(I don’t know who came up with this — there’s a whole series of memes on this theme.)
Marden’s Theorem
If f(z) is a cubic polynomial with complex coefficients, and if the roots of f are three distinct non-collinear points A, B, and C in the complex plane, then the roots of the derivative f′ are the foci of the unique ellipse inscribed in triangle ABC and tangent to the sides at their midpoints.
The theorem is named for Morris Marden, but it had been proven about a century earlier by Jörg Siebeck.
(Dan Kalman, “The Most Marvelous Theorem in Mathematics,” Math Horizons 15:4 [April 2008], 16-17.)
An Early Voice
On October 21, 1889, Prussian field marshal Helmuth von Moltke the Elder made two audio recordings on Thomas Edison’s new cylinder phonograph. The first contains a congratulatory message to Edison and an excerpt from Faust, the second a line from Hamlet.
This is the only voice recording we have of a person born in the 18th century — Moltke had been born in 1800, technically the last year of that century. Ironically, he had been known as der große Schweiger, “the great silent one,” for his taciturnity.
Podcast Episode 282: Helga Estby’s Walk
In 1896, Norwegian immigrant Helga Estby faced the foreclosure of her family’s Washington farm. To pay the debt she accepted a wager to walk across the United States within seven months. In this week’s episode of the Futility Closet podcast we’ll follow her daring bid to win the prize, and its surprising consequence.
We’ll also toast Edgar Allan Poe and puzzle over a perplexing train.
Applied Chemistry
On his May 1997 final exam at the University of Oklahoma School of Chemical Engineering, a Dr. Schlambaugh asked, “Is hell exothermic or endothermic? Support your answer with proof.” Most students based their responses on Boyle’s law, but one gave this answer:
First, we postulate that if souls exist, they must have some mass. If they do, then a mole of souls must have a mass. So at what rate are souls moving into hell and at what rate are souls leaving? I think we can safely assume that once a soul gets to hell it does not leave. Therefore, no souls are leaving. As for souls entering hell, let’s look at the different religions that exist in the world today. Some of the religions state that if you are not a member of their religion, you will go to hell. Since there are more than one of these religions and people do not belong to more than one religion, we can project that all souls go to hell. With the birth and death rates what they are, we can expect the number of souls in hell to increase exponentially. Now, we look at the rate of change in the volume of hell. Boyle’s Law states that in order for the temperature and pressure in hell to stay the same, the ratio of the mass of the souls to the volume needs to stay constant. (1) If hell is expanding at a slower rate than the rate at which souls enter hell, then the temperature and pressure in hell will increase until all hell breaks loose. (2) If hell is expanding at a rate faster than the increase in souls in hell, then the temperature and pressure will drop until hell freezes over. So which is it? If we accept the postulate given to me by Theresa Banyan during Freshman year, ‘It will be a cold night in hell before I sleep with you’ and take into account the fact that I still have not succeeded in having sexual relations with her, then (2) cannot be true. Thus hell is exothermic.
“The student, Tim Graham, got the only A.”
(Dave Morice, “Kickshaws,” Word Ways 31:2 [May 1998], 140-149.)
01/28/2020 This is a legend, apparently starting at the Taylor Instrument Company in the 1920s and accumulating some entertaining variations since then. The text of the Applied Optics piece is here. (Thanks, Dan and Pete.)
An Unexpected Party
J.R.R. Tolkien received this letter in March 1956:
Dear Sir
I hope you do not mind my writing to you, but with reference to your story ‘Lord of the Rings’ running as a serial on the radio under the item on the programme ‘for the schools’ Home Service once a week in the afternoons I was rather interested in how you arrived at the name of one of the characters named Sam Gamgee because that happens to be my name. I haven’t heard the story myself not having a wireless but I know some who have, one being my nephew, bearing the same surname, who is a school teacher and it caused a laugh among his class when it came on. Another, my great neice and the latter’s daughter 9 yrs of age a pupil at a different school, also heard it and caused some surprise among the class when it came on at her school. I know it’s fiction, but it is rather a coincidence as the name is very uncommon, but well known in the medical profession.
The above address is my brothers as I have no permanent address.
