Physics
- Willem 's Gravesande publishes experimental evidence that the formula for kinetic energy of a body in motion is .
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The year 1722 in science and technology involved some significant events.
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. For example, for n = 4,
In mathematics, the determinant is a scalar value that is a certain function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the corresponding linear map is an isomorphism. The determinant of a product of matrices is the product of their determinants.
In mathematics, Euler's identity is the equality
Joseph Louis Gay-Lussac was a French chemist and physicist. He is known mostly for his discovery that water is made of two parts hydrogen and one part oxygen by volume, for two laws related to gases, and for his work on alcohol–water mixtures, which led to the degrees Gay-Lussac used to measure alcoholic beverages in many countries.
In mathematics, de Moivre's formula states that for any real number x and integer n it holds that
Abraham de Moivre FRS was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.
In mathematics, Stirling's approximation is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre.
The year 1707 in science and technology involved some significant events.
Prof Paul Sabatier FRS(For) HFRSE was a French chemist, born in Carcassonne. In 1912, Sabatier was awarded the Nobel Prize in Chemistry along with Victor Grignard. Sabatier was honoured for his work improving the hydrogenation of organic species in the presence of metals.
In linear algebra, it is often important to know which vectors have their directions unchanged by a given linear transformation. An eigenvector or characteristic vector is such a vector. More precisely, an eigenvector of a linear transformation is scaled by a constant factor when the linear transformation is applied to it: . The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor .
Jacques Philippe Marie Binet was a French mathematician, physicist and astronomer born in Rennes; he died in Paris, France, in 1856. He made significant contributions to number theory, and the mathematical foundations of matrix algebra which would later lead to important contributions by Cayley and others. In his memoir on the theory of the conjugate axis and of the moment of inertia of bodies he enumerated the principle now known as Binet's theorem. He is also recognized as the first to describe the rule for multiplying matrices in 1812, and Binet's formula expressing Fibonacci numbers in closed form is named in his honour, although the same result was known to Abraham de Moivre a century earlier.
Moivre may refer to:
James Dodson FRS (c.1705–1757) was a British mathematician, actuary and innovator in the insurance industry.
Ars Conjectandi is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.
The following is a timeline of key developments of geometry:
In mathematics, Clausen's formula, found by Thomas Clausen, expresses the square of a Gaussian hypergeometric series as a generalized hypergeometric series. It states
The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies. Its study in Europe dates to the work of Leonardo Fibonacci in the 13th century AD, which introduced Arabian and Indian ideas to the continent. It has continued to be studied in the modern era.
de Moivre's theorem may be:
Johann Sebastian Bach's chorale cantata cycle is the year-cycle of church cantatas he started composing in Leipzig from the first Sunday after Trinity in 1724. It followed the cantata cycle he had composed from his appointment as Thomaskantor after Trinity in 1723.
