The idiom “square peg in a round hole” expresses a mismatch or misfit, often referring to somebody in the wrong profession. It may also indicate a difficult or impossible task but, of course, it is quite simple to fit a square peg in a round hole, hammering it in until the corners are tight against … Continue reading Unsolved: the Square Peg Problem
Month: December 2016
Twenty Heads in Succession: How Long will we Wait?
If three flips of a coin produce three heads, there is no surprise. But if 20 successive heads show up, you should be suspicious: the chances of this are less than one in a a million, so it is more likely than not that the coin is unbalanced. Waiting Time for a Single Head On average, … Continue reading Twenty Heads in Succession: How Long will we Wait?
The Edward Worth Library: a Treasure Trove of Maths
Infinite Riches in a Little Room. Christopher Marlowe. The Edward Worth Library may be unknown to many readers. Housed in Dr Steevens' Hospital, Dublin, now an administrative centre for the Health Service Executive, the library was collected by hospital Trustee Edward Worth, and bequeathed to the hospital after his death in 1733. The original book … Continue reading The Edward Worth Library: a Treasure Trove of Maths
Raphael Bombelli’s Psychedelic Leap
The story of how Italian Renaissance mathematicians solved cubic equations has elements of skullduggery and intrigue. The method originally found by Scipione del Ferro and independently by Tartaglia, was published by Girolamo Cardano in 1545 in his book Ars Magna. The method, often called Cardano's method, gives the solution of a depressed cubic equation t3 … Continue reading Raphael Bombelli’s Psychedelic Leap
The Shaky Foundations of Mathematics
The claim is often made that mathematical results are immutable. Once proven, they remain forever valid. But things are not so simple. There are problems at the very core of mathematics that cast a shadow of uncertainty. We can never be absolutely sure that the foundations of our subject are rock-solid [TM104 or search for … Continue reading The Shaky Foundations of Mathematics
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