|
Balanced Ternary
Balanced ternary is a ternary numeral system (i.e. base 3 with three Numerical digit, digits) that uses a balanced signed-digit representation of the integers in which the digits have the values −1, 0, and 1. This stands in contrast to the standard (unbalanced) ternary system, in which digits have values 0, 1 and 2. The balanced ternary system can represent all integers without using a separate minus sign; the value of the leading non-zero digit of a number has the sign of the number itself. The balanced ternary system is an example of a Non-standard positional numeral systems, non-standard positional numeral system. It was used in some early computers and has also been used to solve balance puzzles. Different sources use different glyphs to represent the three digits in balanced ternary. In this article, T (which resembles a typographical ligature, ligature of the minus sign and 1) represents −1, while 0 and 1 represent themselves. Other conventions include using '−' and '+ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ternary Numeral System
A ternary numeral system (also called base 3 or trinary) has 3 (number), three as its radix, base. Analogous to a bit, a ternary numerical digit, digit is a trit (trinary digit). One trit is equivalent to binary logarithm, log2 3 (about 1.58496) bits of Units of information, information. Although ''ternary'' most often refers to a system in which the three digits are all non–negative numbers; specifically , , and , the adjective also lends its name to the balanced ternary system; comprising the digits −1, 0 and +1, used in comparison logic and ternary computers. Comparison to other bases Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary numeral system, binary. For example, decimal 365 (number), 365 or senary corresponds to binary (nine bits) and to ternary (six digits). However, they are still far less compact than the corresponding representations in bases such as decimal – see below for a compact way to codi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy ( , , ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist. He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis), pioneered the field complex analysis, and the study of permutation groups in abstract algebra. Cauchy also contributed to a number of topics in mathematical physics, notably continuum mechanics. A profound mathematician, Cauchy had a great influence over his contemporaries and successors; Hans Freudenthal stated: : "More concepts and theorems have been named for Cauchy than for any other mathematician (in elasticity alone there are sixteen concepts and theorems named for Cauchy)." Cauchy was a prolific worker; he wrote approximately eight hundred research articles and five complete textbooks on a variety of topics in the fields of mathematics and mathematical physics. Biography Youth and education Cauchy was the son of Lou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repeating Decimal
A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be ''terminating'', and is not considered as repeating. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating. For example, the decimal representation of becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333.... A more complicated example is , whose decimal becomes periodic at the ''second'' digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144.... Another example of this is , which becomes periodic after the decimal point, repeating the 13-digit pattern "1886792452830" forever, i.e. 11.18867924528301886792452830.... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rounding
Rounding or rounding off is the process of adjusting a number to an approximate, more convenient value, often with a shorter or simpler representation. For example, replacing $ with $, the fraction 312/937 with 1/3, or the expression √2 with . Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid false precision, misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as but is known to be accuracy and precision, accurate only to within a few hundred units is usually better stated as "about ". On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix (radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base. For base ten, the subscript is usually assumed and omitted (together with the enclosing parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems Generally, in a system with radix ''b'' (), a string of digits denotes the number , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer science. Knuth has been called the "father of the analysis of algorithms". Knuth is the author of the multi-volume work '' The Art of Computer Programming''. He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process, he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar, Knuth created the WEB and CWEB computer programming systems des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (mathematics)
In mathematics, parity is the Property (mathematics), property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not.. For example, −4, 0, and 82 are even numbers, while −3, 5, 23, and 69 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers with decimals or fractions like 1/2 or 4.6978. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even—as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix Point
alt=Four types of separating decimals: a) 1,234.56. b) 1.234,56. c) 1'234,56. d) ١٬٢٣٤٫٥٦., Both a full_stop.html" ;"title="comma and a full stop">comma and a full stop (or period) are generally accepted decimal separators for international use. The apostrophe and Arabic decimal separator are also used in certain contexts. A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for the thousands separator used in digit grouping. Any such symbol can be called a decimal mark, decimal marker, or decimal sign. Symbol-specific names are also used; decimal point and decimal comma refer to a dot (either baseline or middle) and comma respectively, when it is used as a decimal separator; these are the usual terms used in English, with the aforementioned generic te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recurrence Relation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surjective Map
In mathematics, a surjective function (also known as surjection, or onto function ) is a function such that, for every element of the function's codomain, there exists one element in the function's domain such that . In other words, for a function , the codomain is the image of the function's domain . It is not required that be unique; the function may map one or more elements of to the same element of . The term ''surjective'' and the related terms ''injective'' and ''bijective'' were introduced by Nicolas Bourbaki, a group of mainly French 20th-century mathematicians who, under this pseudonym, wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. The French word '' sur'' means ''over'' or ''above'', and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain. Any function induces a surjection by restricting its codomain to the image of its domain. Every surject ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String (computer Science)
In computer programming, a string is traditionally a sequence of character (computing), characters, either as a literal (computer programming), literal constant or as some kind of Variable (computer science), variable. The latter may allow its elements to be Immutable object, mutated and the length changed, or it may be fixed (after creation). A string is often implemented as an array data structure of bytes (or word (computer architecture), words) that stores a sequence of elements, typically characters, using some character encoding. More general, ''string'' may also denote a sequence (or List (abstract data type), list) of data other than just characters. Depending on the programming language and precise data type used, a variable (programming), variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears lit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concatenation
In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalizations of concatenation theory, also called string theory, string concatenation is a primitive notion. Syntax In many programming languages, string concatenation is a binary infix operator, and in some it is written without an operator. This is implemented in different ways: * Overloading the plus sign + Example from C#: "Hello, " + "World" has the value "Hello, World". * Dedicated operator, such as . in PHP, & in Visual Basic, and , , in SQL. This has the advantage over reusing + that it allows implicit type conversion to string. * string literal concatenation, which means that adjacent strings are concatenated without any operator. Example from C: "Hello, " "World" has the value "Hello, World". In many scientific publications or standards the con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
