In 1865, Iowa lithographer W.H. Pratt wrote out the text of the Emancipation Proclamation in carefully varied density to produce this result.
Down Under
How is it with those who imagine that there are antipodes opposite to our footsteps? Do they say anything to the purpose? Or is there any one so senseless as to believe that there are men whose footsteps are higher than their heads? Or that the things which with us are in a recumbent position, with them hang in an inverted direction? That the crops and trees grow downwards? That the rains, and snow, and hail fall upwards to the earth? And does any one wonder that hanging gardens are mentioned among the seven wonders of the world, when philosophers make hanging fields, and seas, and cities, and mountains?
— Lactantius, Institutiones Divinae, 303
Urban Sprawl
“Erotic Temple,” an etching from Giovanni Battista Bracelli’s Oddities of Various Figures, 1624.
From the National Gallery of Art.
Shapes of Things
In 2016, University of Buenos Aires computer science student Gonzalo Ciruelos worked out that the roundest country in the world is Sierra Leone, with a roundness index of 0.934 on a scale of 0 to 1.
He’d been inspired by David Barry, who’d found that the world’s most rectangular country is Egypt (0.955 on the same scale).
Metropolitan France is known as the Hexagon. I suppose each country has its claim to fame.
(Gonzalo Ciruelos, “What Is the Roundest Country?”, Math Horizons 26:3 [February 2019], 26-27.)
Unquote
“I see men ordinarily more eager to discover a reason for things than to find out whether the things are so.” — Montaigne
Stained Glass
From Lee Sallows:
(Thanks, Lee!)
The Art of Living
When I am going out for an evening I arrange the fire in my stove so that I do not fail to find a good one when I return, though it would have engaged my frequent attention present. So that, when I know I am to be at home, I sometimes make believe that I may go out, to save trouble. And this is the art of living, too, — to leave our life in a condition to go alone, and not to require a constant supervision. We will then sit down serenely to live, as by the side of a stove.
— Thoreau, Journal, Feb. 20, 1841
In a Word
anfractuous
adj. having many windings and turnings
loof
n. the palm of the hand
penetralia
n. the innermost recesses of a building
swither
n. a state of perplexity
It’s commonly said that you can defeat a hedge maze by placing one hand on a wall and carefully maintaining that contact as you advance. If the hedges are all connected, this method will reliably lead you to the center of the maze (and, indeed, to every other part of it before you return to the entrance).
The Chevening maze, in Kent, was designed deliberately to thwart this technique. Its center is concealed in an “island” of hedges distinct from the outer wall, so following either a left- or a right-hand rule will return you to the entrance without ever passing the goal.
Tops
At the time of its completion under Hadrian, the Pantheon in Rome had the world’s largest unreinforced concrete dome.
It still does. It’s held that record for nearly 2,000 years.
The Erdős–Faber–Lovász Conjecture
This figure contains four “cliques” of four points each, with each of the four points in each clique connected to each of the others, and each pair of cliques intersecting at a single point. Four colors suffice to color all the points so that no two linked points share a color.
Is this always possible? If k cliques, each containing k points, are arranged in similar fashion, can the result always be colored properly with k colors? In 2021, half a century after Paul Erdős first posed the question, Dong Yeap Kang and his colleagues proved that, for sufficiently large k, the conjecture is true.