Venn Primes

https://commons.wikimedia.org/wiki/File:Symmetrical_5-set_Venn_diagram.svg
Image: Wikimedia Commons

The classic three-circle Venn diagram on the left has threefold rotational symmetry, and the more complex five-ellipse diagram on the right (discovered by Branko Grünbaum in 1975) has fivefold symmetry. Pleasingly, it turns out that a Venn diagram with n curves having an n-fold rotational symmetry exists if and only if n is prime.

(The diagram below has four curves and fourfold symmetry, but properly speaking it’s not a Venn diagram because it doesn’t represent all possible intersections of the sets.)

(Stan Wagon and Peter Webb, “Venn Symmetry and Prime Numbers: A Seductive Proof Revisited,” American Mathematical Monthly 115:7 [2008], 645-648; Frank Ruskey, Carla D. Savage, and Stan Wagon, “The Search for Simple Symmetric Venn Diagrams,” Notices of the AMS 53:11 [2006], 1304-1311.)

https://www.template.net/design-templates/print/4-circle-venn-diagram/

| Science & Math

“It Is Not Enough to Mean Well”

Maxims of Theodore Roosevelt:

  • A bad man of ability is worse than a bad man of no ability.
  • It is almost as irritating to be patronized as to be wronged.
  • Timid endurance of wrongdoing may often be to commit one of the greatest evils that one can possibly commit against one’s fellows.
  • The lives of truest heroism are those in which there are no great deeds to look back upon. It is the little things well done that go to make up a successful and truly good life.
  • Our system of government is the best in the world for a people able to carry it on. Only the highest type of people can carry it on.
  • No one ought to submit to being imposed upon, but before you act always stop to consider the rights of others before standing up for your own.
  • The wicked who prosper are never a pleasant sight.
  • It is hard to fail; but it is worse never to have tried to succeed.
  • Don’t let practical politics mean foul politics.
  • For almost every gain there is a penalty.
  • There is grave danger in attempting to establish invariable rules.
  • Woe to all of us if ever as a people we grow to condone evil because it is successful.
  • Remember that the shots that count in war are the ones that hit.
  • What every man needs is robust virtue, that will enable him to go out into the world and remain true to himself.
  • Capacity for work is absolutely necessary, and no man can be said to live in the true sense of the word if he does not work.
  • In doing your work in the great world, it is a safe plan to follow a rule I once heard preached on the football field: Don’t flinch; don’t fall; hit the the line hard.

(More here.)

| Quotations

A Fitting Mascot

https://commons.wikimedia.org/wiki/File:Peter_the_eagle.jpg
Image: Wikimedia Commons

This is almost comically American: Between 1830 and 1836, a bald eagle lived at the Philadelphia Mint. Named Peter, he would roam the city by day and roost in the mint at night. Fatally injured in a coining press, he was stuffed and mounted and is currently on display in the lobby.

He is said (uncertainly) to have been the model for the eagle on U.S. silver dollars issued between 1836 and 1839 and the Flying Eagle cents of 1856-1858.

| History · Oddities

Podcast Episode 285: The Grasshopper Plagues

https://commons.wikimedia.org/wiki/File:Melanoplus_spretusAnnReportAgExpStaUM1902B.jpg

In the 1870s, new farmsteads on the American plains were beset by enormous swarms of grasshoppers sweeping eastward from the Rocky Mountains. The insects were a disaster for vulnerable farmers, attacking in enormous numbers and devouring everything before them. In this week’s episode of the Futility Closet podcast we’ll describe the grasshopper plagues and the settlers’ struggles against them.

We’ll also delve into urban legends and puzzle over some vanishing children.

See full show notes …

| History · Podcast

“A Remarkable Dream”

On Saturday morning a man about 30 years of age, named Benjamin Collins, was found drowned in a small dam belonging to the Whitehall pit, at Wyke. When found he was kneeling in the water with his head down, being only up to the shoulders in the water. He had been drinking for several days, and became restless. He got up about 2 o’clock in the morning, partly dressed himself, and said he could not sleep. Soon afterwards he went out, and about 4 o’clock his uncle, Mr. Mark Collins, of Lower Car Close farm, went in search of him in the barn and stables, but not finding him there returned to the house. Mrs. Collins then desired her husband to go to the place where the body was found, as she had just dreamt her nephew was drowned there. Mr. Collins acted as his wife requested, and, to his amazement and horror, saw the literal fulfillment of her dream.

— York Herald, quoted in The Law Times, Dec. 17, 1864

| Oddities

Wooden Words

https://www.katieholten.com/public-realm/#/new-york-city-tree-alphabet/

Artist Katie Holten has created a New York City Tree Alphabet, a Latin alphabet in which each letter is assigned a drawing of an existing city tree or one that will be planted as a result of the changing climate. There’s a free font that you can play with here and download here.

Holten had planned to plant messages around the city using real trees last spring, and invited people to make suggestions, though I don’t know which were ultimately chosen. “Right now, we’re leaving it completely wide open, so we’ve no idea what messages we’ll be planting,” she told Fast Company in March. “I’m excited to see what people send us. People have been suggesting words like ‘Dream,’ ‘Hope,’ and ‘Peace.’ But we’re also receiving longer messages, love letters, poems, and short stories. We’re curious to see how we could translate a long text into a grove of planted trees. It’s an exciting challenge and we can make up the rules as we go along, so anything could happen.”

(Via MetaFilter.)

| Art · Language