If you’re sharing a pizza with another person, there’s no need to cut it into precisely equal slices. Make four cuts at equal angles through an arbitrary point and take alternate slices, and you’ll both get the same amount of pizza.
Larry Carter and Stan Wagon came up with this “proof without words”: Each piece in an odd-numbered sector corresponds to a congruent piece in an even-numbered sector, and vice versa.
Also: If a pizza has thickness a and radius z, then its volume is pi zza.
(Larry Carter and Stan Wagon, “Proof Without Words: Fair Allocation of a Pizza,” Mathematics Magazine 67:4 [October 1994], 267-267.)
Sculptor Anna Coleman Ladd found an unusual application for her artistry during World War I, creating prostheses for the dramatic injuries produced by machine guns and heavy artillery. After reading about artist Francis Derwent Wood’s “Tin Noses Shop” in London, she moved to London and opened a “Studio for Portrait-Masks.”
Her copper and silver masks, 1/32″ thick and weighing 4-9 ounces, were founded on facial casts and painted to match the precise skin tone of each patient. Held in place by eyeglasses, many included realistic mustaches, eyebrows, and eyelashes. By the end of 1919 Ladd had created 185 of them, charging $18 for each and donating her own services. The Red Cross called them “miracles,” and in 1932 France made her a Chevalier of the Legion of Honour.
On the grounds of the Fortress of Kruševac, in Serbia, is a “window to the past” that depicts the donjon tower as it appeared in its medieval heyday. At its height it served as the entrance to a medieval fortified town, the seat of Moravian Serbia.
High Wycombe, a town of furniture makers, historically celebrated important visitors with arches of chairs. The most famous marked the arrival of Prince Edward in 1880; three years earlier a similar arch had arrested Queen Victoria on her way from Windsor Castle to Hughenden to visit Lord Beaconsfield.
“It was made up of chairs of all kinds, and bore the words, ‘Long Live the Queen,'” read the Annual Register. “Her Majesty’s attention was specially attracted by this curious structure, and the Royal carriage was stopped that its occupants might have a better view.”
In a 1752 letter to Euler, Christian Goldbach suggested that every odd integer is the sum of a prime and twice a square. (At the time, 1 was considered a prime number.)
Only two exceptions, 5777 and 5993, have ever been found.
Fermat’s Last Theorem can be vividly stated in terms of sorting objects into a row of bins, some of which are red, some blue, and the rest unpainted. The theorem amounts to saying that when there are more than two objects, the following statement is never true:
Statement. The number of ways of sorting them that shun both colors is equal to the number of ways that shun neither.
We Fada wa dey een heaben,
leh ebreybody hona ya name.
We pray dat soon ya gwine
rule oba de wol.
Wasoneba ting ya wahn,
leh um be so een dis wol
same like dey een heaben.
Gii we de food wa we need
dis day yah en ebry day.
Fagib we fa we sin,
same like we da fagib
dem people wa do bad ta we.
Leh we dohn hab haad test
wen Satan try we.
Keep we fom ebil.
In 1944, British captives of the Japanese in Sumatra drew morale from an unlikely source: a purebred English pointer who cheered the men, challenged the guards, and served as a model of patient fortitude. In this week’s episode of the Futility Closet podcast we’ll tell the story of Judy, the canine POW of World War II.
We’ll also consider the frequency of different birthdays and puzzle over a little sun.