Published April 27, 2017
Tags: Number Theory, Primes
In the time before computers (BC) various ingenious devices were invented for aiding the extensive calculations required in astronomy, navigation and commerce. In addition to calculators and logarithms, several nomograms were devised for specific applications, for example in meteorology and surveying.
Continue reading ‘A Geometric Sieve for the Prime Numbers’
Seventy percent of the Earth is covered by water and three quarters of the world’s great cities are on the coast. Ever-rising sea levels pose a real threat to more than a billion people living beside the sea. As the climate warms, this is becoming a greater threat every year [TM114 or search for “thatsmaths” at irishtimes.com].
Mean Sea level in Seattle from 1900 to 2013
Continue reading ‘The Water is Rising Fast’
Evangelista Torricelli, a student of Galileo, is remembered as the inventor of the barometer. He was also a talented mathematician and he discovered the remarkable properties of a simple geometric surface, now often called Torricelli’s Trumpet. It is the surface generated when the curve for is rotated in 3-space about the x-axis.
Continue reading ‘Torricelli’s Trumpet & the Painter’s Paradox’
Published April 6, 2017
Tags: Probability, Statistics
Extremely improbable events are commonplace.
“It’s an unusual day if nothing unusual happens”. This aphorism encapsulates a characteristic pattern of events called the Improbability Principle. Popularised by statistician Sir David Hand, emeritus professor at Imperial College London, it codifies the paradoxical idea that extremely improbable events happen frequently. [TM112 or search for “thatsmaths” at irishtimes.com].
From front cover of The Improbability Principle
Continue reading ‘The Improbability Principle’
Published March 30, 2017
Probability theory is full of surprises. Possibly the best-known paradoxical results are the Monty Hall Problem and the two-envelope problem, but there are many others. Here we consider a simple problem using playing cards, first analysed by Pierre Raymond de Montmort (1678–1719).
Shuffle spades in one pile, hearts in another. Place both piles face downwards. Turn over a card from each pile. Do the two cards match?
Continue reading ‘Treize: A Card-Matching Puzzle’
A numerical coincidence is an equality or near-equality between different mathematical quantities which has no known theoretical explanation. Sometimes such equalities remain mysterious and intriguing, and sometimes theory advances to the point where they can be explained and are no longer regarded as surprising.
Cosine of 355 radians is almost exactly equal to -1. Is this a coincidence? Read on!
Continue reading ‘Numerical Coincidences’
Published March 16, 2017
Tags: Mechanics, medicine
Modern science is big: the gravitational wave detector (LIGO) cost over a billion dollars, and the large hadron collider (LHC) in Geneva took decades to build and cost almost five billion euros. It may seem that scientific advances require enormous financial investment. So, it is refreshing to read in Nature Biomedical Engineering (Vol 1, Article 9) about the development of an ultra-cheap centrifuge that costs only a few cents to manufacture [TM111 or search for “thatsmaths” at irishtimes.com].
Whirligig, made from a plastic disk and handles and some string
Continue reading ‘A Life-saving Whirligig’