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Centered Heptagonal Number
A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by the formula :\over2. The first few centered heptagonal numbers are 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953 Centered heptagonal prime A centered heptagonal prime is a centered heptagonal number that is prime. The first few centered heptagonal primes are :43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, ... The centered heptagonal twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ... numbers are :43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, ... See also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Number
In mathematics, the centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers of dots with a constant number of sides. Each side of a polygonal layer contains one more dot than each side in the previous layer; so starting from the second polygonal layer, each layer of a centered ''k''-gonal number contains ''k'' more dots than the previous layer. Examples Each centered ''k''-gonal number in the series is ''k'' times the previous triangular number, plus 1. This can be formalized by the expression \frac +1, where ''n'' is the series rank, starting with 0 for the initial 1. For example, each centered square number in the series is four times the previous triangular number, plus 1. This can be formalized by the expression \frac +1. These series consist of the * centered triangular numbers 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, ... (), * centered square numbers 1, 5, 13, 25, 41, 61, 85, 113, 145, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Figurate Number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The ancient Greek mathematicians already considered triangular numbers, polygonal numbers, tetrahedral numbers, and pyramidal numbers, ReprintedG. E. Stechert & Co., 1934 and AMS Chelsea Publishing, 1944. and subsequent mathematicians have included other classes of these numbers including numbers defined from other types of polyhedra and from their analogs in other dimensions. Terminology Some kinds of figurate number were discussed in the 16th and 17th centuries under the name "figural number". In historical works about Greek mathematics the preferred term used to be ''figured number''. In a use going back to Jacob Bernoulli's Ars Conjectandi, the term ''figurate number'' is used for triangular numbers made up of successive integers, tetrahedral numbers made ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heptagon
In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using ''Wikt:septa-, septa-'' (an elision of ''Wikt:septua-, septua-''), a Latin-derived numerical prefix, rather than ''Wikt:hepta-, hepta-'', a Greek language, Greek-derived numerical prefix (both are cognate), together with the suffix ''-gon'' for , meaning angle. Regular heptagon A regular polygon, regular heptagon, in which all sides and all angles are equal, has internal angles of 5π/7 radians (128 degree (angle), degrees). Its Schläfli symbol is . Area The area (''A'') of a regular heptagon of side length ''a'' is given by: :A = \fraca^2 \cot \frac \simeq 3.634 a^2. This can be seen by subdividing the unit-sided heptagon into seven triangular "pie slices" with Vertex (geometry), vertices at the center and at the heptagon's vertices, and then halving each triangle using the apothem as the common side. The apothem is half the cotangent of \pi/7 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1 (number)
1 (one, unit, unity) is a number, numeral, and glyph. It is the first and smallest positive integer of the infinite sequence of natural numbers. This fundamental property has led to its unique uses in other fields, ranging from science to sports, where it commonly denotes the first, leading, or top thing in a group. 1 is the unit of counting or measurement, a determiner for singular nouns, and a gender-neutral pronoun. Historically, the representation of 1 evolved from ancient Sumerian and Babylonian symbols to the modern Arabic numeral. In mathematics, 1 is the multiplicative identity, meaning that any number multiplied by 1 equals the same number. 1 is by convention not considered a prime number. In digital technology, 1 represents the "on" state in binary code, the foundation of computing. Philosophically, 1 symbolizes the ultimate reality or source of existence in various traditions. In mathematics The number 1 is the first natural number after 0. Each natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
8 (number)
8 (eight) is the natural number following 7 and preceding 9. Etymology English ''eight'', from Old English '', æhta'', Proto-Germanic ''*ahto'' is a direct continuation of Proto-Indo-European '' *oḱtṓ(w)-'', and as such cognate with Greek and Latin , both of which stems are reflected by the English prefix oct(o)-, as in the ordinal adjective ''octaval'' or ''octavary'', the distributive adjective is '' octonary''. The adjective ''octuple'' (Latin ) may also be used as a noun, meaning "a set of eight items"; the diminutive '' octuplet'' is mostly used to refer to eight siblings delivered in one birth. The Semitic numeral is based on a root ''*θmn-'', whence Akkadian ''smn-'', Arabic ''ṯmn-'', Hebrew ''šmn-'' etc. The Chinese numeral, written ( Mandarin: ''bā''; Cantonese: ''baat''), is from Old Chinese ''*priāt-'', ultimately from Sino-Tibetan ''b-r-gyat'' or ''b-g-ryat'' which also yielded Tibetan '' brgyat''. It has been argued that, as the cardinal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
