|
10 Million
10,000,000 (ten million) is the natural number following 9,999,999 and preceding 10,000,001. In scientific notation, it is written as 107. In South Asia except for Sri Lanka, it is known as the crore. In Cyrillic numerals, it is known as the vran (''вран'' — raven). Selected 8-digit numbers (10,000,001–99,999,999) 10,000,001 to 19,999,999 * 10,000,019 = smallest 8-digit prime number * 10,001,628 = smallest triangular number with 8 digits and the 4,472nd triangular number * 10,004,569 = 31632, the smallest 8-digit square * 10,077,696 = 2163 = 69, the smallest 8-digit cube * 10,556,001 = 32492 = 574 * 10,609,137 = Leyland number * 10,976,184 = logarithmic number * 11,111,111 = repunit * 11,316,496 = 33642 = 584 * 11,390,625 = 33752 = 2253 = 156 * 11,405,773 = Leonardo prime * 11,436,171 = Keith number * 11,485,154 = Markov number * 11,881,376 = 265 * 11,943,936 = 34562 * 12,117,361 = 34812 = 594 * 12,252,240 = highly composite number, smallest number divisible by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hebdo-
Hebdo- (symbol H) is an obsolete decimal metric prefix equal to 107. It is derived from the Greek ''hebdοmos'' ( el, ἕβδομος) meaning ''seventh''. The definition of one ''hebdomometre'' or ''hebdometre'' as was originally proposed by Rudolf Clausius for use in an absolute electrodynamic system of units named the quadrant–eleventh-gram–second system (QES system), also known as the hebdometre–undecimogramme–second system (HUS system) in the 1880s. It was based on the meridional definition of the metre which established one ten-millionth of a quadrant, a quarter of an astronomical meridian or the distance from the north pole to the equator, as a metre. See also * 10,000,000 *Crore, South Asian term for 107 *Metric prefix *Metric units *Numeral prefix References {{reflist, refs= {{cite journal , author-first=M. , author-last=Rothen , title=L'état actuel de la question des unités électriques , language=French , journal=Journal Télégraphique , publisher=Le B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Republic (Plato)
The ''Republic'' ( grc-gre, Πολῑτείᾱ, Politeia; ) is a Socratic dialogue, authored by Plato around 375 BCE, concerning justice (), the order and character of the just city-state, and the just man. It is Plato's best-known work, and one of the world's most influential works of philosophy and political theory, both intellectually and historically. In the dialogue, Socrates discusses the meaning of justice and whether the just man is happier than the unjust man with various Athenians and foreigners.In ancient times, the book was alternately titled ''On Justice'' (not to be confused with the spurious dialogue of the same name). They consider the natures of existing regimes and then propose a series of different, hypothetical cities in comparison, culminating in Kallipolis (Καλλίπολις), a utopian city-state ruled by a philosopher-king. They also discuss ageing, love, theory of forms, the immortality of the soul, and the role of the philosopher and of p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell Number
In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of eponymy, they are named after Eric Temple Bell, who wrote about them in the 1930s. The Bell numbers are denoted B_n, where n is an integer greater than or equal to zero. Starting with B_0 = B_1 = 1, the first few Bell numbers are :1, 1, 2, 5, 15, 52, 203, 877, 4140, ... . The Bell number B_n counts the number of different ways to partition a set that has exactly n elements, or equivalently, the number of equivalence relations on it. B_n also counts the number of different rhyme schemes for n -line poems. As well as appearing in counting problems, these numbers have a different interpretation, as moments of probability distributions. In particular, B_n is the n -th moment of a Poisson distribution with mean 1. Counting Set partitions In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repdigit
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit. Examples are 11, 666, 4444, and 999999. All repdigits are palindromic numbers and are multiples of repunits. Other well-known repdigits include the repunit primes and in particular the Mersenne primes (which are repdigits when represented in binary). Repdigits are the representation in base B of the number x\frac where 0 1 and ''n'', ''m'' > 2 : **(''p'', ''x'', ''y'', ''m'', ''n'') = (31, 5, 2, 3, 5) corresponding to 31 = 111112 = 1115, and, **(''p'', ''x'', ''y'', ''m'', ''n'') = (8191, 90, 2, 3, 13) corresponding to 8191 = 11111111111112 = 11190, with 11111111111 is the repunit with thirteen digits 1. *For each sequence of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Colossally Abundant Number
