|
Senary
A senary () numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime (2 and 3). As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to senary. In turn, the senary logic refers to an extension of Jan Łukasiewicz's and Stephen Cole Kleene's ternary logic systems adjusted to explain the logic of statistical tests and missing data patterns in sciences using empirical methods. Formal definition The standard set of digits in senary is given by \mathcal_6 = \lbrace 0, 1, 2, 3, 4, 5\rbrace, with a linear order 0 < 1 < 2 < 3 < 4 < 5. Let be the |
Superior Highly Composite Number
In mathematics, a superior highly composite number is a natural number which has the highest ratio of its number of divisors to ''some'' positive power of itself than any other number. It is a stronger restriction than that of a highly composite number, which is defined as having more divisors than any smaller positive integer. The first 10 superior highly composite numbers and their factorization are listed. For a superior highly composite number ''n'' there exists a positive real number ''ε'' such that for all natural numbers ''k'' smaller than ''n'' we have :\frac\geq\frac and for all natural numbers ''k'' larger than ''n'' we have :\frac>\frac where ''d(n)'', the divisor function, denotes the number of divisors of ''n''. The term was coined by Ramanujan (1915). For example, the number with the most divisors per square root of the number itself is 12; this can be demonstrated using some highly composites near 12. \frac\approx 1.414, \frac=1.5, \frac\approx 1.633, \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duodecimal
The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation numeral system using twelve as its base. The number twelve (that is, the number written as "12" in the decimal numerical system) is instead written as "10" in duodecimal (meaning "1 dozen and 0 units", instead of "1 ten and 0 units"), whereas the digit string "12" means "1 dozen and 2 units" (decimal 14). Similarly, in duodecimal, "100" means "1 gross", "1000" means "1 great gross", and "0.1" means "1 twelfth" (instead of their decimal meanings "1 hundred", "1 thousand", and "1 tenth", respectively). Various symbols have been used to stand for ten and eleven in duodecimal notation; this page uses and , as in hexadecimal, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , , 10. The Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal) use turned digits in their published ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numeral System
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using Numerical digit, digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number ''eleven'' in the decimal numeral system (used in common life), the number ''three'' in the binary numeral system (used in computers), and the number ''two'' in the unary numeral system (e.g. used in Tally marks, tallying scores). The number the numeral represents is called its value. Not all number systems can represent all numbers that are considered in the modern days; for example, Roman numerals have no zero. Ideally, a numeral system will: *Represent a useful set of numbers (e.g. all integers, or rational numbers) *Give every number represented a unique representation (or at least a standard representation) *Reflec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication Table
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 × 9. History In pre-modern time The oldest known multiplication tables were used by the Babylonians about 4000 years ago. However, they used a base of 60. The oldest known tables using a base of 10 are the Chinese decimal multiplication table on bamboo strips dating to about 305 BC, during China's Warring States period. The multiplication table is sometimes attributed to the ancient Greek mathematician Pythagoras (570–495 BC). It is also called the Table of Pythagoras in many languages (for example French, Italian and Russian), so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number (sports)
In team sports, the number, often referred to as the uniform number, squad number, jersey number, shirt number, sweater number, or similar (with such naming differences varying by sport and region) is the number worn on a player's uniform, to identify and distinguish each player (and sometimes others, such as coaches and officials) from others wearing the same or similar uniforms. The number is typically displayed on the rear of the jersey, often accompanied by the surname. Sometimes it is also displayed on the front and/or sleeves, or on the player's shorts or headgear. It is used to identify the player to officials, other players, official scorers, and spectators; in some sports, it is also indicative of the player's position. The International Federation of Football History and Statistics, an organization of association football historians, traces the origin of numbers to a 1911 Australian rules football match in Sydney, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NCAA Basketball
In United States colleges, top-tier basketball is governed by collegiate athletic bodies including National Collegiate Athletic Association (NCAA), the National Association of Intercollegiate Athletics (NAIA), the United States Collegiate Athletic Association (USCAA), the National Junior College Athletic Association (NJCAA), and the National Christian College Athletic Association (NCCAA). Each of these various organizations is subdivided into one to three divisions, based on the number and level of scholarships that may be provided to the athletes. Each organization has different conferences to divide up the teams into groups. Teams are selected into these conferences depending on the location of the schools. These conferences are put in due to the regional play of the teams and to have a structural schedule for each team to play for the upcoming year. During conference play the teams are ranked not only through the entire NCAA, but the conference as well in which they have tourn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unary Numeral System
