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Euler's Disk, invented between 1987 and 1990 by Joseph Bendik, [1] is a trademarked scientific educational toy. [2] It is used to illustrate and study the dynamic system of a spinning and rolling disk on a flat or curved surface. It has been the subject of several scientific papers. [3] Bendik named the toy after mathematician Leonhard Euler. [4]
Euler is regarded as arguably the most prolific contributor in the history of mathematics and science, and the greatest mathematician of the 18th century. [12] [11] His 866 publications and his correspondence are being collected in the Opera Omnia Leonhard Euler which, when completed, will consist of 81 quartos.
Euler Committee of the Swiss Academy of Sciences; Euler equations (fluid dynamics) Euler function; Euler method; Euler numbers; Euler number (physics) Euler–Bernoulli beam theory; Euler–Lagrange equation; Euler–Lotka equation; Euler–Maclaurin formula; Euler–Maruyama method; Euler–Poisson–Darboux equation; Euler–Rodrigues formula ...
The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field. His seminal work had a profound impact in numerous areas of mathematics and he is widely credited for introducing and popularizing modern notation and terminology.
Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis. The polynomials presently known as Eulerian polynomials in Euler's work from 1755, Institutiones calculi differentialis, part 2, p. 485/6. The coefficients of these polynomials are known as Eulerian numbers.
In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers. The original such product was given for the sum of all positive integers raised to a certain power as proven by Leonhard Euler .
The multiplicative inverse of its generating function is the Euler function; by Euler's pentagonal number theorem this function is an alternating sum of pentagonal number powers of its argument. Srinivasa Ramanujan first discovered that the partition function has nontrivial patterns in modular arithmetic , now known as Ramanujan's congruences .
In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem. It was proposed by Leonhard Euler in 1769. It states that for all integers n and k greater than 1, if the sum of n many k th powers of positive integers is itself a k th power, then n is greater than or equal to k :