A little mathematics goes a long, long way; in the adventure recounted below, elementary geometry brought an intrepid band of six men 800 sea miles across the treacherous Southern Ocean, and led to the saving of 28 lives. Endurance For eight months, Ernest Shackleton's expedition ship Endurance was carried along, ice-bound, until it was finally … Continue reading Shackleton’s spectacular boat-trip
Category: Occasional
The Popcorn Function
Continuity is not what it seems. In 1875, the German mathematician Carl Johannes Thomae defined a function P(x) with the following extraordinary property: P(x) is discontinuous if x is rational P(x) is continuous if x is irrational. A graph of this function on the interval (0,1) is shown below. The function has many names. We … Continue reading The Popcorn Function
Falling Slinky
If you drop a slinky from a hanging position, something very surprising happens. The bottom remains completely motionless until the top, collapsing downward coil upon coil, crashes into it. How can this be so? We all know that anything with mass is subject to gravity, and this is certainly true of the lower coils of … Continue reading Falling Slinky
The End of Smallpox
Daniel Bernoulli was born in 1700 into a remarkably talented family. He excelled in mathematics, but also studied and lectured in medicine, botany and physics. In 1760, he submitted a paper to the Academy of Sciences in Paris dealing with the effects of inoculation on morbidity. The practice of inoculation, the deliberate introduction of a … Continue reading The End of Smallpox
The Beautiful Game
What is the most beautiful rectangular shape? What is the ratio of width to height that is most aesthetically pleasing? This question has been considered by art-lovers for centuries and one value appears consistently, called the golden ratio or Divine proportion. I must admit that the notion of an ideal ratio makes me uncomfortable. How … Continue reading The Beautiful Game
No Maths Involved!
Whether or not you enjoy solving them, those 9x9 grids with numbers and blank cells cannot have escaped your notice. Sudoku puzzles have swept the world since exploding on the scene in 2005. They are found in newspapers everywhere, providing daily amusement to all who like a minor mathematical challenge. The objective of Sudoku is … Continue reading No Maths Involved!
Sproutology
Sprouts is a simple and delightfully subtle pencil-and-paper game for two players. The game is set up by marking a number of spots on a page. Each player makes a move by drawing a curve that joins two spots, or that loops from a spot back to itself, without crossing any lines drawn earlier, and … Continue reading Sproutology
Napier’s Nifty Rules
Spherical trigonometry is not in vogue. A century ago, a Tripos student might resolve a half-dozen spherical triangles before breakfast. Today, even the basics of the subject are unknown to many students of mathematics. That is a pity, because there are many elegant and surprising results in spherical trigonometry. For example, two spherical triangles that … Continue reading Napier’s Nifty Rules
The Two Cultures
The Two Cultures Of course I've heard of Beethoven, but who is this guy Gauss? The “Two Cultures”, introduced by the British scientist and novelist C. P. Snow in an influential Rede Lecture in 1959, are still relevant. Ludwig von Beethoven and Carl Friedrich Gauss were at the height of their creativity in the early … Continue reading The Two Cultures
ThatsMaths 