The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number ''N'', a symbol representing 1 is repeated ''N'' times. In the unary system, the number 0 (zero) is represented by the empty string, that is, the absence of a symbol. Numbers 1, 2, 3, 4, 5, 6, ... are represented in unary as 1, 11, 111, 1111, 11111, 111111, ... Unary is a Bijective numeration, bijective numeral system. However, because the value of a digit does not depend on its position, it is not a form of positional notation, and it is unclear whether it would be appropriate to say that it has a Radix, base (or "radix") of 1 (number), 1, as it behaves differently from all other bases. The use of tally marks in counting is an application of the unary numeral system. For example, using the tally mark | (𝍷), the number 3 is represented as |||. In East Asian cultures, the number 3 is represented as wikt:三#Translingual, 三, a character drawn with th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Number Gestures
Chinese number gestures are a method to signify the natural numbers one through ten using one hand. This method may have been developed to bridge the many varieties of Chinese—for example, the numbers 4 () and 10 () are hard to distinguish in some dialects. Some suggest that it was also used by business people during bargaining (i.e., to convey a bid by feeling the hand gesture in a sleeve) when they wish for more privacy in a public place. These gestures are fully integrated into Chinese Sign Language. Methods While the five digits on one hand can easily express the numbers one through five, six through ten have special signs that can be used in commerce or day-to-day communication. The gestures are rough representations of the Chinese numeral characters they represent. The system varies in practice, especially for the representation of "7" to "10". Two of the systems are listed below: * Six ( 六) **The little finger and thumb are extended, other fingers closed, sometime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positional Notation
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred (however, the value may be negated if placed before another digit). In modern positional systems, such as the decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string. The Babylonian numeral system, base 60, was the first positional system to be developed, and its influence is present today ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product (mathematics)
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called ''factors''. For example, 30 is the product of 6 and 5 (the result of multiplication), and x\cdot (2+x) is the product of x and (2+x) (indicating that the two factors should be multiplied together). The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the ''commutative law'' of multiplication. When matrices or members of various other associative algebras are multiplied, the product usually depends on the order of the factors. Matrix multiplication, for example, is non-commutative, and so is multiplication in other algebras in general as well. There are many different kinds of products in mathematics: besides being able to multiply just numbers, polynomials or matrices, one can also define products on many different algebraic structures. Product of two numbers Product of a seque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Casting Out Nines
Casting out nines is any of three arithmetical procedures: *Adding the decimal digits of a positive whole number, while optionally ignoring any 9s or digits which sum to a multiple of 9. The result of this procedure is a number which is smaller than the original whenever the original has more than one digit, leaves the same remainder as the original after division by nine, and may be obtained from the original by subtracting a multiple of 9 from it. The name of the procedure derives from this latter property. *Repeated application of this procedure to the results obtained from previous applications until a single-digit number is obtained. This single-digit number is called the "digital root" of the original. If a number is divisible by 9, its digital root is 9. Otherwise, its digital root is the remainder it leaves after being divided by 9. *A sanity test in which the above-mentioned procedures are used to check for errors in arithmetical calculations. The test is carried ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Totative
In number theory, a totative of a given positive integer is an integer such that and is coprime to . Euler's totient function φ(''n'') counts the number of totatives of ''n''. The totatives under multiplication modulo ''n'' form the multiplicative group of integers modulo ''n''. Distribution The distribution of totatives has been a subject of study. Paul Erdős conjectured that, writing the totatives of ''n'' as : 0 < a_1 < a_2 \cdots < a_ < n , the mean square gap satisfies : for some constant ''C'', and this was proven by and Hugh Montgomery. See also * |
.jpg "Click for more on -> Number (sports)")
