Leonhard Euler considered a problem known as *The Seven Bridges of Königsberg.* It involves a walk around the city now known as Kaliningrad, in the Russian exclave between Poland and Lithuania. Since Kaliningrad is out of the way for most of us, let’s have a look closer to home, at the bridges of Paris. [TM073: search for “thatsmaths” at irishtimes.com ]

## Posts Tagged 'Euler'

### The Bridges of Paris

Published August 4, 2015 Irish Times Leave a CommentTags: Algorithms, Euler, Topology

### Clothoids Drive Us Round the Bend

Published April 17, 2014 Irish Times Leave a CommentTags: Euler, Geometry, Mechanics, modelling

The article in this week’s *That’s Maths* column in the* Irish Times* ( TM043 ) is about the mathematical curves called clothoids, used in the design of motorways.

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### Experiment and Proof

Published December 26, 2013 Occasional Leave a CommentTags: Arithmetic, Euler, Number Theory

Many mathematicians spend their time proving results. The (very old) joke is that they are machines for turning coffee into theorems. A *theorem* is a statement that has been shown, by a sequence of irrefutable steps, to follow logically from a set of fundamental assumptions known as axioms.

These axioms themselves may be self-evident, or may simply be assumed to be true. Given this, the statement contained in a theorem is known with certainty to be true.

This week, *That’s Maths* in *The Irish Times* ( TM032 ) is about Euler’s Polyhedron Formula and its consequences.

**Euler’s Polyhedron Formula**

The highlight of the thirteenth and final book of Euclid’s *Elements* was the proof that there are just five “Platonic solids”. Recall that a regular polygon is a plane figure with all sides and angles equal, for example a square. By joining identical polygons together, we can form solid bodies called regular polyhedra. Continue reading ‘Euler’s Gem’