Published December 31, 2015
The circular functions occur throughout mathematics. Fourier showed that, under very general assumptions, an arbitrary function can be decomposed into components each of which is a circular function. The functions get their name from their use in defining a circle in parametric form: if
then , the usual equation for a circle in Cartesian coordinates. In the figure, we plot the familiar sinusoid, which has a period of .
Continue reading ‘Squaring the Circular Functions’
Published December 24, 2015
Tags: Arithmetic, Games
How many ways can a deck of cards be arranged? It is very easy to calculate the answer, but very difficult to grasp its significance.
Continue reading ‘Factorial 52: A Stirling Problem’
We all know the festive carol The Twelve Days of Christmas. Each day, “my true love” receives an increasing number of gifts. On the first day there is one gift, a partridge in a pear tree. On the second, two turtle doves and another partridge, making three. There are six gifts on the third day, ten on the fourth, fifteen on the fifth, and so on.
Here is a Christmas puzzle: what is the total number of gifts over the twelve days? [TM083, or search for “thatsmaths” at irishtimes.com]
Continue reading ‘How many Christmas Gifts?’
Published December 10, 2015
Galileo noticed the regular swinging of a candelabra in the cathedral in Pisa and speculated that the swing period was constant. This led him to use a pendulum to measure intervals of time for his experiments in dynamics. Bu not all pendulums behave like clock pendulums.
The ping pong pendulum.
Continue reading ‘The Ping Pong Pendulum’
Golf balls fly further today, thanks to new materials and mathematical design. They are a triumph of chemical engineering and aerodynamics. They are also big business, and close to a billion balls are sold every year. [TM081: search for “thatsmaths” at Irish Times ].
Continue reading ‘The Flight of a Golf Ball’