Is it possible to divide a circle into n parts of equal area using only a straightedge and compasses?
Author: Greg Ross
Counter Play 2
Lee Sallows sent this clever puzzle, a followup to one we presented in 2010:
In the square shown above, any 3 counters in a straight line sum to 15.
Puzzle: Reposition the counters (again, one to each cell) to produce a new square again showing eight collinear triplets summing to 15, but with 1 now placed in a corner square.
Extempore
We never did stop ad libbing. No two performances were ever quite the same. One matinee, during the second month in New York, I cooked up a little surprise for Groucho. During one of his quieter scenes, while I was offstage, I selected a blond cutie from the chorus, and asked her if she’d like a bigger part in the show. She was willing and eager. I told her all she had to do was run screaming across the stage. She did, and I tore after her in full pursuit, leaping and bounding and honking my horn. It broke up Groucho’s scene, but when the laughs subsided, Groucho was ready to top it. ‘First time I ever saw a taxi hail a passenger,’ he said.
— Harpo Marx, Harpo Speaks!, 1961
The Perpetual Diamond
This is bewildering: This diamond isn’t moving, and its luminance and texture are unchanging. Yet when it’s surrounded with very thin edge strips whose luminance changes with respect to the background, the whole diamond seems to move. Using the controls at the bottom, you can even direct the illusion to send the diamond drifting “up,” “down,” “left,” or “right.” But it ain’t moving.
See the paper below for details.
(Oliver J. Flynn and Arthur G. Shapiro, “The Perpetual Diamond: Contrast Reversals Along Thin Edges Create the Appearance of Motion in Objects,” i-Perception 9:6 [2018], 2041669518815708.)
Black and White
A densely imaginative little problem by Joseph C.J. Wainwright. White to mate in two moves.
Light and Shadow
Building Blocks, by Kumi Yamashita. “I sculpt using both light and shadow. I construct single or multiple objects and place them in relation to a single light source. The complete artwork is therefore comprised of both the material (the solid objects) and the immaterial (the light or shadow).”
A Catalog of Clever Expedients
Henry T. Brown’s 1868 mechanical encyclopedia Five Hundred and Seven Mechanical Movements is being animated on this fascinating site — see working demonstrations of hundreds of mechanical linkages from the age of steam.
Note that it’s a work in progress — the movements that have been animated are indicated with colored thumbnails. Owner Matt Keveney plans eventually to animate all 507 movements in Brown’s original text.
(Thanks, Sharon.)
Unquote
“Consistency is the last refuge of the unimaginative.” — Oscar Wilde
“Consistency requires you to be as ignorant today as you were a year ago.” — Bernard Berenson
“Convictions are variable; to be always consistent is to be sometimes dishonest.” — Ambrose Bierce
Podcast Episode 251: Joseph Palmer’s Beard
In 1830 Joseph Palmer created an odd controversy in Fitchburg, Massachusetts: He wore a beard when beards were out of fashion. For this social sin he was shunned, attacked, and ultimately jailed. In this week’s episode of the Futility Closet podcast we’ll tell the story of a bizarre battle against irrational prejudice.
We’ll also see whether a computer can understand knitting and puzzle over an unrewarded long jump.
Misc
- At the equinox, the sun rises due east at every latitude.
- UPPER TYPEWRITER ROW is typed on the upper row of a typewriter.
- 32785 = 3 + 2 × 7 + 85
- In the Mbabaram Aboriginal language of north Queensland, dog means dog.
- The London Times has published no obituary for Sherlock Holmes. Therefore he exists.
(Thanks, Sanford.)