22 (number)
22 (twenty-two) is the natural number following 21 and preceding 23. In mathematics 22 is a semiprime, a Smith number, and an Erdős–Woods number. \frac = 3.14\ldots is a commonly used approximation of the irrational number , the ratio of the circumference of a circle to its diameter. 22 can read as "two twos", which is the only fixed point of John Conway's look-and-say function. The number 22 appears prominently within sporadic groups. The Mathieu group M22 is one of 26 sporadic finite simple groups, defined as the 3-transitive permutation representation on 22 points. There are also 22 regular complex apeirohedra. 22 has been proven to be a Lychrel number in base 2, since after 4 steps it reaches 10110100, after 8 steps it reaches 1011101000, after 12 steps it reaches 101111010000, and in general after steps it reaches a number consisting of 10, followed by ones, followed by 01, followed by zeros. This number obviously cannot be a palindrome, and none of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
43 (number)
43 (forty-three) is the natural number following 42 (number), 42 and preceding 44 (number), 44. Mathematics 43 is a prime number, and a twin prime of 41 (number), 41. 43 is the smallest prime that is not a Chen prime. 43 is also a Wagstaff prime, and a Heegner number. 43 is the fourth term of Sylvester's sequence. 43 is the largest prime which divides the order of the Janko group J4, Janko group J4. Netherlands, Dutch mathematician Hendrik Lenstra wrote a mathematical research paper discussing the properties of the number, titled ''Ode to the number 43.'' Notes Further reading Hendrik Lenstra, Lenstra, Hendrik (2009)''Ode to the number 43'' (In Dutch). Nieuw Archief voor Wiskunde, Nieuw Arch. Wiskd. Amsterdam, NL: Koninklijk Wiskundig Genootschap (5) 10, No. 4: 240-244. {{Integers, zero Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
71 (number)
71 (seventy-one) is the natural number following 70 and preceding 72. __TOC__ In mathematics 71 is the 20th prime number. Because both rearrangements of its digits (17 and 71) are prime numbers, 71 is an emirp and more generally a permutable prime. 71 is a centered heptagonal number. It is a regular prime, a Ramanujan prime, a Higgs prime, and a good prime. It is a Pillai prime, since 9!+1 is divisible by 71, but 71 is not one more than a multiple of 9. It is part of the last known pair (71, 7) of Brown numbers, since 71^=7!+1. 71 is the smallest of thirty-one discriminants of imaginary quadratic fields with class number of 7, negated (see also, Heegner number In number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from int ...s). 71 is the largest number which occurs as a prim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
106 (number)
106 (one hundred ndsix) is the natural number following 105 and preceding 107 107 may refer to: *107 (number), the number *AD 107, a year in the 2nd century AD *107 BC, a year in the 2nd century BC *107 (New Jersey bus) *107 Camilla, a main-belt asteroid *Peugeot 107, a city car See also *10/7 (other) *Bohrium, .... In mathematics 106 is a centered pentagonal number, a centered heptagonal number, and a regular 19-gonal number. There are 106 mathematical trees with ten vertices. See also * 106 (other) References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
148 (number)
For the progressive house album by C418, please go to C418's websithere 148 (one hundred [and] forty-eight) is the natural number following 147 (number), 147 and before 149 (number), 149. In mathematics 148 is the second number to be both a heptagonal number and a centered heptagonal number (the first is 1). It is the twelfth member of the Mian–Chowla sequence, the lexicographically smallest sequence of distinct positive integers with distinct pairwise sums. There are 148 perfect graphs with six Vertex (graph theory), vertices, and 148 ways of partitioning four people into subsets, ordering the subsets, and selecting a leader for each subset. In other fields Dunbar's number is a theoretical cognitive limit to the number of people with whom one can maintain stable interpersonal relationships. Dunbar predicted a "mean group size" of 148, but this is commonly rounded to 150. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
197 (number)
197 (one hundred ndninety-seven) is the natural number following 196 and preceding 198. In mathematics * 197 is a prime number, the third of a prime quadruplet: 191, 193, 197, 199 * 197 is the smallest prime number that is the sum of seven consecutive primes: 17 + 19 + 23 + 29 + 31 + 37 + 41, and is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 * 197 is a centered heptagonal number, a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers * 197 is a Schröder–Hipparchus number, counting for instance the number of ways of subdividing a heptagon In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using ''Wikt:septa-, septa-'' (an elision of ''Wikt:septua-, septua-''), a Latin-derived numerical prefix, rather than ... by a non-crossing set of its dia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
