Mnemonic

This French alexandrine encodes π to 126 decimal places:

Que j’aime à faire apprendre un nombre utile aux sages!
Immortel Archimède, artiste ingénieur,
Qui de ton jugement peut priser la valeur?
Pour moi, ton problème eut de pareils avantages.
Jadis, mystérieux, un problème bloquait
Tout l’admirable procédé, l’œuvre grandiose
Que Pythagore découvrit aux anciens Grecs.
Ô quadrature! vieux tourment du philosophe!
Insoluble rondeur, trop longtemps vous avez
Défié Pythagore et ses imitateurs.
Comment intégrer l’espace plan circulaire?
Former un triangle auquel il équivaudra?
Nouvelle invention: Archimède inscrira
Dedans un hexagone; appréciera son aire,
Fonction du rayon. Pas trop ne s’y tiendra:
Dédoublera chaque élément antérieur;
Toujours de l’orbe calculée approchera;
Définira limite; enfin, l’arc, le limiteur
De cet inquiétant cercle, ennemi trop rebelle!
Professeur, enseignez son problème avec zèle!

Translation:

How I like to teach this number useful to the wise.
Immortal Archimedes, artist, engineer,
In your opinion who could estimate its value?
For me, your problem had equal advantages.
Long ago, mysterious, a problem blocked
All the honorable process, the great work
That Pythagoras revealed to the Ancient Greeks.
Oh quadrature! Old philosopher’s torment
Unsolvable roundness, for too long you have
Defied Pythagoras and his imitators.
How to integrate the plain circular space?
Form a triangle to which it is equivalent?
New invention: Archimedes will inscribe
Inside a hexagon; will appreciate its area
Function of a ray. Not too much to hold onto there:
Will split each previous element;
Always the calculated orb will approach
Will define the limit; finally, the arc, the limiter
Of this disturbing circle, an enemy too rebellious
Teacher, teach its problem with zeal.

I don’t know who came up with it — Alfred Posamentier traces it as far back as the Nouvelle Correspondence Mathematique of Brussels, 1879.

May 23, 2018May 23, 2018 | Poems · Science & Math

The Empty Set

Mathematician John Rainwater has published 10 research papers in functional analysis, notably in the geometric theory of Banach spaces and in convex functions. The University of Washington has named a regular seminar after him, and Rainwater’s Theorem is an important result in summability theory.

This is most impressive because he doesn’t exist. In 1952 UW grad student Nick Massey received a blank registration card by mistake, and he invented a fictional student, naming him John Rainwater because it was raining at the time. “Rainwater” was adopted by the other students and began to submit solutions to problems posed in the American Mathematical Monthly, and he’s gone on to a 60-year (so far) career of considerable distinction — his top paper has 19 citations.

Asked why he’d published that paper under Rainwater’s name, John Isbell quoted Friedrich Schiller: “Man is only fully human when he plays.”

May 17, 2018 | Oddities · Science & Math

Sure Enough

sallows 16 square

From Lee Sallows, “A novel geometric proof that 16 is a square number.” :)

(Thanks, Lee!)

May 17, 2018May 16, 2018 | Language · Science & Math

Microbial Art

https://commons.wikimedia.org/wiki/File:FPbeachTsien.jpg — Image: Wikimedia Commons

Biochemist Roger Tsien won the 2008 Nobel prize in chemistry for his contributions to knowledge of green fluorescent protein, a complex of amino acid residues that glow vividly when exposed to ultraviolet light.

Inspired, Nathan Shaner, a researcher in Tsien’s lab, painted this San Diego beach scene using an eight-color palette of bacterial colonies expressing fluorescent proteins.

Alexander Fleming was drawing “germ paintings” in the 1930s.

May 16, 2018 | Art · Science & Math

Skyward

When Gabe McCubbins’ daughter needed a project for her seventh grade science fair, they decided to mount a GoPro video camera in a bowling ball and fire it out of a cannon.

Launch starts at 1:50.

May 16, 2018May 15, 2018 | Science & Math

A One and a Two

https://commons.wikimedia.org/wiki/File:Lion_Kings_(2743998524).jpg — Image: Wikimedia Commons

In 2013, Georgia Institute of Technology mechanical engineer David Hu and his colleagues discovered a “law of urination”: All mammals weighing more than 1 kilogram empty their full bladders in about 21 seconds (standard deviation 13 seconds).

Last year Hu followed that up with a law of defecation: Despite a rectum length varying from 4 to 40 centimeters, mammals from cats to elephants defecate within a nearly constant duration of 12 ± 7 seconds. A layer of mucus helps feces slide through the large intestine; larger animals have more feces but also thicker layers of mucus, which aids their ejection.

From the journal Soft Matter, whose cover artist deserves some kind of award.

(David L. Hu et al., “Hydrodynamics of Defecation,” Soft Matter 13:29 [August 2017], 4960-4970.) (Thanks, Colin.)

May 15, 2018 | Science & Math

Troxler’s Fading

Stare at the cross from a short distance away without moving your eyes. After a few seconds, the colors will fade away.

The effect was discovered by Swiss physician Ignaz Paul Vital Troxler in 1804. The reasons for it aren’t clear — possibly neurons in the visual system adapt to unchanging stimuli and they drop out of our awareness.

May 11, 2018May 10, 2018 | Oddities · Science & Math

Two by Two

In poker, suppose you’re dealt a pair. Is the probability that your opponent also holds a pair higher, lower, or the same as it would be if you held nothing?

	Select Click for Answer
It’s higher. If you’re holding a pair then you’ve left more pair combinations in the remaining deck than if you were holding a non-pair. A simple way to see this is to consider a deck of only 8 cards, four 2s and four 3s. If we remove a 2 and a 3, the remaining deck of 6 cards contains three pair combinations of 2s and three pair combinations of 3s, for a total of 6. But if we remove a pair of 2s, the remaining deck contains 7 pair combinations, one pair combination of 2s and six pair combinations of 3s. Here’s a more rigorous analysis of the effect in a real game — it’s small, but it’s there. (Thanks, John.)

Click for Answer

May 10, 2018May 9, 2018 | Puzzles · Science & Math

Robinson Tiles

Berkeley mathematician Raphael Robinson discovered this remarkable set of aperiodic tiles in 1978. The six shapes will neatly tile a plane, as shown below, and though the pattern cannot be regular, it reliably produces a hierarchical design: Each small orange square sits at the corner of a larger orange square, which sits at the corner of a still larger one, and so on ad infinitum. This is because subgroups of tiles form “supertiles” with similar properties — see here.