Leonhard+Euler+Biography

===During this course, each student is required to complete a biography on a mathematician and present the information in front of the class. My Biography was on Leonhard Euler. On this page you will find a link to my PowerPoint presentation as well as my submitted paper.===

PowerPoint Presentation:

Biography can be viewed below, or at the following link:

Leonhard Euler was born on April 15, 1707 in Switzerland. He was the oldest of four children. His mother was a homemaker and his father a minister. His first teachers were his parents. His mother taught him Greek and Roman, while his father was able to provide elementary mathematics.

The mathematical textbook he originally began learning from was titled //Coss//, by Christoff Rudolff. This text book studied primarily Algebra. In this book you will find that it first explains place-value notation and then addition, subtraction, multiplication, and division. After these basics, it moves on to study first, second, and third degree equations. Oddly enough, these were all done in verbal form. He was eight years old when he finished all 434 problems in this text; keep in mind these were including third degree equations. Euler’s father had forseen him not a mathematician, but in the field of philosophy following in his footsteps. When this dreamed proved untrue his father pushed him towards the medical field. It was by luck of the contacts Euler had already made at Basal, such as Bernoulli, that he was able to pursue a career of mathematics.

At age thirteen Euler attended the University of Basel, more directly the school of arts and sciences. This age was normal to enter a University at that time. He discovered his photographic mind during this time. He also was under tutoring of mathematician Johann Bernoulli who was on the faculty at Basel. Bernoulli realized Euler’s potential, and instead tutoring him as he would normally, he told Euler to go home and read really advanced books and mark down points he could not understand. Then Bernoulli would help him with these points. Bernoulli thought that this method was the best way to achieve Euler’s potential. In college, along with mathematics, Euler studied theology and Hebrew. He obtained his masters degree at the age of sixteen. It was not until 1727 that Euler left the University of Basel. He moved to St. Petersburg Academy of Sciences in Russia where he joined the faculty there. In 1733 he became the chairman of mathematics there.

In 1735 Euler lost sight in one eye while he had worked nonstop for three days solving a mathematics problem. This same problem had taken multiple other mathematicians months to solve. While in Russia he also derived the equation that linked velocity and pressure. This became known as Bernoulli’s equation because he had collaborated with Bernoulli on it. He also discovered then that pressure was something that could change from point to point through fluid.

In 1741, Euler moved to Berlin where he became a mathematics professor at the Berlin Academy of Sciences. While there, he transformed it into a major academy. He remained in Berlin for twenty-five years. During this time period he prepared at least 380 pages to be published. He returned in 1766 to St. Petersburg. Shortly after he returned he became almost completely blind. However he continued to solve mathematic equations mentally. Euler died of a stroked on September 18, 1783.

Euler’s work consists of mainly mathematics and physics. He has work containing all sorts of ideas and methods in both of these topics. Euler’s work also shows that he held a great deal of knowledge in astronomy, engineering, and philosophy. A major mathematical accomplishment was being responsible for shaping calculus into a useful math which is capable of solving all sorts of problems. Some of these involved physics. In his “PreCalculus” book, Euler promoted the ideas of functions. Many of the notations and algorithms we use in modern times are the same as what he used in his notes and published books. Euler made significant strides in advancing algebra, his notes show that he came extremely close to proving the Fundamental Theorem of Algebra.

Euler rediscovered Fermat’s number theory and found correct proof’s of Fermat’s statements. Fermat’s number theory is a method in finding whether a number is prime by using a series of computations. ‘N’ is any whole number, and ‘P’ is any prime number. Raise ‘N’ to the power of ‘P’ and then subtract ‘N’. If ‘P’ is a prime number, then the result of these computations can be divided evenly by ‘P’.

Example: N=8 P=3 83 – 8=504 504/3=168 Therefore, 3 is a prime number.

Fermat is responsible for finding this equation, however there was no proof that this would work for all situations and his work did not consist of any proofs.

Euler was also the first person to use sine and cosine as functions of an angle, and was the first person to define them using the unit circle. He is responsible for the modern day “Newton’s Law.” The term “Newton’s Law” actually refers to three laws in physics. The most popular one is known at Newton’s First Law. This says that an object in motion stays in motion. This law was obviously discovered and created by a man named Newton, but Euler was able to prove it and work it into the equations mathematicians and scientists use today. Another mathematical theme Euler invented was the use of the letter //e// as the name of the number which is the base of the natural logarithm. The natural logarithm of a number //x// is the power to which //e// would have to be raised to equal //x//.

In geometry Euler studied triangles and eventually discovered a basic theorem about solid polyhedron. This theorem stated that given a polyhedron, V – E + F = 2, where V= it’s amount of vertices E= it’s amount of edges and F = its amount of faces. It was later discovered that this formula only works for simple polyhedron. However, this formula is useful for things such as discovering there is no simple polyhedron with seven edges, or that there is no simple polyhedron with ten faces and seventeen vertices. This formula saves time rather than having to attempt to draw or construct a polyhedron with a given amount of edges, vertices, or faces not knowing whether it is even possible.

Another equation Euler discovered is the equation for what we call Euler’s Line. The Euler Line is a line found in any triangle that is not equilateral. This line is formed by points determined by the triangle such as the orthocenter, centroid, and circumcenter. By connecting any two of these points, and continuing the line, you are drawing the Euler Line. This equation is useful because you can plug in points into the equation and find out if they fall onto the Euler line of a triangle.

Euler was a mathematician of many trades. He has many formulas, equations, and discoveries in physics and is often correlated with physics rather than math. When studying him, it is hard to find just mathematical discoveries of his.


 * Citations**

Berlinghoff, William, Gouvêa, Fernando, &,. (2002). //Math through the ages: a gentle// //history for teachers and others//. Farmington, Maine: Oxton House Pub.

Bradley, R.E., & Sandifer, C.E. (2007). //Leonhard euler: life, work and legacy//. Netherlands: Elsevier.

Boyer, C.B. (n.d.). Science and technology: Leonhard Euler. //Britanica encyclopedia//. Retrieved (2010, January 30) from []

//U.s.// //centennial flight of commission//. (n.d.). Retrieved from []

Kirk, A. (2007, June). //Euler's polyhedron formula//. Retrieved from []

//Number theory - fermat's theorem//. (n.d.). Retrieved from http://science.jrank.org/pages/4771/Number-Theory-Fermat-s-theorem.html