Historically, the problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond d ' Alembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange.

* Leonhard Euler solves the Basel problem, first posed by Pietro Mengoli in 1644, and the Seven Bridges of Königsberg problem.

Later, the mathematicians Joseph Louis Lagrange and Leonhard Euler provided an analytical solution to the problem.

Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock.

In the same way the hyperspherical space of 3D rotations can be parameterized by three angles ( Euler angles ), but any such parameterization is degenerate at some points on the hypersphere, leading to the problem of gimbal lock.

Euler proved that the problem has no solution.

As in the classic problem, no Euler walk is possible ; coloring does not affect this.

* Ed Sandifer, How Euler Did It -- Estimating the Basel problem ( 2003 )

In Europe this problem was studied by Brouncker, Euler and Lagrange.

The Euler – Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the tautochrone problem.

Lagrange solved this problem in 1755 and sent the solution to Euler.

They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736.

The problem of the gimbal lock appears when one uses the Euler angles in an application of mathematics, for example in a computer program ( 3D modeling, embedded navigation systems, 3D video games, metaverses, ...).

This similarity between linear coordinates and angular coordinates makes Euler angles very intuitive, but unfortunately they suffer from the gimbal lock problem.

Note that the gimbal lock problem does not make Euler angles " wrong " ( they always play at least their role of a well-defined coordinates system ), but it makes them unsuited for some practical applications.

For example if we use three angles ( Euler angles ), such parameterization is degenerate at some points on the hypersphere, leading to the problem of gimbal lock.

Gimbal lock is a problem when the derivative of the map is not full rank, which occurs with Euler angles and Tait – Bryan angles, but not for the other choices.

* Leonhard Euler solves the Basel problem, first posed by Pietro Mengoli in 1644, and the Seven Bridges of Königsberg problem.

However, when the flow problem is put into a non-dimensional form, the viscous Navier – Stokes equations converge for increasing Reynolds numbers towards the inviscid Euler equations, suggesting that the flow should converge towards the inviscid solutions of potential flow theory – having the zero drag of the d ' Alembert paradox.

* The Basel problem is posed by Pietro Mengoli, and will puzzle mathematicians until solved by Leonhard Euler in 1731.

This very equation was posed as a problem in 1657 by the French mathematician Pierre de Fermat, but its solution was unknown in Europe until the time of Euler in the 18th century.

The Basel problem is a famous problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1735.

The Euler – MacLaurin formula can be understood as a curious application of some ideas from Banach spaces and functional analysis.

The Euler equations were extended to incorporate the effects of viscosity in the first half of the 1800s, resulting in the Navier-Stokes equations.

They were first studied by Giulio Fagnano and Leonhard Euler.

The nobility were suspicious of the academy's foreign scientists, and thus cut funding and caused other difficulties for Euler and his colleagues.

Euler wrote over 200 letters to her in the early 1760s, which were later compiled into a best-selling volume entitled Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess.

The development of infinitesimal calculus was at the forefront of 18th Century mathematical research, and the Bernoullis — family friends of Euler — were responsible for much of the early progress in the field.

Starting around the 15th century, new algorithms based on infinite series revolutionized the computation of, and were used by mathematicians including Madhava of Sangamagrama, Isaac Newton, Leonhard Euler, Carl Friedrich Gauss, and Srinivasa Ramanujan.

The values of the Riemann zeta function at even positive integers were computed by Euler.

Other attempts were made by Euler ( 1749 ), de Foncenex ( 1759 ), Lagrange ( 1772 ), and Laplace ( 1795 ).

These last four attempts assumed implicitly Girard's assertion ; to be more precise, the existence of solutions was assumed and all that remained to be proved was that their form was a + bi for some real numbers a and b. In modern terms, Euler, de Foncenex, Lagrange, and Laplace were assuming the existence of a splitting field of the polynomial p ( z ).

Venn diagrams are very similar to Euler diagrams, which were invented by Leonhard Euler ( 1708 – 1783 ) in the 18th century.

Venn diagrams and Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement in the 1960s.

The components of the angular velocity pseudovector were first calculated by Leonhard Euler using his Euler angles and an intermediate frame made out of the intermediate frames of the construction:

Under this heading, the Board made many lesser awards, including some awards in total £ 5, 000 made to John Harrison before he received his main prize, an award of £ 3, 000 to the widow of Tobias Mayer, whose lunar tables were the basis of the lunar data in the early decades of the Nautical Almanac, £ 300 to Leonhard Euler for his ( assumed ) contribution to the work of Mayer, £ 50 each to Richard Dunthorne and Israel Lyons for contributing methods to shorten the calculations connected with lunar distances, and awards made to the designers of improvements in chronometers.

In solving it, he developed new methods that were refined by Leonhard Euler into what the latter called ( in 1766 ) the calculus of variations.

These were developed intensively from the second half of the eighteenth century ( by, for example, D ' Alembert, Euler, and Lagrange ) until the 1930s.

In the eighteenth century, two of the innovators of mathematical physics were Swiss: Daniel Bernoulli ( for contributions to fluid dynamics, and vibrating strings ), and, more especially, Leonhard Euler, ( for his work in variational calculus, dynamics, fluid dynamics, and many other things ).

Amongst the fruits of his industry may be mentioned a laborious investigation of the disturbances of Jupiter by Saturn, the results of which were employed and confirmed by Euler in his prize essay of 1748 ; a series of lunar observations extending over fifty years ; some interesting researches in terrestrial magnetism and atmospheric electricity, in the latter of which he detected a regular diurnal period ; and the determination of the places of a great number of stars, including at least twelve separate observations of Uranus, between 1750 and its discovery as a planet.

However, the concept was developed in 1727 by Leonhard Euler, and the first experiments that used the concept of Young's modulus in its current form were performed by the Italian scientist Giordano Riccati in 1782, predating Young's work by 25 years.

Euler noted that if there were only a finite number of primes, then the product on the right would clearly converge, contradicting the divergence of the harmonic series.

Some coordinate systems in mathematics behave as if there were real gimbals used to measure the angles, notably Euler angles.

The digital forms of Euler characteristic theorem and Gauss – Bonnet theorem were obtained by Chen et al.