“The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.” — Aristotle
Science & Math
A Mathematical Palindrome
111111111 x 111111111 = 12345678987654321
The Bridges of Konigsberg
In old Konigsberg there were seven bridges:
Villagers used to wonder: Is it possible to leave your door, walk through the town, and return home having crossed each bridge exactly once?
Swiss mathematician Leonhard Euler had to invent graph theory to answer the question rigorously, but there’s a fairly intuitive informal proof. Can you find it?
Great Red Spot
Jupiter’s Great Red Spot is one continous cyclone that has lasted at least 340 years.
It’s more than twice the size of Earth.
A Tennessee Parthenon
Nashville’s Centennial Park contains a full-scale replica of the Parthenon.
Like the original in Athens, it’s “more perfect than perfect”: To counter optical effects, the columns swell slightly as they rise, and the platform on which they stand curves slightly upward. So the temple looks even more symmetrical than it actually is.
Cadaeic Cadenza
Opening excerpt from “Cadaeic Cadenza,” a short story written in 1996 by Mike Keith:
One
A Poem: A Raven
Midnights so dreary, tired and weary,
Silently pondering volumes extolling all by-now obsolete lore.
During my rather long nap — the weirdest tap!
An ominous vibrating sound disturbing my chamber’s antedoor.
“This,” I whispered quietly, “I ignore.” …
If you write out the number of letters in each word, they form the first 3,834 digits of pi.
The Weather Outside Is Frightful …
What are these?
They’re snow crystals, magnified by a scanning electron microscope.
The Stars Align
It’s only a happy accident that our moon “fits” over the sun’s disc during a solar eclipse. The sun is 400 times the diameter of the moon, but it’s nearly 400 times farther from Earth, so to us the two have almost exactly the same angular size.
Nazca From Space
Most people are familiar with the drawings in Peru’s Nazca Desert:
It’s thought they were created by local peoples between 200 B.C. and 600 A.D. They’re remarkably well realized, considering that the builders probably couldn’t have viewed them from the air. Here’s a view from a satellite:
It’s easy to decide that they’re the work of visiting extraterrestrials — the airliners that first spotted them in the 1920s described them as “primitive landing strips” — but researcher Joe Nickell has shown that a small team of people can reproduce a drawing in 48 hours, without aerial supervision, using Nazcan technology. Still, well done.
(Top image: Wikimedia Commons)
D’Agapeyeff Cipher
Alexander d’Agapeyeff included this “challenge cipher” in Codes and Ciphers (1939), his introductory textbook in cryptography:
75628 28591 62916 48164 91748 58464 74748 28483 81638 18174
74826 26475 83828 49175 74658 37575 75936 36565 81638 17585
75756 46282 92857 46382 75748 38165 81848 56485 64858 56382
72628 36281 81728 16463 75828 16483 63828 58163 63630 47481
91918 46385 84656 48565 62946 26285 91859 17491 72756 46575
71658 36264 74818 28462 82649 18193 65626 48484 91838 57491
81657 27483 83858 28364 62726 26562 83759 27263 82827 27283
82858 47582 81837 28462 82837 58164 75748 58162 92000
No one could solve it, and he later admitted he’d forgotten how he’d encrypted it.
It remains unsolved to this day.