Alison’s Triangle

alison's triangle

I’m not sure who came up with this — this simple diagram reflects all possible true trigonometric identities of the form x ÷ y = z or x × y = z, where x, y, and z are the basic trigonometric functions of the same angle t.

For any three neighboring functions on the perimeter of the star, the product of the ends always equals the middle (e.g., tan t × cos t = sin t) and the middle function divided by one of the end functions is equal to the other end function (e.g., sin t ÷ tan t = cos t and sin t ÷ cos t = tan t). If you memorize the diagram you can reel off a list of 18 simple relations.

I found it in Michael Stueben’s Twenty Years Before the Blackboard, 1998.

| Science & Math

One on One

http://commons.wikimedia.org/wiki/File:Lyndon_Johnson_and_Richard_Russell.jpg

Thomas Jefferson looks on nervously while Lyndon Johnson “confers” with Sen. Richard Russell (D-Ga.). At 6’4″, Johnson tied Abraham Lincoln as the tallest U.S. president, and he used his physical presence to advance his agenda, cornering his targets in out-of-the-way places and leaning “so close to you,” one staffer recalled, “that your eyeglasses bumped.” In their 1966 book The Exercise of Power, Rowland Evans and Robert Novak dubbed this The Treatment:

The Treatment could last ten minutes or four hours. It came, enveloping its target, at the Johnson Ranch swimming pool, in one of Johnson’s offices, in the Senate cloakroom, on the floor of the Senate itself — wherever Johnson might find a fellow Senator within his reach. Its tone could be supplication, accusation, cajolery, exuberance, scorn, tears, complaint and the hint of threat. It was all of these together. It ran the gamut of human emotions. Its velocity was breathtaking, and it was all in one direction. Interjections from the target were rare. Johnson anticipated them before they could be spoken. He moved in close, his face a scant millimeter from his target, his eyes widening and narrowing, his eyebrows rising and falling. From his pockets poured clippings, memos, statistics. Mimicry, humor, and the genius of analogy made The Treatment an almost hypnotic experience and rendered the target stunned and helpless.

LBJ denied this. “I’d have to be some sort of acrobatic genius to carry it off,” he told an interviewer, “and the senator in question, well, he’d have to be pretty weak and pretty meek to be simply standing there like a paralyzed idiot.”

| History

Rubbing Elbows

http://commons.wikimedia.org/wiki/File:Palais_Ferstel.jpg

Vienna’s Café Central was crowded with intellectuals at the turn of the 20th century, including Freud, Lenin, the Vienna Circle of logical positivists, and endless chessplayers.

When Victor Adler made the argument that war would provoke a revolution in Russia, Leopold Berchtold replied, “And who will lead this revolution? Perhaps Mr. Bronstein sitting over there at the Café Central?”

Mr. Bronstein was Leon Trotsky.

| Society

Shape Reference

thomas whales

The index to the fourth edition of George Thomas’ Calculus and Analytic Geometry contains an entry for “Whales” on page 188. That page contains no reference to whales, but it does include the figure above.

http://commons.wikimedia.org/wiki/File:Bessel-Hagen,Erich_1920_G%C3%B6ttingen.jpg?uselang=de

German mathematician Erich Bessel-Hagen was often teased for his protruding ears.

In 1923 his colleague Béla Kerékjártó published a book, Vorlesungen Über Topologie, whose index lists a reference to Bessel-Hagen on page 151.

That page makes no mention of Bessel-Hagen, but it does contain this figure:

2011-03-23-shape-reference-2

Is that libel?

| Science & Math

In a Word

sottisier
n. a list of written stupidities

Unfortunate lines in poetry, collected in D.B. Wyndham Lewis’ The Stuffed Owl, 1930:

