Leonhard Euler

Hence, you cannot visit each of the bridges of Königsberg without retracing your steps. In a four-year career, Oswalt has compiled a 63-27 record with a 3.11 ERA and a 3.76 strikeout-to-walk ratio (666-to-177) in 739 innings pitched. The seven bridges problem is neither an Euler circuit nor Euler path. . This means that it is possible to travel each line exactly once without retracing your steps, but you will not end where you began. He bats and throws right handed. An Euler path has exactly two odd vertices. Roy Edward Oswalt [OWES-walt] (born August 29, 1977 in Weir, Mississippi) is a starting pitcher in Major League Baseball who plays for the Houston Astros (since 2001).

This means it is possible to travel each line exactly once without retracing your steps and end at the same point in which you started. Upon first seeing Oswalt in 2001, former Los Angeles Dodgers' manager Tommy Lasorda remarked, "This guy is the next Orel Hershiser.". An Euler circuit has all its points of even degree. The pitchers were Oswalt, Pete Munro, Kirk Saarloos, Brad Lidge, Octavio Dotel and Billy Wagner. Looking at how many lines came into a point gave that point a degree (a point with three lines touching it has a degree of three). On June 11, 2003, Houston set a major league record for combined pitchers in a no-hitter with six, against the Yankees. The solution to the seven bridges problem reduced the land masses to points and the bridges to lines (or edges) connecting those points. Olympic gold medalist (2000).

In 1736 Euler solved, or rather proved insoluble, a problem known as the seven bridges of Königsberg, publishing a paper Solutio problematis ad geometriam situs pertinentis which was the earliest application of graph theory or topology. TSN Rookie of the Year (2001). A generalization of Euler's formula for arbitrary planar graphs exists: F - E + V - C = 1, where C is the number of components in the graph. 3-time Top 10 in voting for the Cy Young Award (5th, 2001; 4th, 2002; 3rd, 2004). The Euler characteristic of a simply-connected manifold such as a sphere or a plane is 2. Led NL in games started (35, 2004). For nonplanar graphs, there is a generalization: If the graph can be embedded in a manifold M, then F - E + V = χ(M), where χ is the Euler characteristic of the manifold, a constant which is invariant under continuous deformations. Led National League in winning games (20, 2004).

The theorem also applies to any planar graph. All-Star (2005). i.e.: F - E + V = 2. Given such a polyhedron, the sum of the vertices and the faces is always the number of edges plus two. In geometry and algebraic topology, there is a relationship (also called Euler's Formula) which relates the number of edges, vertices, and faces of a simply connected polyhedron.

In economics, Euler showed that if each factor of production is paid the value of its marginal product, then (under constant returns to scale) the total income and output will be completely exhausted. Euler wrote Tentamen novae theoriae musicae in 1739 which was an attempt to combine mathematics and music; a biography comments that the work was "for musicians too advanced in its mathematics and for mathematicians too musical". He is a co-discoverer of the Euler-Maclaurin formula which is an extremely useful tool for calculation of difficult integrals, sums, and series. Also in 1735, Euler defined the Euler-Mascheroni constant useful for differential equations:.

What Richard Feynman called "The most remarkable formula in mathematics" (more commonly called Euler's identity) is an easy consequence:. In essence, all functions studied in elementary analysis are either variations of the exponential function or they are polynomials. This is Euler's formula, which establishes the central role of the exponential function. He also showed the usefulness, consistency, and simplicity of defining the exponent of an imaginary number by means of the formula.

where ζ(s) is the Riemann zeta function. Euler established his fame in 1735 by solving the long-standing Basel problem:. In mathematical analysis, it was Euler who synthesised Leibniz's differential calculus with Isaac Newton's method of fluxions. For example, φ(8) = 4 since the four numbers 1, 3, 5 and 7 are coprime to 8.

The totient φ(n) of a positive integer n is defined to be the number of positive integers less than or equal to n and coprime to n. In number theory, Euler invented the totient function. The most famous of these approximations is known as Euler's method. In particular, he is known for creating a series of approximations which are used in computational mechanics.

Euler made important contributions to the theory of differential equations. They are interesting chiefly because of the existence of shock waves. These equations are formally identical to the Navier-Stokes equations with zero viscosity. He also deduced the Euler equations, a set of laws of motion in fluid dynamics, directly from Newton's laws of motion.

