Down Under

https://commons.wikimedia.org/wiki/File:La_rotondit%C3%A9_de_la_Terre,_Image_du_monde_(cropped).jpg

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

| History · Science & Math

Shapes of Things

https://commons.wikimedia.org/wiki/File:Sierra_Leone-Mappa.gif

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.)

| Science & Math · Trivia

In a Word

https://www.pinterest.com/pin/the-chevening-maze-in-kent-is-the-first-multiplyconnected-puzzle-maze-this-means-it-cannot-be-solved-by-the-put-your-left-hand--48624870947902374/

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.

| Puzzles · Science & Math

The Erdős–Faber–Lovász Conjecture

https://commons.wikimedia.org/wiki/File:Erd%C5%91s%E2%80%93Faber%E2%80%93Lov%C3%A1sz_conjecture.svg

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.

| Science & Math

Swivel Engineering

The Wallace–Bolyai–Gerwien theorem, first proven in 1807, states that any two polygons of equal area must have a common dissection. That is, there’s always a way to cut up the first one and assemble the pieces to form the second.

But what if the pieces must be connected by hinges? In his “haberdasher” puzzle of 1907, Henry Dudeney showed that it’s possible to convert a triangle into a square by cutting it in pieces and turning it “inside out”:

https://commons.wikimedia.org/wiki/File:Hinged_haberdasher_square.svg
Image: Wikimedia Commons

Is it always possible to arrange such a “hinged dissection” between two polygons of equal area? The question remained open until 2007, when Erik Demaine showed that the answer is yes — and provided an algorithm to find it.

02/25/2026 UPDATE: Reader Simon Schneider directed me to this interactive visualization of the Wallace–Bolyai–Gerwien theorem, which lets you draw two polygons and then converts one to the other before your eyes. It’s hypnotizing. Here’s a paper on the dissection algorithm used. (Thanks, Simon.)

| Science & Math

Sibling Rivalry

https://commons.wikimedia.org/wiki/File:Mark_and_Scott_Kelly_at_the_Johnson_Space_Center,_Houston_Texas.jpg

The peculiar circumstances of life aboard the International Space Station both advanced and retarded astronaut Scott Kelly’s age relative to that of his identical twin brother Mark, who remained on the ground.

Radiation, weightlessness, and changes in diet shortened Scott’s telomeres more quickly than his brother’s, effectively causing him to age more quickly.

At the same time, due to relativistic effects, Scott aged about 8.6 milliseconds less than Mark during his year in space.

| Oddities · Science & Math

Set Piece

https://reference-global.com/article/10.2478/rmm-2025-0010
Image: Recreational Mathematics Magazine

The numbers 1-7 are disposed among the regions in this figure such that each of the circular sets yields the same sum. This makes it a “magic Venn diagram,” a concept that occurred to mathematician David Robinson while teaching a course in mathematical logic at the University of West Georgia. His article appears in the December 2025 issue of Recreational Mathematics Magazine.

(David Robinson and Anja Remshagen, “Magic Venn Diagrams,” Recreational Mathematics Magazine 12:21 [December 2025], 25-44.)

| Science & Math

Toil and Trouble

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

We tend to think that mirrors reverse left to right, but in fact they reverse “back to front,” along an axis perpendicular to the mirror’s surface. Our confusion arises when we misinterpret this.

“[I]magine a back-front reversal of yourself, with your nose, face, eyes, and so forth pushed through to the back of the head, and your back somehow oozed through to the front,” writes University of Auckland psychologist Michael C. Corballis. “You might then ‘feel’ your watch as having remained on the left wrist (say), while back and front have reversed. However it is likely that you will also experience a strong compulsion to recalibrate your internal axes, and then feel the watch to be on the right wrist. In short, a back-front reversal is reinterpreted as a left-right reversal.”

(Michael C. Corballis, “Much Ado About Mirrors,” Psychonomic Bulletin & Review 7:1 [2000], 163-169. More mirror puzzles.)

| Science & Math