This remarkable phenomenon was discovered by Cambridge mathematician James Grime. Number five six-sided dice as follows:

A: 2, 2, 2, 7, 7, 7
B: 1, 1, 6, 6, 6, 6
C: 0, 5, 5, 5, 5, 5
D: 4, 4, 4, 4, 4, 9
E: 3, 3, 3, 3, 8, 8

Now, on average:

A beats B beats C beats D beats E beats A

and

A beats C beats E beats B beats D beats A.

Interestingly, though, if each die is rolled twice rather than once, then the first of the two chains above remains unchanged except that D now beats C — and the second chain is reversed:

A beats D beats B beats E beats C beats A.

As a result, if each of two opponents chooses one of the five dice, a third opponent can always find a remaining die that beats them both (so long as he’s allowed to choose whether the dice will be rolled once or twice).

(Ward Heilman and Nicholas Pasciuto, “What Nontransitive Dice Exist Among Us?,” Math Horizons 24:4 [April 2017], 14-17.)

From Pi Mu Epsilon Journal, November 1950:

(1/2)³ < (1/2)².

Taking the logarithm to the base 1/2 of each member of the above inequality, we write

3 log_1/2(1/2) < 2 log_1/2(1/2).

But log_bb = 1. Therefore

3 < 2.

In his 1985 commonplace book Michelangelo’s Snowman, George Herrick gives a notable mnemonic for the bones of the wrist:

Some Lovers Try Positions That They Can’t Handle

(scaphoid, lunate, triquetrum, pisiform, trapezium, trapezoid, capitate, hamate)

Two more, from the r/Anatomy subreddit:

According to Frank M. Chapman’s Color Key to North American Birds (1912), the hooded warbler sings You must come to the woods, or you won’t see me.

Ohm’s law states that V = IR, where V is the voltage measured across a conductor, I is the current through the conductor, and R is the conductor’s resistance. In the image mnemonic at left (easily remembered by the word “viral”), covering any of the unknowns gives the formula in terms of the remaining parameters: V = IR, I = V/R, R = V/I.

Wikimedia user CMG Lee has devised other mnemonics in the same style for high-school physics students (right). For example, F = ma, m = F/a, a = F/m. In the corresponding SVG file you can hover over a symbol to see its meaning and formula.

Have the love and fear of God ever before thine eyes; God confirm your faith in Christ and that you may live accordingly, Je vous recommende a Dieu. If you meet with any pretty insects of any kind keep them in a box.

— Sir Thomas Browne, letter to his son, 1661

If you’re driving on the highway and pass a car traveling in the opposite direction, the frequency of its engine noise seems to drop. In 1980, Liverpool Polytechnic mathematician J.M.H. Peters realized that this pitch drop might be used to estimate the speed of the passing vehicle. Pleasingly, he discovered that each semitone in the interval corresponds to 21 miles per hour (to within 2 percent). If the other car’s engine seems to descend a whole tone in pitch as it passes you, then it’s traveling at approximately 43 mph; if it drops a minor third then it’s traveling at 64 mph; and so on.

“The reader should practise by humming a given note pianissimo increasing gradually to fortissimo at which point the hum is lowered by a chosen interval, … diminishing again to pianissimo, this being meant to imitate the effect of being suddenly passed on a quiet country lane by a fast moving high powered motor vehicle.”

(J.M.H. Peters, “64.8 Estimating the Speed of a Passing Vehicle,” Mathematical Gazette 64:428 [June 1980], 122-124.)

03/03/2025 UPDATE: My mistake — the observer is stationary, not moving. Thanks to readers Seth Cohen and Jon Jerome for pointing this out. The cited paper is behind a paywall, but the Physics Stack Exchange had a discussion on the same topic in 2017.