E (mathematical constant)The number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of natural logarithms. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series It is also the unique positive number a such that the graph of the function y = ax has a slope of 1 at x = 0.
ExponentiationIn mathematics, exponentiation is an operation involving two numbers, the base and the exponent or power. Exponentiation is written as bn, where b is the base and n is the power; this is pronounced as "b (raised) to the (power of) n". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: The exponent is usually shown as a superscript to the right of the base.
FactorialIn mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book Sefer Yetzirah.
Natural logarithmThe natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.
John NapierJohn Napier of Merchiston. (ˈneɪpiər; 1 February 1550 – 4 April 1617), nicknamed Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioannes Neper. John Napier is best known as the discoverer of logarithms. He also invented the so-called "Napier's bones" and made common the use of the decimal point in arithmetic and mathematics. Napier's birthplace, Merchiston Tower in Edinburgh, is now part of the facilities of Edinburgh Napier University.
Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
MathematicsMathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.
PiThe number pi (paɪ; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number pi appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern.
Floating-point arithmeticIn computing, floating-point arithmetic (FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. For example, 12.345 is a floating-point number in base ten with five digits of precision: However, unlike 12.345, 12.3456 is not a floating-point number in base ten with five digits of precision—it needs six digits of precision; the nearest floating-point number with only five digits is 12.
Geometric meanIn mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite set of real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers a1, a2, ..., an, the geometric mean is defined as or, equivalently, as the arithmetic mean in logscale: Most commonly the numbers are restricted to being non-negative, to avoid complications related to negative numbers not having real roots, and frequently they are restricted to being positive, to enable the use of logarithms.
