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# Secondary Magazine - Issue 31: From the editor

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 01 April 2009 by ncetm_administrator
Updated on 27 April 2009 by ncetm_administrator

# Euler

Leonhard Paul Euler was a Swiss mathematician.  Born in Basel on 15 April 1707, Euler lost the sight in one eye as a young man, and later was virtually blind as he had a cataract on the other eye. He had an amazing memory and an ability to visualise problems which enabled him to carry on doing mathematics and publishing his results by dictating them. He published over 800 mathematical papers in his lifetime.

Having been tutored by Johann Bernoulli, Euler moved to Russia to work with one of Bernoulli’s sons in St Petersburg. It was in St Petersburg that he married and had 13 children (only five of whom survived infancy). Euler worked in Berlin for 25 years but returned to St Petersburg and died there in 1783.

 The impact of Euler’s mathematical work is far-ranging. Most pupils will be affected by his work on standardising mathematical notation: he introduced the symbol ‘e’ to represent the base of the system of natural logarithms (see Secondary Magazine Issue 20 ‘Focus on e’), established the use of the Greek letter π for the ratio of circumference to diameter in a circle, used the small letters a, b, c to represent the sides of a triangle and A, B, C for the opposite angles.

Many pupils will also have met Euler’s problem The Bridges of Königsberg. The city of Könisberg in Prussia (now Kaliningrad, Russia) was situated on the Pregel River, and included two large islands which were connected to each other and the mainland by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and return to the starting point. Euler used the idea of arcs, vertices and regions to solve the problem; this area of mathematics is now known as topology, the most famous example of which is the London Underground Map.

Euler also noticed that there is a formula giving the relationship between the number of faces, vertices and edges for polyhedra, which is accessible to most pupils. It may be interesting to ‘notice’ this formula with your pupils:

 Polyhedron Faces Vertices Edges Cube Cuboid Tetrahedron Square-based pyramid Octahedron

Euler is a prominent mathematician of the 18th century and one of the greatest of all time. How will you celebrate his birthday month in your classroom?

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