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223 (number)
223 (two hundred ndtwenty-three) is the natural number following 222 and preceding 224. In mathematics 223 is a prime number. Among the 720 permutations of the numbers from 1 to 6, exactly 223 of them have the property that at least one of the numbers is fixed in place by the permutation and the numbers less than it and greater than it are separately permuted among themselves. In connection with Waring's problem, 223 requires the maximum number of terms (37 terms) when expressed as a sum of positive fifth powers, and is the only number that requires that many terms. In other fields * .223 (other), the caliber of several firearm cartridges * The years 223 __NOTOC__ Year 223 ( CCXXIII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Maximus and Aelianus (or, less frequently, year 976 ' ... and 223 BC * The number of synodic months of a Saros Refere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal numbers'', and numbers used for ordering are called ''ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports jersey numbers). Some definitions, including the standard ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural numbers form a set. Many other number sets are built by succe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
222 (number)
222 (two hundred ndtwenty-two) is the natural number following 221 and preceding 223. In mathematics It is a decimal repdigit and a strobogrammatic number (meaning that it looks the same turned upside down on a calculator display). It is one of the numbers whose digit sum in decimal is the same as it is in binary. 222 is a noncototient, meaning that it cannot be written in the form ''n'' − φ(''n'') where φ is Euler's totient function counting the number of values that are smaller than ''n'' and relatively prime to it. There are exactly 222 distinct ways of assigning a meet and join operation to a set of ten unlabelled elements in order to give them the structure of a lattice, and exactly 222 different six-edge polystick In recreational mathematics, a polystick (or polyedge) is a polyform with a line segment (a 'stick') as the basic shape. A polystick is a connected set of segments in a regular grid. A square polystick is a connected subset of a regula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
224 (number)
224 (two hundred ndtwenty-four) is the natural number following 223 and preceding 225. In mathematics 224 is a practical number, and a sum of two positive cubes . It is also , making it one of the smallest numbers to be the sum of distinct positive cubes in more than one way. 224 is the smallest ''k'' with λ(''k'') = 24, where λ(''k'') is the Carmichael function. The mathematician and philosopher Alex Bellos suggested in 2014 that a candidate for the lowest uninteresting number would be 224 because it was, at the time, "the lowest number not to have its own page on he English-language version ofWikipedia". In other areas In the SHA-2 family of six cryptographic hash functions, the weakest is SHA-224, named because it produces 224-bit hash values. It was defined in this way so that the number of bits of security it provides (half of its output length, 112 bits) would match the key length of two-key Triple DES. The ancient Phoenician shekel was a standardized measure o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set , namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of sci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waring's Problem
In number theory, Waring's problem asks whether each natural number ''k'' has an associated positive integer ''s'' such that every natural number is the sum of at most ''s'' natural numbers raised to the power ''k''. For example, every natural number is the sum of at most 4 squares, 9 cubes, or 19 fourth powers. Waring's problem was proposed in 1770 by Edward Waring, after whom it is named. Its affirmative answer, known as the Hilbert–Waring theorem, was provided by Hilbert in 1909. Waring's problem has its own Mathematics Subject Classification, 11P05, "Waring's problem and variants". Relationship with Lagrange's four-square theorem Long before Waring posed his problem, Diophantus had asked whether every positive integer could be represented as the sum of four perfect squares greater than or equal to zero. This question later became known as Bachet's conjecture, after the 1621 translation of Diophantus by Claude Gaspard Bachet de Méziriac, and it was solved by Joseph-Louis Lag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
223 (other)
__NOTOC__ Year 223 ( CCXXIII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Maximus and Aelianus (or, less frequently, year 976 ''Ab urbe condita''). The denomination 223 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Asia * Battle of Dongkou: The Chinese state of Cao Wei is defeated by Eastern Wu. Births * Ji Kang, Chinese poet and philosopher (d. 262) * Wang Hun, Chinese general and politician (d. 297) Deaths * May 6 – Cao Ren (or Zixiao), Chinese general (b. 168) * June 10 – Liu Bei, Chinese warlord and emperor (b. 161) * August 1 – Cao Zhang, Chinese prince and warlord * August 11 – Jia Xu, Chinese official and politician (b. 147) * Xing Yong (or Zi'ang), Chinese official and politician * Zhang Ji Zhang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
223 BC
__NOTOC__ Year 223 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Flaminus and Philus (or, less frequently, year 531 ''Ab urbe condita''). The denomination 223 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Seleucid Empire * The Seleucid king Seleucus III is assassinated in Phrygia by members of his army while on campaign against Attalus of Pergamon. * Seleucus is succeeded by his younger brother, Antiochus III. From the previous administration, Antiochus III retains Hermeias as his chief minister, Achaeus as governor of Anatolia, and Molon and his brother Alexander as governors of the eastern provinces of Media and Persis. Roman Republic * Gaius Flaminius is elected consul for the first time and, with Publius Furius Philus, he forces the Cisalpine Gauls to submit to Rome, creating ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synodic Month
In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month. Variations In Shona, Middle Eastern, and European traditions, the month starts when the young crescent moon first becomes visible, at evening, after conjunction with the Sun one or two days before that evening (e.g., in the Islamic calendar). In ancient Egypt, the lunar month began on the day when the waning moon could no longer be seen just before sunrise. Others run from full moon to full moon. Yet others use calculation, of varying degrees of sophistication, for example, the Hebrew calendar or the ecclesiastical lunar calendar. Calendars count integer days, so months may be 29 or 30 days in length, in some regular or irregular sequence. Lunar cycles are prominent, and calculated with great precision, in the ancient Hindu Panchangam calendar, widely used in the Indian subcont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saros (astronomy)
The saros () is a period of exactly 223 synodic months, approximately 6585.3211 days, or 18 years, 10, 11, or 12 days (depending on the number of leap years), and 8 hours, that can be used to predict eclipses of the Sun and Moon. One saros period after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, a near straight line, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle. A sar is one half of a saros. A series of eclipses that are separated by one saros is called a ''saros series''. It corresponds to: *6,585.321347 solar days *18.029 years *223 synodic months *241.999 draconic months *18.999 eclipse years (38 eclipse seasons) *238.992 anomalistic months The 19 eclipse years means that if there is a solar eclipse (or lunar eclipse), then after one saros a new moon will take place at the same node of the orbit of the Moon, and under these circumstances another eclipse can occur. History The earliest disc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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