  • He suddenly dropt dead of heart-disease. (Tennyson, “Sea-Dreams”)
  • Her smile was silent as the smile on corpses three hours old. (Earl of Lytton, “Love and Sleep”)
  • Irks care the crop-full bird? Frets doubt the maw-crammed beast? (Browning, “Rabbi Ben Ezra”)
  • Then I fling the fisherman’s flaccid corpse / At the feet of the fisherman’s wife. (Alfred Austin, “The Wind Speaks”)
  • With a goad he punched each furious dame. (Chapman, translation of the Iliad)
  • Forgive my transports on a theme like this, / I cannot bear a French metropolis. (Johnson, “London”)
  • So ’tis with Christians, Nature being weak, / While in this world, are liable to leak. (William Balmford, The Seaman’s Spiritual Companion)
  • Now Vengeance has a brood of eggs, / But Patience must be hen. (George Meredith, “Archduchess Anne”)
  • O Sire of Song! Sonata-King! Sublime and loving Master, / The sweetest soul that ever struck an octave in disaster! (Eric Mackay, “Beethoven at the Piano”)
  • The vales were saddened by a common gloom, / When good Jemima perished in her bloom. (Wordsworth, “Epitaph on Mrs. Quillinan”)
  • Such was the sob and the mutual throb / Of the knight embracing Jane. (Thomas Campbell, “The Ritter Bann”)
  • Poor South! Her books get fewer and fewer, / She was never much given to literature. (J. Gordon Coogler)
  • Reach me a Handcerchiff, Another yet, / And yet another, for the last is wett. (Anonymous, A Funeral Elegie Upon the Death of George Sonds, Esq., 1658)
  • Tell me what viands, land or streams produce, / The large, black, female, moulting crab excel? (Grainger, The Sugar-Cane)

In The Razor’s Edge, Larry Darrell says, “The dead look so terribly dead when they’re dead.” Isabel asks, “What do you mean exactly?” He says, “Just that.”

| Language · Literature

Backtalk

Bilingual palindromes, offered by Luc Étienne in Palindromes Bilingues, 1984:

  • Mon Eva rêve ton image, bidet! = Ted, I beg, am I not ever a venom?
  • Untrodden russet! = T’es sûr, Ned dort nu?
  • Sir, I ate merely on it. = Tino, y le remet à Iris.
  • Isadora rêve = Ever a rod as I?
  • Ton minet t’adora = A rod, at ten, I’m not!
  • Crop, editor, not any Bob = Bob, y n’a ton rôti de porc!

I offer you a sentence which does not indeed read backward and forward the same, but reads forward in English and backward in Latin,– making sense, it seems to me, both ways; granting that it is hardly classical Latin.

Anger? ‘t is safe never. Bar it! Use love!

Evoles ut ira breve nefas sit; regna!

Which being freely translated, may mean,

Rise up, in order that your anger may be but a brief madness; control it!

— John Townsend Trowbridge, ed., Our Young Folks, 1866

| Language

Social Studies

From Benoni Lanctot’s Chinese and English Phrase Book (1867), phrases for English-speaking employers of Chinese-Americans:

  • Can you get me a good boy?
  • He wants $8.00 per month.
  • He ought to be satisfied with $6.00.
  • When I find him useful, I will give him more.
  • I think he is very stupid.
  • Do you know how to count?
  • If you want to go out, you must ask me.
  • Come at seven every morning.
  • Go home at eight every night.
  • This lamp is not clean.
  • See that the money is weighed.
  • If there is any thing short, I will make him pay the difference.
  • Take this plate away.
  • Change this napkin.
  • Did you prepare any toast?
  • The tea is too strong.
  • Make me a pigeon pie.
  • Get a bottle of beer.
  • Please carve that capon.
  • Tell the cook to roast it better next time.
  • This wine glass is not clean.
  • The cook is very strange.
  • Sometimes he spoils the dishes.
  • Tell the cook to fry some pancakes.
  • Don’t burn them.
  • He did very bad last time.
  • I want to cut his wages.
  • This tea is very bad.
  • Get out of the way.
  • Don’t speak with me.
  • Who gives you permission?
  • Don’t be lazy.
  • You ought not to do so.
  • Pick this up.
  • This is nothing to you.
  • He is fit for nothing.
  • That belongs to me.
  • Carry it up stairs.
  • You ought to be contented.

Phrases for Chinese speakers:

  • Good morning sir.
  • When shall I begin?
  • I beg your pardon.
  • Lunch is on the table, sir.
  • I beg you to consider again.
  • It is my duty.
  • Sir, what will you have for dinner to-day?
  • You must excuse me.
  • You must not strike me.
| Society

Shop Talk

http://commons.wikimedia.org/wiki/File:Americana_1920_Theodore_Roosevelt.jpg

From a letter from Theodore Roosevelt to his son Kermit, Oct. 2, 1903:

There! You will think this a dreadfully preaching letter! I suppose I have a natural tendency to preach just at present because I am overwhelmed with my work. I enjoy being President, and I like to do the work and have my hand on the lever. But it is very worrying and puzzling, and I have to make up my mind to accept every kind of attack and misrepresentation. It is a great comfort to me to read the life and letters of Abraham Lincoln. I am more and more impressed every day, not only with the man’s wonderful power and sagacity, but with his literally endless patience, and at the same time unflinching resolution.

| History