In mathematics, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in a particular, rigorous sense, has many divisors. Formally, a number ''n'' is said to be colossally abundant if there is an ε > 0 such that for all ''k'' > 1, :\frac\geq\frac where ''σ'' denotes the sum-of-divisors function. All colossally abundant numbers are also superabundant numbers, but the converse is not true. The first 15 colossally abundant numbers, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800 are also the first 15 superior highly composite numbers, but neither set is a subset of the other. History Colossally abundant numbers were first studied by Ramanujan and his findings were intended to be included in his 1915 paper on highly composite numbers. Unfortunately, the publisher of the journal to which Ramanujan submitted his work, the London Mathematical Society, was in financ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Motzkin Number
In mathematics, the th Motzkin number is the number of different ways of drawing non-intersecting chords between points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have diverse applications in geometry, combinatorics and number theory. The Motzkin numbers M_n for n = 0, 1, \dots form the sequence: : 1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019, 142547559, 400763223, 1129760415, 3192727797, 9043402501, 25669818476, 73007772802, 208023278209, 593742784829, ... Examples The following figure shows the 9 ways to draw non-intersecting chords between 4 points on a circle (): : The following figure shows the 21 ways to draw non-intersecting chords between 5 points on a circle (): : Properties The Motzkin numbers satisfy the recurrence relations :M_=M_+\sum_^M_iM_=\fracM_+\fracM_. The Motzkin numbers can be express ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Woodall Number
In number theory, a Woodall number (''W''''n'') is any natural number of the form :W_n = n \cdot 2^n - 1 for some natural number ''n''. The first few Woodall numbers are: :1, 7, 23, 63, 159, 383, 895, … . History Woodall numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly defined Cullen numbers. Woodall primes Woodall numbers that are also prime numbers are called Woodall primes; the first few exponents ''n'' for which the corresponding Woodall numbers ''W''''n'' are prime are 2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, ... ; the Woodall primes themselves begin with 7, 23, 383, 32212254719, ... . In 1976 Christopher Hooley showed that almost all Cullen numbers are composite. In October 1995, Wilfred Keller published a paper discussing several new Cullen primes and the efforts made to factorise other Cullen and Woodall numbers. Included in that paper is a personal communication to Kel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
24-bit Color
In computer architecture, 4-bit integers, or other data units are those that are 4 bits wide. Also, 4-bit central processing unit (CPU) and arithmetic logic unit (ALU) architectures are those that are based on registers, or data buses of that size. Memory addresses (and thus address buses) for 4-bit CPUs are generally much larger than 4-bit (since only 16 memory locations would be very restrictive), such as 12-bit or more, while they could in theory be 8-bit. A group of four bits is also called a nibble and has 24 = 16 possible values. Some of the first microprocessors had a 4-bit word length and were developed around 1970. Traditional (non-quantum) 4-bit computers are by now obsolete, while recent quantum computers are 4-bit, but also based on qubits, such as the IBM Q Experience. See also: Bit slicing#Bit-sliced quantum computers. The first commercial microprocessor was the binary-coded decimal (BCD-based) Intel 4004, developed for calculator applications in 1971; it had a 4- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexadecimal
In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, hexadecimal uses 16 distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9, and "A"–"F" (or alternatively "a"–"f") to represent values from 10 to 15. Software developers and system designers widely use hexadecimal numbers because they provide a human-friendly representation of binary-coded values. Each hexadecimal digit represents four bits (binary digits), also known as a nibble (or nybble). For example, an 8-bit byte can have values ranging from 00000000 to 11111111 in binary form, which can be conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value would be expressed in hexadecimal as . In programming, a number of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pell Number
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , and , so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29. The numerators of the same sequence of approximations are half the companion Pell numbers or Pell–Lucas numbers; these numbers form a second infinite sequence that begins with 2, 6, 14, 34, and 82. Both the Pell numbers and the companion Pell numbers may be calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally to powers of the silver ratio 1 + . As well as being used to approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations to the right isosceles triangle, and to solve certain combinat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
