Mathematics in sport I

Abstract

Newton's laws and coded sequences are used to explore sport mathematically. Track and field athletics, American, association, Gaelic and rugby football, golf, rowing, skating, snooker and hockey, among others, provide illustrations. Mathematical considerations include classical mechanics; linear and angular momentum, work, impulse, kinetic and gravitational energy, simple harmonic motion, friction, rolling, rotating frames, Euler angles and projectiles.

Some mathematical tools used are differential and integral calculus, vectors and vector spaces, dot and cross products, multiple integrals, orthogonal coordinate systems, fluid mechanics, invariance principles, non‐Abelian algebra, matrices, variational principles, optimization, trigonometry, coordinate geometry, modelling, set theory, transverse and longitudinal waves, elementary statistics, dimensional analysis, combinatorics, partitions and prime numbers, parity, encryption and codes.

It is concluded that at all levels of education, primary, secondary and tertiary, sport and games may be used to illustrate and motivate mathematics and for that matter, physics.

In paper I, we concentrate on natural impulse and spin.