Archive for July, 2019

Billiards & Ballyards

In (mathematical) billiards, the ball travels in a straight line between impacts with the boundary, when it changes suddenly and discontinuously We can approximate the hard-edged, flat-bedded billiard by a smooth sloping surface, that we call a “ballyard”. Then the continuous dynamics of the ballyard approach the motions on a billiard.


Elliptical tray in the form of a Ballyard.

Continue reading ‘Billiards & Ballyards’

Learning Maths without even Trying

Children have an almost limitless capacity to absorb knowledge if it is presented in an appealing and entertaining manner. Mathematics can be daunting, but it is possible to convey key ideas visually so that they are instantly accessible. Visiting Explorium recently, I saw such a visual display demonstrating the theorem of Pythagoras, which, according to Jacob Bronowski, “remains the most important single theorem in the whole of mathematics” [TM167 or search for “thatsmaths” at].


Continue reading ‘Learning Maths without even Trying’

Boxes and Loops

We will describe some generic behaviour patterns of dynamical systems. In many systems, the orbits exhibit characteristic patterns called boxes and loops. We first describe orbits for a simple pendulum, and then look at some systems in higher dimensions.


Phase portrait for a simple pendulum. Each line represents a different orbit.

Continue reading ‘Boxes and Loops’

What did the Romans ever do for Maths?

The ancient Romans developed many new techniques for engineering and architecture. The citizens of Rome enjoyed fountains, public baths, central heating, underground sewage systems and public toilets. All right, but apart from sanitation, medicine, education, irrigation, roads and aqueducts, what did the Romans ever do for maths? [TM166 or search for “thatsmaths” at].


Roman aqueduct at Segovia, Spain.

Continue reading ‘What did the Romans ever do for Maths?’

Last 50 Posts