Euler, with Daniel Bernoulli, established the law that the torque on a thin elastic beam is proportional to a measure of the elasticity of the material and the second moment of area of a cross section, about an axis through the center of mass and perpendicular to the plane of the moment, see Euler-Bernoulli beam equation. When Euler died, the mathematician and philosopher Marquis de Condorcet commented, "...et il cessa de calculer et de vivre" (and he ceased to calculate and to live). However, a widely told anecdote that says that Euler challenged Denis Diderot at the court of Catherine the Great with "Sir, (a+b)ⁿ/n = x; hence God exists, reply!" is false. Euler was a deeply religious Calvinist throughout his life.

It is reported by Legendre that often he would write down a complete mathematical proof between the first and the second call for supper. It was not till the year 1910 that a collection of his complete works was published; it took about 70 volumes. It has been calculated that it would take eight-hours work per day for 50 years to copy all his works by hand. It is reported that once he let his assistant calculate a series to 17 summands and noticed that his own result and the assistant's result differed in the 50th digit—a recalculation showed that Euler was right.

Euler continued to be very productive, despite a complete loss of vision, due to his extraordinary powers of memory and mental calculation. Petersburg in 1766, ruled by Catherine the Great at that time, and he remained there for the rest of his life. Therefore he returned to St. His time in Berlin was very productive; however, he did not have an easy position due to a lack of the king's favor.

In the year 1741 Euler became director of the mathematical class at the Prussian Academy of Sciences in Berlin. The descendants of these children, however, were in high positions in Russia in the 19th century. They had thirteen children, of whom only three sons and two daughters survived. In 1733 he married Katharina Gsell, the daughter of the director of the academy of arts.

In 1735 he lost much of his vision in the right eye due to excessive observation of the sun. Euler was the first to publish a systematic introduction to mechanics in 1736: Mechanica sive motus scientia analytice exposita ("Mechanics or motion explained with analytical science"—that is, calculus). Petersburg by Catherine I of Russia and became professor of physics in 1730, with an additional mathematics appointment in 1733. In 1727 Euler was called to St.

When Daniel and Nikolaus Bernoulli asked him to allow his son to study mathematics he finally agreed and Euler began to study mathematics. Paul Euler had attended Jakob Bernoulli's mathematical lectures and respected his family. There Euler met Daniel and Nikolaus Bernoulli, who noticed Euler's skills in mathematics. In 1720 Euler began his studies at the University of Basel.

Although in his childhood he exhibited great mathematical talents, his father wanted him to study theology and become a minister. Leonhard Euler was born in Basel, Switzerland, the son of Paul Euler, a Lutheran minister. . The asteroid 2002 Euler is named in his honour.

He was completely blind for the last seventeen years of his life, during which time he produced almost half of his total output. He dominated 18th century mathematics and deduced many consequences of the newly invented calculus. He is the most prolific mathematician of all time, his collected work filling 75 volumes. Petersburg.

Petersburg, later in Berlin, and then returned to St. He worked as a professor of mathematics in St. Born and educated in Basel, he was a mathematical child prodigy. He is credited with being one of the first to apply calculus to physics.

Leonhard Euler was the first to use the term "function" (defined by Leibniz in 1694) to describe an expression involving various arguments; i.e., y = F(x). He is considered to be one of the greatest mathematicians who ever lived. Leonhard Euler [oi'lər] (April 15, 1707–September 18, 1783) was a Swiss mathematician and physicist. Lexikon der Naturwissenschaftler, Spektrum Akademischer Verlag Heidelberg, 2000.

Fermats letzter Satz, Munich: Deutscher Taschenbuch Verlag. (2000). Singh, Simon. The giant book of scientists: The 100 greatest minds of all time, Sydney: The Book Company.

(1996). Simmons, J. Die großen Deutschen, volume 2, Berlin: Ullstein Verlag. 1956.

Heimpell, Hermann, Theodor Heuss, Benno Reifenberg (editors). ISBN 0-88385-328-0. Euler: The Master of Us All, Washington: Mathematical Association of America. Dunham, William (1999).

English translation Introduction to Analysis of the Infinite by John Blanton (Book I, ISBN 0387968245, Springer-Verlag 1988; Book II, ISBN 0387971327, Springer-Verlag 1989). Introductio in analysin infinitorum. Euler, Leonhard (1748). Euler Leonhardt : "Lettres à une Princesse d'Allemagne " ; free book at : http://www.bookmine.org ;.

"Read Euler: he is our master in everything." —Pierre-Simon Laplace.