Yale statistician Frank Anscombe devised this demonstration in 1973. Here are four datasets, each with 11 (x,y) points:

I		II		III		IV
x	y	x	y	x	y	x	y
10.0	8.04	10.0	9.14	10.0	7.46	8.0	6.58
8.0	6.95	8.0	8.14	8.0	6.77	8.0	5.76
13.0	7.58	13.0	8.74	13.0	12.74	8.0	7.71
9.0	8.81	9.0	8.77	9.0	7.11	8.0	8.84
11.0	8.33	11.0	9.26	11.0	7.81	8.0	8.47
14.0	9.96	14.0	8.10	14.0	8.84	8.0	7.04
6.0	7.24	6.0	6.13	6.0	6.08	8.0	5.25
4.0	4.26	4.0	3.10	4.0	5.39	19.0	12.50
12.0	10.84	12.0	9.13	12.0	8.15	8.0	5.56
7.0	4.82	7.0	7.26	7.0	6.42	8.0	7.91
5.0	5.68	5.0	4.74	5.0	5.73	8.0	6.89

Each set produces the same summary statistics (mean, standard deviation, and correlation). But their graphs are strikingly different:

The lesson, Anscombe said, is to “make both calculations and graphs. Both sorts of output should be studied; each will contribute to understanding.”

Justin Matejka and George Fitzmaurice created a similar collection in 2017: the Datasaurus Dozen.

(Thanks, Rick.)

09/05/2021 UPDATE: Here’s an animation of the Datasaurus Dozen. (Thanks, Eric.)

Certainly rectangular cuboids exist whose edges and face diagonals all have integer lengths.

For example, in 1719 Paul Halcke discovered one with edges (a, b, c) = (44, 117, 240) and face diagonals (d, e, f ) = (125, 244, 267).

But does one exist whose space diagonal (here shown in red) also has integer length?

As of last September, none has been found and no one has proven that none exist.

When a tornado struck Mayfield, Ohio, in 1842, Western Reserve College mathematician Elias Loomis noticed that several fowl had been picked almost clean of their feathers. To find out what wind velocity could accomplish this, he charged a cannon with 5 ounces of gunpowder and inserted a freshly killed chicken in place of a ball:

As the gun was small, it was necessary to press down the chicken with considerable force, by which means it was probably somewhat bruised. The gun was pointed vertically upwards and fired; the feathers rose twenty or thirty feet, and were scattered by the wind. On examination they were found to be pulled out clean, the skin seldom adhering to them. The body was torn into small fragments, only a part of which could be found. The velocity is computed at five hundred feet per second, or three hundred and forty one miles per hour. A fowl, then, forced through the air with this velocity, is torn entirely to pieces; with a less velocity, it is probable most of the feathers might be pulled out without mutilating the body.

“If I could have the use of a suitable gun I would determine this velocity by experiment,” he ended. “It is presumed to be not far from a hundred miles per hour.”

(Elias Loomis, “On a Tornado Which Passed Over Mayfield, Ohio, February 4th, 1842,” American Journal of Science 43:2 [July-September 1842], 278-301.)

Famously, in a group of 23 randomly chosen people, the chance is slightly higher than 50 percent that two will share a birthday.

In 2014, James Fletcher considered the birth dates of players in the World Cup, who were conveniently organized into squads of 23 people each. He found that 16 of the 32 squads had at least one shared birthday. If data from 2010 World Cup was included, 31 of 64 squads had shared birthdays, still quite close to 50 percent.

If a group numbers 366 people, the probability of a shared birthday is 100 percent (neglecting leap years). But to reach 99 percent certainty we need only 55 people. “It is almost unbelievable that such a small difference between the probabilities 99% and 100% can lead to such a big difference between the numbers of people,” writes Gabor Szekely in Paradoxes in Probability Theory and Mathematical Statistics (1986). “This paradoxical phenomenon is one of the main reasons why probability theory is so wide-ranging in its application.”

Discovered by Princeton mathematician John Horton Conway: If the sides meeting at each vertex of a triangle are extended by the length of the opposite side, as shown, the six resulting endpoints will lie on a circle — and that circle is concentric with a circle inscribed in the triangle.

Also, pleasingly, Wikipedia has a list of things named after John Horton Conway.

In Mathematics in Fun and in Earnest (2006), Nathan Altshiller-Court describes an ancient method of finger arithmetic to compute the product of two numbers in the range 6-10. Each number is assigned to a finger (on both hands):

6: little finger
7: ring finger
8: middle finger
9: index finger
10: thumb

Now, to multiply 7 by 9, hold your hands before you with the thumbs up and touch the ring finger of one hand to the index finger of the other. These two fingers and all the others physically below them number six and count for 60 toward the final result. Above the joined fingers are three fingers on one hand and one on the other — multiply those two values, add the result (3) to the existing 60, and you get the final answer: 7 × 9 = (6 × 10) + (3 × 1) = 63.

“Besides its arithmetical uses, this clever trick may also serve, with telling effect, to enhance the prestige of an ambitious grandfather in the eyes of a bright fourth-grade grandson,” Altshiller-Court observes. “Competent observers report that it is still resorted to by the Wallachian peasants of southern Rumania.”

The unassuming Japanese perennial Paris japonica may have the largest genome of any living organism.

With 150 billion base pairs, the DNA from a single cell stretched out end to end would cover more than 300 feet.

These compounds are named housane, churchane, basketane, and penguinone.

Below: To celebrate the 2012 London Olympics, chemists Graham Richards and Antony Williams offered a molecule of five rings. They called it olympicene.