A Geometric Sieve for the Prime Numbers

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. A Nomogram for Multiplication The graph of a parabola $latex {y=x^2}&fg=000000$ can be used … Continue reading A Geometric Sieve for the Prime Numbers →

The Water is Rising Fast

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 [TM113 or search for “thatsmaths” … Continue reading The Water is Rising Fast →

Torricelli’s Trumpet & the Painter’s Paradox

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 $latex {y=1/x}&fg=000000$ for $latex {x\ge1}&fg=000000$ is rotated in 3-space … Continue reading Torricelli’s Trumpet & the Painter’s Paradox →

The Improbability Principle

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]. We … Continue reading The Improbability Principle →