And the yellow triangle is
So:
The Voting Paradox
Suppose we hold an election with three candidates, X, Y, and Z. And suppose the voters fall into three groups:
Group 1 prefers, in order, X, Y, Z
Group 2 prefers, in order, Y, Z, X
Group 3 prefers, in order, Z, X, Y
Now, if Candidate X wins, his opponents can rightly object that a majority of voters would have preferred Candidate Z. And corresponding arguments can be made against the other candidates. So even though we’ve held a fair election, it’s impossible to establish majority rule.
The Marquis de Condorcet noted this oddity in the 1700s; it’s sometimes known as Condorcet’s paradox.
R.I.P.
Epitaph in the churchyard of Llangerrig, Montgomeryshire:
— Charles Bombaugh, Facts and Fancies for the Curious From the Harvest-Fields of Literature, 1860
Plying the Blue
Phantom ships, as they have been called, have repeatedly been seen by various observers. Mr. Scoresby, in his voyage to Greenland, in 1822, saw an inverted image of a ship in the air, so well defined that he could distinguish by a telescope every sail, the peculiar rig of the ship, and its whole general character, insomuch that he confidently pronounced it to be his father’s ship, the Fame, which it afterwards proved to be.
— Charles Kingsley, The Boys’ and Girls’ Book of Science, 1881
See also The Wizard of Mauritius.
Math Notes
32 – 23 = 3 – 2
Thunderstruck
Georg Wilhelm Richmann was attending a meeting at the St. Petersburg Academy of Sciences in August 1753 when he heard thunder. He ran home with another man, hoping to record how an insulated rod responded to an electrical storm.
He succeeded, in a way: A ball of lightning leapt from the rod and struck Richmann in the head, killing him instantly and knocking his companion unconscious. That makes Richmann the first person in history to die while conducting electrical experiments.
Joseph Priestley wrote, “It is not given to every electrician to die in so glorious a manner as the justly envied Richmann.” That’s one way to look at it.
Unquote
“One may be humble out of pride.” — Montaigne
“Rhyming Words Wanted”
A whimsical letter written by W. S. Gilbert notes ‘a great want’ among poets. ‘I should like to suggest,’ he says, ‘that any inventor who is in need of a name for his invention, would confer a boon on the rhymsters, and at the same time insure himself many gratuitous advertisements, if he would select a word that rhymes to one of the many words in common use, which have but few rhymes or none at all. A few more words rhyming with ‘love’ are greatly wanted; ‘revenge’ and ‘avenge’ have no rhyming word, except ‘Penge’ and ‘Stonehenge’; ‘coif’ has no rhyme at all; ‘starve’ has no rhyme except (oh, irony!) ‘carve’; ‘scarf’ has no rhyme, though I fully expect to be told that ‘laugh,’ ‘calf,’ and ‘half’ are admissible, which they certainly are not.’
— Miscellaneous Notes and Queries, March 1894