For many years there has been an ongoing debate about the importance of phase changes in music. Some people claim that we cannot hear the effects of phase errors, others claim that we can. Who is right? The figure below shows a waveform of a perfect fifth, with components in the ratio $latex {3 : … Continue reading Don’t be Phased by Waveform Distortions
Month: February 2019
Multiple Discoveries of the Thue-Morse Sequence
It is common practice in science to name important advances after the first discoverer or inventor. However, this process often goes awry. A humorous principle called Stigler's Law holds that no scientific result is named after its original discoverer. This law was formulated by Professor Stephen Stigler of the University of Chicago in his publication … Continue reading Multiple Discoveries of the Thue-Morse Sequence
Folding Maps: A Simple but Unsolved Problem
Paper-folding is a recurring theme in mathematics. The art of origami is much-loved by many who also enjoy recreational maths. One particular folding problem is remarkably easy to state, but the solution remains elusive: Given a map with M × N panels, how many different ways can it be folded? Each panel is considered to … Continue reading Folding Maps: A Simple but Unsolved Problem
Rambling and Reckoning
A walk on the beach, in the hills or along a river bank provides great opportunities for mathematical reflection. How high is the mountain? How many grains of sand are on the beach? How much water is flowing in the river? [TM156 or search for “thatsmaths” at irishtimes.com]. Daily average flow (cubic metres per second) at … Continue reading Rambling and Reckoning
