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Leonhard Euler was born in the spring of 1707 and lived until the autumn of 1783, 76 years. Euler was born in Switzerland near the town of Basel to a father whom was a Protestant clergyman and a mother who can from an equally pastoral family. It was expected from them that he would also become a man of the church. As a youth he had the capability to memorize almost anything easily, he also had the ability to work with numbers in his head without the use of a calculator (Dunham xix). At the age of 14 Euler entered the University of Basel, it was in this school that Euler met his mentor: Johann Bernoulli. At this time Johann thought himself to be the worlds greatest mathematician and he willingly gave Euler any information and guidance that Euler needed in the field of mathematics.
At this school Euler earned a masters degree in philosophy and he went on to a divinity school to study ministry; soon he left that for his destiny math. By the age of 20 Euler won acknowledgement for the analysis of the placement of masts on sailing ships (Dunham xxi). In 1727 Euler moved to St. Petersburg and found himself in the St. Petersburg Academy.
It was here in St. Petersburg that Euler met his wife Katharina Grill. Together they had 13 children; sadly only 5 survived to adolescence, and a mere 3 outlived their parents (Dunham xxii). Many years and accomplishments later Euler and his family moved to Berlin with the invitation of Fredrick the Great in 1741. In a matter of 25 years spent here Euler wrote 380 articles, and countless books on the calculus of variations, the calculation of planetary orbits, artillery and ballistics, analysis, shipbuilding and navigation, the motion of the moon, and differential calculus. In 1766 Euler returned to St.
Petersburg to stay forever. With in a few years two tragedies occurred in Euler? s life: by 1771 he was completely blind and in 1773 his wife died. Euler?
s courage and ambition was like no other, although he virtually had no way to see or write he was unstoppable. In 1775 he was still averaging one mathematical paper per week, he only had dictators to write for him. His memory was just as good as ever before; he could still mentally work tedious problems out in his head with virtually no problems (Dunham xxvi). Three years after his wife died he married her half sister remained with her and still diligently studying until the end of his life in 1783. Euler literally had hundreds of accomplishments throughout his lifetime, one of them being the Euler diagram. These diagrams help people understand many statements like: all A are B, ?
some A are B? , and? no A are B? (Schmidt). This is an example of? all A are B? (all cats have whiskers). The diagrams gives you a mental description of what is being asked so that it is easier to understand statements and come up with solutions. If we were to say some cats have whiskers than the two circles would overlap; if we were to say no cats have whiskers than the two circles would be entirely separate, not touching at all.
Another one of Euler? s accomplishments is his number theory; although it seems so natural and easy, it is actually quite complex and difficult (Dunham 1). In this theory Euler revises and finishes a theory that Euclid in 300 BCE started, in their theory they talk about perfect numbers (Dunham 1). When Euclid started this theory he stated that? A perfect number is that which is equal to its own parts? , translated today as? A whole number is perfect if it is equal to the sum of its proper divisors? (Dunham 2).
An example of this would be the number 6: this numbers proper divisor are 1, 2, and 3. if you add these numbers up you get 6 (the actual number in question). Later when Euler came into the picture he introduced a new idea to that of perfect numbers: ? o (n) is the sum of all whole number divisors of n? (Dunham 8).
In short this means that where Euclid only thought that the proper divisors were important Euler thought that ALL the divisors should be put into question. Using this Euler came up the theorem? If N is a perfect number, then N = 2 k+ 1 (2 k- 1), where 2 k- 1 is prime (Dunham 10). Euler also made great contributions to the reasoning of logarithms in a conceptual manner (most of the work was done before his time. Euler? s key definition in the concept in this matter was?
a function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities? (Dunham 17). Besides the contribution of this definition Euler also perceived the significance of what is known as the? natural? logarithm, explicitly recognized the inverse nature of logs and exponential's, and applied his results to theoretical matters far removed from mere computations (Dunham 18). Another great achievement given by Euler was in the area of the infinite series. not finished if you need more than e mail me.
Dunham, William. Euler The Master of Us All. The Mathematical Association of America, 1999. Blanton, John. Introduction to Analysis of the Infinite. Springer?
Verlag Mew York Inc, 1988. I also used several websites: web web web
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