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280 (number)
280 (two hundred ndeighty) is the natural number after 279 and before 281. In mathematics The denominator of the eighth harmonic number, 280 is an octagonal number. 280 is the smallest octagonal number that is a half of another octagonal number. There are 280 plane tree In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only ...s with ten nodes. As a consequence of this, 18 people around a round table can shake hands with each other in non-crossing ways, in 280 different ways (this includes rotations). References {{DEFAULTSORT:280 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
279 (number)
279 (two hundred ndseventy-nine) is the natural number following 278 and preceding 280. In mathematics *279 is an odd composite number with two prime factors. * Waring’s Conjecture is g(n)=2n+⌊(3/2)n⌋-2. When 8 is plugged in for n, the result is 279. That means that any positive integer In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positiv ... can be formed with at most 279 numbers to the 8th power. *279 is the smallest number whose product of digits is 7 times the sum of its digits. *279 can be written as the sum of 4 nonzero perfect squares. References {{Improve categories, date=October 2023 Integers Numbers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
281 (number)
281 is the natural number following 280 and preceding 282. It is also a prime number. In mathematics 281 is a twin prime with 283, Sophie Germain prime, sum of the first fourteen primes, sum of seven consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53), Chen prime, Eisenstein prime with no imaginary part, and a centered decagonal number. 281 is the smallest prime ''p'' such that the decimal period length of the reciprocal of ''p'' is (''p''−1)/10, i.e. the period length of 1/281 is 28. However, in binary, it has period length 70. The generalized repunit In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for "repeated unit" and was coined in 1966 by Albert H. Beiler in his book ''Recr ... number \frac is composite for all prime ''p'' < 60000. References Int ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Number
In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: H_n= 1+\frac+\frac+\cdots+\frac =\sum_^n \frac. Starting from , the sequence of harmonic numbers begins: 1, \frac, \frac, \frac, \frac, \dots Harmonic numbers are related to the harmonic mean in that the -th harmonic number is also times the reciprocal of the harmonic mean of the first positive integers. Harmonic numbers have been studied since antiquity and are important in various branches of number theory. They are sometimes loosely termed harmonic series, are closely related to the Riemann zeta function, and appear in the expressions of various special functions. The harmonic numbers roughly approximate the natural logarithm function and thus the associated harmonic series grows without limit, albeit slowly. In 1737, Leonhard Euler used the divergence of the harmonic series to provide a new proof of the infinity of prime numbers. His work was extended into the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octagonal Number
In mathematics, an octagonal number is a figurate number. The ''n''th octagonal number ''o''''n'' is the number of dots in a pattern of dots consisting of the outlines of regular octagons with sides up to ''n'' dots, when the octagons are overlaid so that they share one vertex (geometry), vertex. The octagonal number for ''n'' is given by the formula 3''n''2 − 2''n'', with ''n'' > 0. The first few octagonal numbers are : 1 (number), 1, 8 (number), 8, 21 (number), 21, 40 (number), 40, 65 (number), 65, 96 (number), 96, 133 (number), 133, 176 (number), 176, 225 (number), 225, 280 (number), 280, 341, 408, 481, 560, 645, 736, 833, 936 The octagonal number for ''n'' can also be calculated by adding the square of ''n'' to twice the (''n'' − 1)th pronic number. Octagonal numbers consistently alternate parity (mathematics), parity. Octagonal numbers are occasionally referred to as "star numbers", though that term is more commonly used to refer to centered dodecagonal numbers. Appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree (graph Theory)
In graph theory, a tree is an undirected graph in which any two vertices are connected by path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A directed tree, oriented tree,See .See . polytree,See . or singly connected networkSee . is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. The various kinds of data structures referred to as trees in computer science have underlying graphs that are trees in graph theory, although such data structures are generally rooted trees. A rooted tree may be directed, called a directed rooted tree, either making all its edges point away from the root—in which case it is called an arborescence or out-tree� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