Yrs faithfully
Sam Gamgee
Tolkien wrote back, “It was very kind of you to write. You can imagine my astonishment, when I saw your signature! I can only say, for your comfort I hope, that the ‘Sam Gamgee’ of my story is a most heroic character, now widely beloved by many readers, even though his origins are rustic. So that perhaps you will not be displeased by the coincidence of the name of this imaginary character (of supposedly many centuries ago) being the same as yours.”
He later said, “For some time I lived in fear of receiving a letter signed ‘S. Gollum’. That would have been more difficult to deal with.”
Exchange
In 1951 Clement Attlee received this message from 15-year-old Ann Glossop, who had completed her final exams at Penrhos College only to discover that under recent reforms she was considered too young to graduate and must wait a year and go through them again:
Would you please explain, dear Clement
Just why it has to be
That Certificates of Education
Are barred to such as me?
I’ve worked through thirteen papers
But my swot is all in vain
Because at this time next year
I must do them all again.
Please have pity, Clement,
And tell the others too.
Remove the silly age-limit
It wasn’t there for you.
He replied:
I received with real pleasure
Your verses, my dear Ann.
Although I’ve not much leisure
I’ll reply as best I can.
I’ve not the least idea why
They have this curious rule
Condemning you to sit and sigh
Another year at school.
You’ll understand that my excuse
For lack of detailed knowledge
Is that school certs were not in use
When I attended college.
George Tomlinson is ill, but I
Have asked him to explain
And when I get the reason why
I’ll write to you again.
He lost office shortly thereafter, so Ann’s problem was never solved.
SRO
A gracious moment between Samuel Johnson and the actress Sarah Siddons:
When Mrs. Siddons came into the room, there happened to be no chair ready for her, which he observing, said with a smile, ‘Madam, you who so often occasion a want of seats to other people, will the more easily excuse the want of one yourself.’
(From Boswell’s Life of Johnson.)
Math Notes
There are only five integer-sided triangles in which the area equals the perimeter:
(5, 12, 13) (6, 8, 10) (6, 25, 29) (7, 15, 20) (9, 10, 17)
Only two of them are right triangles.
(Lee Markowitz, “Area = Perimeter,” Mathematics Teacher 74:3 [March 1981], 222-223.)
The Grave Creek Stone
This flat, polished sandstone pebble was found in a 2,000-year-old burial mound in West Virginia in 1838. Though it seemed to bear 25 pseudo-alphabetic characters, no one could agree on their meaning. In 1845 ethnologist Henry Rowe Schoolcraft consulted “noted antiquarians” and concluded that the inscription contains “four characters corresponding to the Ancient Greek; four Etruscan; five Runic; six ancient Gallic; seven old Erse; ten Phoenician; fourteen old British; sixteen Celtiberic, with some resemblance to the Hebrew.” In the 1870s physician R.J. Farquharson compiled wildly varying translations of the inscription from three different scholars:
- “Thy orders are laws, thou shines in thy impetuous clan, and rapid as the chamois.”
- “The chief of emigration who reached these places (or island), has fixed these decrees forever.”
- “The grave of one who was murdered here; to revenge him may God strike his murderer, suddenly taking away his existence.”
Also in the 1870s, antiquarian M.C. Reid asked a law student, a schoolgirl, a pharmacist, and a college professor to create “twenty or more arbitrary characters not resembling any figures or alphabetical characters known to them.” Their characters resembled those in Old World alphabets, just as did those on the Grave Creek stone. Reid was “compelled to conclude that there is nothing in the form of the characters of the Grave Creek Stone which require us to decide that they are old, that they are alphabetical, or if alphabetical that they are derived from any known alphabet.”
Today it seems most likely that the stone was forged by James W. Clemens, a local physician who had financed the original excavation and wanted to sell rights to exploit the mound. In 2008 anthropologist David Oestreicher discovered the same sequences of markings in a 1752 book by a Spanish historian, An Essay on the Alphabets of the Unknown Letters That Are Found in the Most Ancient Coins and Monuments of Spain. It appears that Clemens simply copied these characters onto the stone and planted it in the mound.