In a family of convex sets in the Euclidean plane, if the intersection of each triple is non-empty, then the intersection of the whole collection is non-empty.
Discovered by Austrian mathematician Eduard Helly in 1913.
The Great Raft
For more than half a millennium, between the 12th century and the 19th, an enormous log jam clogged the Red River in the Southern United States. By the early 1830s, it stretched more than 160 miles, with new logs and vegetation accreting at its upper end while older material decayed and washed out at the lower.
By the start of the 19th century the mass was blocking settlement in the area west of Shreveport, so the U.S. Army Corps of Engineers hired steamboat entrepreneur Henry Miller Shreve, who spent nine years clearing a navigable path using specially designed “snag boats.”
A grateful public named the city of Shreveport after him, but a second raft soon began to form upstream, extending eventually as far as the Arkansas state line. That would have to be removed as well.
(Thanks, Kevin.)
Math Notes
s = 1 + 2 + 4 + 8 + 16 + ... = 1 + 2(1 + 2 + 4 + 8 + ...) = 1 + 2s, so -1 = 1 + 2 + 4 + 8 + 16 + ...
(Regular summation gives a sum of infinity, but the idea above does make a certain sense.)
(Thanks, Murtadha.)
Impromptu
If the man who turnips cries
Cry not when hs father dies,
‘Tis a proof that he had rather
Have a turnip than his father.
— Samuel Johnson
R.I.P.
This stone, behind St. Peter’s Church in Heysham, Lancashire, commemorates the lives of James Jones and his two wives, Sarah and Sadie.
Which of them earned this epithet, and how, is not clear.
(Thanks, Dave.)
Piecework
Austrian artist Thomas Medicus’ 2014 anamorphic sculpture Emulsifier arranges 160 hand-painted glass strips to present each of four different images, depending on the viewer’s perspective.
Head Instructor, below, uses the same technique. More at his website.
Inspiration
Anna Rabinowitz’s 80-page poem Darkling is an acrostic of Thomas Hardy’s 1900 poem “The Darkling Thrush” — taking the first letter of each line in Rabinowitz’s poem spells out Hardy’s.
“I found myself … haunted by ‘The Darkling Thrush,'” she said, “by its tone of millennial mourning, by its note of hope in the thrush’s song, and most especially by its opening line which situates the poet at he meditates on the passing century: ‘I leant upon a coppice gate.'”
“Fifth Philosopher’s Song”
A million million spermatozoa,
All of them alive;
Out of their cataclysm but one poor Noah
Dare hope to survive.
And among that billion minus one
Might have chanced to be
Shakespeare, another Newton, a new Donne —
But the One was Me.
Shame to have ousted your betters thus,
Taking ark while the others remained outside!
Better for all of us, froward Homunculus,
If you’d quietly died!
— Aldous Huxley
Hand Holding
From an old copy of Games magazine:
Four players describe the cards they held in their last game of five-card poker:
Harry: “I had the two, nine, and jack of hearts, and the two and nine of diamonds.”
Edna: “I held four fives and the queen of spades.”
Dave: “I had a black straight flush.”
Frankie: “I held a club flush.”
Georgiana: “I had a straight. Two of my cards were spades; the others weren’t.”
Cleo: “I just had one lousy pair.” (to Frankie:) “But my lowest-ranking card was higher than any of yours.”
An onlooker asks how many of the undealt cards were black, and Dave answers, “No more than three.” What were the contents of Dave’s, Frankie’s, Georgiana’s, and Cleo’s hands?
Jumping Kangaroos
A puzzle by National Security Agency mathematician David B., from the agency’s October 2017 Puzzle Periodical:
Joey, the baby kangaroo has been kidnapped and placed at 2100 on a number line.
His mother, Kandice the Kangaroo, is at 0 on the number line, and will try to save him. Kandice normally jumps forward 6 units at a time. Guards have been placed at n3 on the number line, for every integer n≥1. If Kandice lands on a number with a guard on it, she will be caught and her mission will fail. Otherwise, she will safely sneak past the guard. Whenever she successfully sneaks past a guard, she gets an adrenaline rush that causes her next jump (the first jump after passing the guard) to take her 1 unit farther than it normally would (7 units instead of 6). (After a single 7-unit jump, she resumes jumping 6 units at a time, until the next time she sneaks past a guard.)
Will Kandice the Kangaroo reach (or pass) her son Joey safely?
