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 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, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation ; every complex number can be expressed in the form , where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number , a is called the real part, and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world.
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants . The determinant of a matrix A is denoted det(A), det A, or |A|.
In mathematics, the Fibonacci numbers, commonly denoted Fn , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes from 1 and 2. Starting from 0 and 1, the first few values in the sequence are:
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
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, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, and (x – 2)(x + 2) is a factorization of the polynomial x2 – 4.
In mathematics, Stirling's approximation is an 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.
Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe. Thus Graham's number cannot be expressed even by physical universe-scale power towers of the form .
The year 1707 in science and technology involved some significant events.
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by , is the factor by which the eigenvector is scaled.
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.
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.
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.
A timeline of algebra and geometry
In mathematics, Clausen's formula, found by Thomas Clausen (1828), expresses the square of a Gaussian hypergeometric series as a generalized hypergeometric series. It states
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
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 Law is a survival model applied in actuarial science, named for Abraham de Moivre. It is a simple law of mortality based on a linear survival function.
