LEONHARD EULER FUN FACTS HOW TO

He discovered the imaginary logarithms of negative numbers and showed that each complex number has an infinite number of logarithms.Įuler’s textbooks in calculus, Institutiones calculi differentialis in 1755 and Institutiones calculi integralis in 1768–70, have served as prototypes to the present because they contain formulas of differentiation and numerous methods of indefinite integration, many of which he invented himself, for determining the work done by a force and for solving geometric problems, and he made advances in the theory of linear differential equations, which are useful in solving problems in physics. He was responsible for treating trigonometric functions-i.e., the relationship of an angle to two sides of a triangle-as numerical ratios rather than as lengths of geometric lines and for relating them, through the so-called Euler identity (e iθ = cos θ + i sin θ), with complex numbers (e.g., 3 + 2 Square root of √ −1). He is known for familiar results in elementary geometry-for example, the Euler line through the orthocentre (the intersection of the altitudes in a triangle), the circumcentre (the centre of the circumscribed circle of a triangle), and the barycentre (the “centre of gravity,” or centroid) of a triangle. He did for modern analytic geometry and trigonometry what the Elements of Euclid had done for ancient geometry, and the resulting tendency to render mathematics and physics in arithmetical terms has continued ever since.

In 1748, in his Introductio in analysin infinitorum, he developed the concept of function in mathematical analysis, through which variables are related to each other and in which he advanced the use of infinitesimals and infinite quantities. Petersburg Academy, which granted him a pension.Įuler's identity: the most beautiful of all equations See all videos for this article

Then, invited by Frederick the Great in 1741, he became a member of the Berlin Academy, where for 25 years he produced a steady stream of publications, many of which he contributed to the St. Overtaxing himself, Euler in 1735 lost the sight of one eye. By means of his numerous books and memoirs that he submitted to the academy, Euler carried integral calculus to a higher degree of perfection, developed the theory of trigonometric and logarithmic functions, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of pure mathematics. Petersburg Academy of Sciences and in 1733 succeeded Daniel Bernoulli to the chair of mathematics. Petersburg, where he became an associate of the St. He not only made decisive and formative contributions to the subjects of geometry, calculus, mechanics, and number theory but also developed methods for solving problems in observational astronomy and demonstrated useful applications of mathematics in technology and public affairs.Įuler’s mathematical ability earned him the esteem of Johann Bernoulli, one of the first mathematicians in Europe at that time, and of his sons Daniel and Nicolas. Petersburg, Russia), Swiss mathematician and physicist, one of the founders of pure mathematics. Leonhard Euler, (born April 15, 1707, Basel, Switzerland-died September 18, 1783, St.

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LEONHARD EULER FUN FACTS HOW TO

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Leonhard euler fun facts