Euler's polyhedron formula


By Jordan Burgess, Simon Langton Grammar

Euler's formula (V - E + F = 2) Was created by Leonhard
Euler (1707-1783). Euler was a great mathematician,
mechanic and a great man who let nothing but death get
in the way of accomplishing everything.

external image Euler_1_web.jpg



Euler’s Life

Euler went to a school which was poor by their standards, he didn’t learn. Although this was the case Euler was still fascinated by our everyday mathematics, he would often listen to his father (Paul Euler) speak about maths. He would also read mathematic books and texts on his own and have private lessons on maths. Euler went on to the University of Basil to prepare for the ministry, as his father had instructed. He was admitted to University in 1720 at the age 14. Johann Bernoulli (Euler’s Tutor) soon discovered Euler's great potential for maths in private tuition. This is a written account from Euler:

... I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. ... True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand ...

In 1723 Euler completed his Master's degree in philosophy, later that year he began his study of theology, as his father had instructed, but he was not as enthusiastic about theology, Greek and Hebrew, as he was about Mathematics. Euler received consent from his father to change his study to mathematics after Johann Bernoulli had persuaded him to.

Euler completed his studies in 1726. In 1727 he published another article on reciprocal trajectories and submitted an entry for the 1727 Grand Prize of the Paris Academy on the best arrangement of masts on a ship. The Prize of 1727 went to Bouguer, an expert on mathematics relating to ships, but Euler's essay won him second place.

Euler had to find himself an academic appointment and when Nicolaus Bernoulli died that created a vacancy, and Euler was offered a place which included teaching mathematics and mechanics to physiology. He accepted the post but stated that he did not want to travel to Russia until the following year as he wanted time to study the topics of his new post and because there was a post free at the University of Basil as the professor of physics had died there. Euler wrote an article on acoustics, which is now a classic article, to ask for this position. He, however, was not admitted to go forward and claim the post. Some say that this was a terrible prospect of his youth, however others suggest that it actually benefited Euler as he then went on to live in a small republic which was perfect for his research.

As soon as he knew he would not be appointed to the post, Euler left Basel on 5 April 1727. He travelled down the Rhine by boat, crossed the German states by post wagon, then by boat from Lübeck arriving in St Petersburg on 17 May 1727. He had joined the St Petersburg Academy of Sciences two years after it had been founded. Through the requests of Daniel Bernoulli and Jakob Hermann, Euler was appointed to the mathematical-physical division of the Academy rather than to the physiology post he had originally been offered.

Euler served as a medical lieutenant in the Russian navy from 1727 to 1730. Euler became professor of physics at the Academy in 1730. Daniel Bernoulli held the senior chair in mathematics at the Academy but when he left St Petersburg to return to Basel in 1733 Euler was appointed to the senior chair of mathematics.

The financial improvement which came from this appointment allowed Euler to marry which he did on 7 January 1734, marrying Katharina Gsell. They had 13 children altogether although only five survived their infant stages. Euler claimed that he made some of his greatest mathematical discoveries while holding a baby in his arms with other children playing round his feet.

Euler went on to create theories, formulas and more mathematical discoveries. He worked with many different people and died in 1783. This is a quotation from one of his friends and work associate:

On 18 September 1783 Euler spent the first half of the day as usual. He gave a mathematics lesson to one of his grandchildren, did some calculations with chalk on two boards on the motion of balloons; then discussed with Lexell and Fuss the recently discovered planet Uranus. About five o'clock in the afternoon he suffered a brain haemorrhage and uttered only "I am dying" before he lost consciousness. He died about eleven o'clock in the evening.

The Work of Euler

After 1730 he carried out state projects dealing with cartography, science education, magnetism, fire engines, machines, and ship building. The core of his research program was now set in place: number theory; infinitary analysis including its emerging branches, differential equations and the calculus of variations; and rational mechanics. He viewed these three fields as intimately interconnected. Studies of number theory were vital to the foundations of calculus, and special functions and differential equations were essential to rational mechanics.