Archive for May, 2023

Wonky Wheels on Wacky Roads

Tricycles with three square wheels, each a different size. Image from the Museum of Mathematics, New York.

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’

The Potency of Pattern: Mind the Gap

Theodor Benfey’s periodic table (1964) [image Wikimedia Commons].

In his book 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]. Continue reading ‘The Potency of Pattern: Mind the Gap’

A Topological Proof of Euclid’s Theorem

The twelve-line topological proof of Euclid’s Theorem by Hillel Furstenberg.

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.

Continue reading ‘A Topological Proof of Euclid’s Theorem’

Broken Symmetry and Atmospheric Waves, 2

Part II: Stationary Mountains and Travelling Waves

Jule Charney (1917–1981) and Philip Drazin (1934–2002).

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.

Continue reading ‘Broken Symmetry and Atmospheric Waves, 2’

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