The history of probability theory has been influenced strongly by paradoxes, results that seem to defy intuition. Many of these have been reviewed in a recent book by Prakash Gorroochurn [2012]. We will have a look at Bertrand's Paradox (1889), a simple result in geometric probability. Let's start with an equilateral triangle and add an … Continue reading Bertrand’s Chord Problem
Month: February 2016
Vanishing Zigzags of Unbounded Length
We will construct a sequence of functions on the unit interval such that it converges uniformly to zero while the arc-lengths diverge to infinity. Hopping Animals Let us compare a sequence of frog hops, cricket hops and flea hops. We assume each hop is a semi-circle so that the length is easily calculated. If the … Continue reading Vanishing Zigzags of Unbounded Length
Franc-carreau or Fair-square
Franc-carreau is a simple game of chance, like the roll-a-penny game often seen at fairs and fêtes. A coin is tossed or rolled down a wooden chute onto a large board ruled into square segments. If the player's coin lands completely within a square, he or she wins a coin of equal value. If the … Continue reading Franc-carreau or Fair-square
The Mathematics of Voting
Selection of leaders by voting has a history reaching back to the Athenian democracy. Elections are essentially arithmetical exercises, but they involve more than simple counting, and have some subtle mathematical aspects [TM085, or search for “thatsmaths” at irishtimes.com]. The scientific study of voting and elections, which began around the time of the French Revolution, is called … Continue reading The Mathematics of Voting
ThatsMaths 