Johann Gutenberg

The Gutenberg Galaxy and Project Gutenberg commemorate Gutenberg's name. Hence, you cannot visit each of the bridges of Königsberg without retracing your steps. There are many statues of Gutenberg in Germany, one of the more famous being a work by Thorvaldsen, in Mainz, which is also home to the Gutenberg Museum. The seven bridges problem is neither an Euler circuit nor Euler path. The term incunabulum refers to a western printed book produced between the first work of Gutenberg and the end of the year 1500. This means that it is possible to travel each line exactly once without retracing your steps, but you will not end where you began. Gutenberg's inventions are sometimes considered the turning point from the Mediaeval Era to the Early Modern Period. An Euler path has exactly two odd vertices.

Literacy also increased as a result. 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. It fed the growing Renaissance, and since it greatly facilitated scientific publishing, was a major factor in originating the scientific revolution. An Euler circuit has all its points of even degree. Although Gutenberg was financially unsuccessful in his lifetime, his invention spread quickly, and news and books began to travel across Europe far faster than before. 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). The Bible was not Gutenberg's first printed work, for he produced approximately two dozen editions of Ars Minor, a portion of Aelius Donatus's schoolbook on Latin grammar, the first edition of which is believed to have been printed between 1451 and 1452. The solution to the seven bridges problem reduced the land masses to points and the bridges to lines (or edges) connecting those points.

As of 2003, the Gutenberg Bible census includes 11 complete copies on vellum, 1 copy of the New Testament only on vellum, 48 substantially complete integral copies on paper, with another divided copy on paper, and an illiminated page (the Bagford fragment). 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. The Gutenberg Bibles surviving today are sometimes called the oldest surviving books printed with movable type, although the oldest surviving book was published in Korea in 1377. 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. Gutenberg was also known to spend what little money he had on alcohol, so the Archbishop arranged for him to be paid in food and lodging, instead of coin. The Euler characteristic of a simply-connected manifold such as a sphere or a plane is 2. Gutenberg was subsidized by the Archbishop of Mainz until his death. 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.

So, while Gutenberg ran a print shop until just before his death in Mainz in 1468, Fust became the first printer to publish a book with his name on it. The theorem also applies to any planar graph. Fust sued, and the court's ruling not only effectively bankrupted Gutenberg, it awarded control of the type used in his Bible, plus much of the printing equipment, to Fust. i.e.: F - E + V = 2. The money Gutenberg earned at the fair was not enough to pay Fust back for his investments. Given such a polyhedron, the sum of the vertices and the faces is always the number of edges plus two. The one copy of the Biblia Sacra dated 1455 went to Paris and was dated by the binder. 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.

This was the equivalent of approximately three years' wages for an average clerk, but it was significantly cheaper than a handwritten Bible, which could take a single monk 20 years to transcribe. 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. In 1455 Gutenberg demonstrated the power of the printing press by selling copies of a two-volume Bible (Biblia Sacra) for 300 florins each. 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". His first efforts enabled him to mass-produce indulgences, printed slips of paper sold by the Catholic Church to remit the temporal punishments in Purgatory for sins committed in this life. He is a co-discoverer of the Euler-Maclaurin formula which is an extremely useful tool for calculation of difficult integrals, sums, and series. Knowing that wood-block type involved a great deal of time and expense to reproduce because it had to be hand carved, Gutenberg concluded that metal type could be reproduced much more quickly once a single mould had been fashioned. Also in 1735, Euler defined the Euler-Mascheroni constant useful for differential equations:.

Gutenberg began experimenting with metal typography after he had moved from his native town of Mainz to Strassburg (then in Germany, now Strasbourg, France) around 1430. What Richard Feynman called "The most remarkable formula in mathematics" (more commonly called Euler's identity) is an easy consequence:. Gutenberg was a poor businessman, and made little money from his printing system. In essence, all functions studied in elementary analysis are either variations of the exponential function or they are polynomials. Gutenberg certainly introduced efficient methods into book production, leading to a boom in the production of texts in Europe, in large part due to the popularity of the Gutenberg Bibles, the first mass-produced work, starting on February 23, 1455. This is Euler's formula, which establishes the central role of the exponential function. Some also claim Dutchman Laurens Coster as the first European to invent movable type. He also showed the usefulness, consistency, and simplicity of defining the exponent of an imaginary number by means of the formula.

It is not clear whether Gutenberg knew of these existing techniques or invented them independently. where ζ(s) is the Riemann zeta function. The Koreans and Chinese knew about movable metal types at the time, but due to the complex nature of the Chinese writing system, printed material was not as abundant as that of Renaissance Europe. Euler established his fame in 1735 by solving the long-standing Basel problem:. Block printing, whereby individual sheets of paper were pressed into wooden blocks with the text and illustrations carved in, was in use in Europe and East Asia long before Gutenberg. 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.

Gutenberg was born in the German city of Mainz, as the son of a merchant named Friele Gensfleisch zur Laden, who adopted the surname "zum Gutenberg" after the name of the neighborhood into which the family had moved. 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. By combining these elements into a production system, he allowed for the rapid printing of written materials and an information explosion in Renaissance Europe. In number theory, Euler invented the totient function. Tradition credits him with inventing movable type in Europe, an improvement on the block printing already in use there. The most famous of these approximations is known as Euler's method. Johannes Gensfleisch zur Laden zum Gutenberg (circa 1398 – February 3, 1468), a German metal-worker and inventor, achieved fame for his contributions to the technology of printing during the 1440s, including a type metal alloy and oil-based inks, a mould for casting type accurately, and a new kind of printing press based on presses used in wine-making. In particular, he is known for creating a series of approximations which are used in computational mechanics.

World Almanac's Ten Most Influential People of the Second Millennium. Euler made important contributions to the theory of differential equations. William Caxton. They are interesting chiefly because of the existence of shock waves. Francysk Skaryna. These equations are formally identical to the Navier-Stokes equations with zero viscosity. Incunabulum. He also deduced the Euler equations, a set of laws of motion in fluid dynamics, directly from Newton's laws of motion.

Typography. 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. Printing. 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.