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Binary Logarithm
In mathematics, the binary logarithm () is the power to which the number must be raised to obtain the value . That is, for any real number , :x=\log_2 n \quad\Longleftrightarrow\quad 2^x=n. For example, the binary logarithm of is , the binary logarithm of is , the binary logarithm of is , and the binary logarithm of is . The binary logarithm is the logarithm to the base and is the inverse function of the power of two function. As well as , an alternative notation for the binary logarithm is (the notation preferred by ISO 31-11 and ISO 80000-2). Historically, the first application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ. Binary logarithms can be used to calculate the length of the representation of a number in the binary numeral system, or the number of bits needed to encode a message in information theory. In computer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Logarithm Plot With Ticks
Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that takes two arguments * Binary relation, a relation involving two elements * Binary-coded decimal, a method for encoding for decimal digits in binary sequences * Finger binary, a system for counting in binary numbers on the fingers of human hands Computing * Binary code, the digital representation of text and data * Bit, or binary digit, the basic unit of information in computers * Binary file, composed of something other than human-readable text ** Executable, a type of binary file that contains machine code for the computer to execute * Binary tree, a computer tree data structure in which each node has at most two children Astronomy * Binary star, a star system with two stars in it * Binary planet, two planetary bodies of comparable ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tournament
A tournament is a competition involving at least three competitors, all participating in a sport or game. More specifically, the term may be used in either of two overlapping senses: # One or more competitions held at a single venue and concentrated into a relatively short time interval. # A competition involving a number of matches, each involving a subset of the competitors, with the overall tournament winner determined based on the combined results of these individual matches. These are common in those sports and games where each match must involve a small number of competitors: often precisely two, as in most team sports, racket sports and combat sports, many card games and board games, and many forms of competitive debating. Such tournaments allow large numbers to compete against each other in spite of the restriction on numbers in a single match. These two senses are distinct. All golf tournaments meet the first definition, but while match play tournaments meet the second, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virasena
Acharya Virasena (792-853 CE), also known as Veerasena, was a Digambara monk and belonged to the lineage of Acharya Kundakunda. He was an Indian mathematician and Jain philosopher and scholar. He was also known as a famous orator and an accomplished poet. His most reputed work is the Jain treatise ''Dhavala''. The late Dr. Hiralal Jain places the completion of this treatise in 816 AD. Virasena was a noted mathematician. He gave the derivation of the volume of a frustum by a sort of infinite procedure. He worked with the concept of ''Ardha Chheda'': the number of times a number could be divided by 2; effectively base-2 logarithms. He also worked with logarithms in base 3 (trakacheda) and base 4 (caturthacheda). Virasena gave the approximate formula ''C'' = 3''d'' + (16''d''+16)/113 to relate the circumference of a circle, ''C'', to its diameter, ''d''. For large values of ''d'', this gives the approximation π ≈ 355/113 = 3.14159292.. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jain
Jainism ( ), also known as Jain Dharma, is an Indian religion. Jainism traces its spiritual ideas and history through the succession of twenty-four tirthankaras (supreme preachers of ''Dharma''), with the first in the current time cycle being Rishabhadeva, whom the tradition holds to have lived millions of years ago, the twenty-third ''tirthankara'' Parshvanatha, whom historians date to the 9th century BCE, and the twenty-fourth ''tirthankara'' Mahavira, around 600 BCE. Jainism is considered to be an eternal ''dharma'' with the ''tirthankaras'' guiding every time cycle of the cosmology. The three main pillars of Jainism are ''ahiṃsā'' (non-violence), ''anekāntavāda'' (non-absolutism), and '' aparigraha'' (asceticism). Jain monks, after positioning themselves in the sublime state of soul consciousness, take five main vows: ''ahiṃsā'' (non-violence), '' satya'' (truth), '' asteya'' (not stealing), ''brahmacharya'' (chastity), and '' aparigraha'' (non-possessiveness). Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Stifel
Michael Stifel or Styfel (1487 – April 19, 1567) was a German monk, Protestant reformer and mathematician. He was an Augustinian who became an early supporter of Martin Luther. He was later appointed professor of mathematics at Jena University. Life Stifel was born in Esslingen am Neckar in southern Germany. He joined the Order of Saint Augustine and was ordained a priest in 1511. Tensions in the abbey grew after he published the poem ''Von der Christförmigen, rechtgegründeten leer Doctoris Martini Luthers'' (1522, i.e. On the Christian, righteous doctrine of Doctor Martin Luther) and came into conflict with Thomas Murner. Stifel then left for Frankfurt, and soon went to Mansfeld, where he began his mathematical studies. In 1524, upon a recommendation by Luther, Stifel was called by the Jörger family to serve at their residence, Tollet Castle in Tollet (close to Grieskirchen, Upper Austria). Due to the tense situation in the Archduchy of Austria in the wake of the execu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Number
In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols, \sigma_1(n)=2n where \sigma_1 is the sum-of-divisors function. For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 = 28. This definition is ancient, appearing as early as Euclid's ''Elements'' (VII.22) where it is called (''perfect'', ''ideal'', or ''complete number''). Euclid also proved a formation rule (IX.36) whereby q(q+1)/2 is an even perfect number whenever q is a prime of the form 2^p-1 for positive integer p—what is now called a Mersenne prime. Two millennia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid–Euler Theorem
The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and only if it has the form , where is a prime number. The theorem is named after mathematicians Euclid and Leonhard Euler, who respectively proved the "if" and "only if" aspects of the theorem. It has been conjectured that there are infinitely many Mersenne primes. Although the truth of this conjecture remains unknown, it is equivalent, by the Euclid–Euler theorem, to the conjecture that there are infinitely many even perfect numbers. However, it is also unknown whether there exists even a single odd perfect number. Statement and examples A perfect number is a natural number that equals the sum of its proper divisors, the numbers that are less than it and divide it evenly (with remainder zero). For instance, the proper divisors of 6 are 1, 2, and 3, which sum to 6, so 6 is perfect. A Mersenne prime is a prime number of the fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorization
In mathematics, factorization (or factorisation, see American and British English spelling differences#-ise, -ize (-isation, -ization), English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several ''factors'', usually smaller or simpler objects of the same kind. For example, is a factorization of the integer , and is a factorization of the polynomial . Factorization is not usually considered meaningful within number systems possessing division ring, division, such as the real number, real or complex numbers, since any x can be trivially written as (xy)\times(1/y) whenever y is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by Greek mathematics, ancient Greek mathematicians in the case of integers. They proved the fundamental theorem o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid's Elements
The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. ''Elements'' is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century. Euclid's ''Elements'' has been referred to as the most successful and influential textbook ever written. It was one of the very earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first printing i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonhard Euler - Edit1 (1921-2014), German author & historian
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Leonhard may refer to: *Leonhard Euler (1707–1783), Swiss mathematician and physicist *Leonhard Hutter (1563–1616), German theologian *Karl Leonhard (1904–1988), German psychiatrist *Jim Leonhard (1982– ), American football safety *LEONHARD (2009– ), Oslo-based DJ collective *Leonhard Rauwolf (1535–1596), German physician and botanist *Leonhard Stejneger (1851–1943), American herpetologist *Wolfgang Leonhard Wolfgang Leonhard (16 April 1921 – 17 August 2014) was a German political author and historian of the Soviet Union, the German Democratic Republic and Communism. A German Communist whose family had fled Hitler's Germany and who was educated i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating Point
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: 12.345 = \underbrace_\text \times \underbrace_\text\!\!\!\!\!\!^ In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common. The term ''floating point'' refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
