First vanishing point
Masaccio’s Holy Trinity is possibly the earliest surviving work of art to use a single vanishing point. His work and that of Brunelleschi triggered a Renaissance explosion of mathematical perspective in art.
Nontransitive dice
Consider three special dice: A, B, and C. On a fair roll, A is more likely to beat B. B is more likely to beat C. But C is more likely to beat A. These are nontransitive dice.
Hyperbolic crochet
In 1997, professor of mathematics and crochet enthusiast Daina Taimiņa found a way to join those two passions in order to craft durable sections of hyperbolic surfaces.
The false positive paradox
Consider a medical test for a disease suffered by 1% of the population, which has a 5% “false positive” error rate. If you test positive, what are the chances that you are actually ill? In fact, it’s less than 17%.
Infinite pi
The Indian mathematician Mādhava was the first to use infinite series to calculate pi, some time around 1400 CE.
The end of the tower
According to a popular myth, the solution of a 64-piece Tower of Hanoi puzzle will herald the end of the world.
Pi approximation
The closest approximation of Pi for nearly a thousand years was calculated by Chinese mathematician Zu Chongzhi around 480 CE, using an algorithm developed by Liu Hui.
Volume harmony
Take a cone, sphere, and cylinder of equal height and radius. The volume of the cone plus the volume of the sphere is equal to the volume of the cylinder.
Sequences in pi
Within the first thousand digits of pi there are six nines in a row. This should not be a surprise.
Automatic ant
The cellular automaton Langton’s Ant follows just two simple commands, and in doing so moves in turn from symmetry to chaos to implacable order.
Pi poetry
“One. A Poem. A Raven. Midnights so dreary, tired and weary, silently pondering volumes extolling all by-now obsolete lore.” The beginning of a short story that also encodes the first 3835 digits of pi.
Elementary programming
If you want a job as a programmer, you need to know how to fizz buzz.
Word frequency laws
In 1945 the linguist George Zipf observed two strange word frequency phenomena: the longer a word is, the less common it is; and the most common word is used twice as much as the second most common, three times more than the third.
Truly large numbers
Imagine an experiment which only works one time in a thousand. If you do that experiment a thousand times, what’s the probability that it works at least once? Counter-intuitively, it’s 63.2%.
Baroque perspective
There is a courtyard gallery in the Palazzo Spada in Rome that is designed to fool the eye. It looks like it should be 37 metres long, but in fact it’s only 8 metres in total.
