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## Credo Reference

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## Mathematics

- Addition: Topic PageA mathematical operation performed on two numbers (addends) to give a third (the sum). It can also be regarded as the process of increasing one number (the addend) by another (the augend). Addition of integers is equivalent to the process of accumulating sets of objects. Addition of fractions is performed by putting each in terms of a common denominator, and adding the numerators.
- Algebra Topic PageBranch of mathematics in which the general properties of numbers are studied by using symbols, usually letters, to represent variables and unknown quantities.
- Calculus: Topic PageCalculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value. The English physicist Isaac Newton and the German mathematician G. W. Leibniz, working independently, developed the calculus during the 17th cent. The calculus and its basic tools of differentiation and integration serve as the foundation for the larger branch of mathematics known as analysis.
- Geometry Topic PageBranch of mathematics concerned with the properties of space, usually in terms of plane (two-dimensional, or 2D) and solid (three-dimensional, or 3D) figures. The subject is usually divided into pure geometry, which embraces roughly the plane and solid geometry dealt with in Greek mathematician Euclid's Stoicheia/Elements, and analytical or coordinate geometry, in which problems are solved using algebraic methods. A third, quite distinct, type includes the non-Euclidean geometries.
- Mathematics Topic PageMathematics, deductive study of numbers, geometry, and various abstract constructs, or structures; the latter often "abstract" the features common to several models derived from the empirical, or applied, sciences, although many emerge from purely mathematical or logical considerations. Mathematics is very broadly divided into foundations, algebra, analysis, geometry, and applied mathematics, which includes theoretical computer science.
- Multiplication Topic Pagemathematical operation in which two numbers are combined to give a third number (the product). It is denoted by a x b or a x b, or (for symbols) by ab. Multiplication of integers can be regarded as repeated addition: for example, 2 x 3 = 6 is the integer obtained by adding three 2's (2 + 2 + 2). This is the same as adding two 3's (3 + 3), a demonstration of the commutative nature of multiplication of numbers.
- Non Euclidean Geometry: Topic PageNon-Euclidean geometry, branch of geometry in which the fifth postulate of Euclidean geometry, which allows one and only one line parallel to a given line through a given external point, is replaced by one of two alternative postulates. Allowing two parallels through any external point, the first alternative to Euclid's fifth postulate, leads to the hyperbolic geometry developed by the Russian N. I. Lobachevsky in 1826 and independently by the Hungarian Janos Bolyai in 1832. The second alternative, which allows no parallels through any external point, leads to the elliptic geometry developed by the German Bernhard Riemann in 1854. The results of these two types of non-Euclidean geometry are identical with those of Euclidean geometry in every respect except those propositions involving parallel lines, either explicitly or implicitly (as in the theorem for the sum of the angles of a triangle).
- Numerals: Topic PageNumeral, symbol denoting a number. The symbol is a member of a family of marks, such as letters, figures, or words, which alone or in a group represent the members of a numeration system. The earliest numerals were undoubtedly marks used to make a tally of a count of a number of acts or objects, one mark per object. This would be a unary system. About 3000 b.c. the ancient Egyptians began to use a demotic (a simplified cursive style of hieroglyphics) system of numerals based on a decimal system. The Egyptians formed numerals by putting basic symbols together. This system did not include a symbol for zero nor did it use the principle of place value. About a thousand years later, the Babylonians devised a system of wedge-shaped cuneiform symbols in conjunction with a numeration system based on a sexigesimal (base 60) numeration system. The majority of ancient peoples, however, including the Chinese, the Greeks, the Romans, and the Hebrews, used the decimal system.
- Percentage: Topic PageWay of representing a number as a fraction of 100. For example, 45 percent (45%) equals 45/100, and 45% of 20 is 45/100 × 20 = 9.
- Trigonometry Topic PageTrigonometry [Gr.,=measurement of triangles], a specialized area of geometry concerned with the properties of and relations among the parts of a triangle. Spherical trigonometry is concerned with the study of triangles on the surface of a sphere rather than in the plane; it is of considerable importance in surveying, navigation, and astronomy.