Viète's formulaIn mathematics, Viète's formula is the following infinite product of nested radicals representing twice the reciprocal of the mathematical constant pi: It can also be represented as: The formula is named after François Viète, who published it in 1593. As the first formula of European mathematics to represent an infinite process, it can be given a rigorous meaning as a limit expression, and marks the beginning of mathematical analysis. It has linear convergence, and can be used for calculations of pi, but other methods before and since have led to greater accuracy.
Nested radicalIn algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include which arises in discussing the regular pentagon, and more complicated ones such as Some nested radicals can be rewritten in a form that is not nested. For example, Another simple example, Rewriting a nested radical in this way is called denesting. This is not always possible, and, even when possible, it is often difficult.
Madhava seriesIn mathematics, a Madhava series is one of the three Taylor series expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th century Kerala by the mathematician and astronomer Madhava of Sangamagrama (c. 1350 – c. 1425) or his followers in the Kerala school of astronomy and mathematics. Using modern notation, these series are: All three series were later independently discovered in 17th century Europe.
Machin-like formulaIn mathematics, Machin-like formulae are a popular technique for computing pi (the ratio of the circumference to the diameter of a circle) to a large number of digits. They are generalizations of John Machin's formula from 1706: which he used to compute pi to 100 decimal places. Machin-like formulas have the form where is a positive integer, are signed non-zero integers, and and are positive integers such that .
William OughtredWilliam Oughtred (5 March 1574 – 30 June 1660), also Owtred, Uhtred, etc., was an English mathematician and Anglican clergyman. After John Napier invented logarithms and Edmund Gunter created the logarithmic scales (lines, or rules) upon which slide rules are based, Oughtred was the first to use two such scales sliding by one another to perform direct multiplication and division. He is credited with inventing the slide rule in about 1622. He also introduced the "×" symbol for multiplication and the abbreviations "sin" and "cos" for the sine and cosine functions.
Reuleaux triangleA Reuleaux triangle ʁœlo is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed from the intersection of three circular disks, each having its center on the boundary of the other two. Constant width means that the separation of every two parallel supporting lines is the same, independent of their orientation.
Isaac BarrowIsaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for proof of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve. He is also notable for being the inaugural holder of the prestigious Lucasian Professorship of Mathematics, a post later held by his student, Isaac Newton.
List of mathematical jargonThe language of mathematics has a vast vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in lectures, and sometimes in print, as informal shorthand for rigorous arguments or precise ideas. Much of this is common English, but with a specific non-obvious meaning when used in a mathematical sense. Some phrases, like "in general", appear below in more than one section.
Lemniscate constantIn mathematics, the lemniscate constant π is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter, analogous to the definition of pi for the circle. Equivalently, the perimeter of the lemniscate is 2π. The lemniscate constant is closely related to the lemniscate elliptic functions and approximately equal to 2.62205755. The symbol π is a cursive variant of π; see Pi § Variant pi. Gauss's constant, denoted by G, is equal to π /pi ≈ 0.8346268.
Ancient Egyptian mathematicsAncient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt () 3000 to c. , from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplication and fractions. Evidence for Egyptian mathematics is limited to a scarce amount of surviving sources written on papyrus.
