Imagine trying to cycle along a road with a wavy surface. Could anything be done to minimise the ups-and-downs? In general, this would be very difficult, but in ideal cases a simple solution might be possible. Continue reading ‘Wonky Wheels on Wacky Roads’

## Archive for May, 2023

### Wonky Wheels on Wacky Roads

Published May 25, 2023 Occasional Leave a CommentTags: Geometry, Mechanics

### The Potency of Pattern: Mind the Gap

Published May 18, 2023 Irish Times Leave a CommentTags: Group Theory, Physics

*A Mathematician’s Apology*, leading British mathematician G H Hardy wrote “A

*mathematician*, like a painter or poet, is a maker of

*patterns*.” He observed that the mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; beauty is the acid test [TM245 or search for “thatsmaths” at irishtimes.com]. Continue reading ‘The Potency of Pattern: Mind the Gap’

### A Topological Proof of Euclid’s Theorem

Published May 11, 2023 Occasional Leave a CommentTags: Number Theory, Primes

**Theorem (Euclid): There are infinitely many prime numbers.**

Euclid’s proof of this result is a classic. It is often described as a proof by contradiction but, in fact, Euclid shows how, given a list of primes up to any point, we can find, by a finite process, another prime number; so, the proof is constructive.

### Broken Symmetry and Atmospheric Waves, 2

Published May 4, 2023 Occasional Leave a CommentTags: Geophysics

**Part II: Stationary Mountains and Travelling Waves**

Atmospheric flow over mountains can generate large-scale waves that propagate upwards. Although the mountains are stationary(!), the waves may have a component that propagates towards the west. In this post, we look at a simple model that explains this curious asymmetry.