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28th (Maori) Infantry Battalion
28 (twenty-eight) is the natural number following 27 and preceding 29. In mathematics It is a composite number, its proper divisors being 1, 2, 4, 7, and 14. Twenty-eight is the second perfect number - it is the sum of its proper divisors: 1+2+4+7+14=28. As a perfect number, it is related to the Mersenne prime 7, since 2^\times (2^-1)=28. The next perfect number is 496, the previous being 6. Twenty-eight is the sum of the totient function for the first nine integers. Since the greatest prime factor of 28^+1=785 is 157, which is more than 28 twice, 28 is a Størmer number. Twenty-eight is a harmonic divisor number, a happy number, a triangular number, a hexagonal number, a Leyland number of the second kind and a centered nonagonal number. It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these). It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its decimal digits: 2, 8, 10, ... [...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 number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, 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 Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Størmer Number
In mathematics, a Størmer number or arc-cotangent irreducible number is a positive integer n for which the greatest prime factor of n^2+1 is greater than or equal to 2n. They are named after Carl Størmer. Sequence The first few Størmer numbers are: Density John Todd proved that this sequence is neither finite nor cofinite. More precisely, the natural density of the Størmer numbers lies between 0.5324 and 0.905. It has been conjectured that their natural density is the natural logarithm of 2, approximately 0.693, but this remains unproven. Because the Størmer numbers have positive density, the Størmer numbers form a large set. Application The Størmer numbers arise in connection with the problem of representing the Gregory numbers (arctangents of rational numbers) G_=\arctan\frac as sums of Gregory numbers for integers (arctangents of unit fractions). The Gregory number G_ may be decomposed by repeatedly multiplying the Gaussian integer In number theory, a Gaussian inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Uniform Honeycomb
In geometry, a convex uniform honeycomb is a uniform polytope, uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex polyhedron, convex uniform polyhedron, uniform polyhedral cells. Twenty-eight such honeycombs are known: * the familiar cubic honeycomb and 7 truncations thereof; * the alternated cubic honeycomb and 4 truncations thereof; * 10 prismatic forms based on the #Prismatic_stacks, uniform plane tilings (11 if including the cubic honeycomb); * 5 modifications of some of the above by elongation and/or gyration. They can be considered the three-dimensional analogue to the List of uniform planar tilings, uniform tilings of the plane. The Voronoi diagram of any Lattice (group), lattice forms a convex uniform honeycomb in which the cells are zonohedra. History * 1900: Thorold Gosset enumerated the list of semiregular convex polytopes with regular cells (Platonic solids) in his publication ''On the Regular and Semi-Regular Figures in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Square
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number of integers along one side (''n''), and the constant sum is called the ' magic constant'. If the array includes just the positive integers 1,2,...,n^2, the magic square is said to be 'normal'. Some authors take magic square to mean normal magic square. Magic squares that include repeated entries do not fall under this definition and are referred to as 'trivial'. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant this gives a ''semimagic square (sometimes called orthomagic square). The mathematical study of magic squares typically deals with their construction, classification, and enumeration. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, and the Bay of Bengal on the southeast, it shares land borders with Pakistan to the west; China, Nepal, and Bhutan to the north; and Bangladesh and Myanmar to the east. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives; its Andaman and Nicobar Islands share a maritime border with Thailand, Myanmar, and Indonesia. Modern humans arrived on the Indian subcontinent from Africa no later than 55,000 years ago., "Y-Chromosome and Mt-DNA data support the colonization of South Asia by modern humans originating in Africa. ... Coalescence dates for most non-European populations average to between 73–55 ka.", "Modern human beings—''Homo sapiens''—originated in Africa. Then, int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odd Prime
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 pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonardo Of Pisa
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci'', was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for ('son of Bonacci'). However, even earlier in 1506 a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci". Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of ''Liber Abaci'' (''Book of Calculation''). He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in ''Liber Abaci''. Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in Bugia (Béjaïa) in modern- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keith Number
In number theory, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number n in a given number base b with k digits such that when a sequence is created such that the first k terms are the k digits of n and each subsequent term is the sum of the previous k terms, n is part of the sequence. Keith numbers were introduced by Mike Keith in 1987. They are computationally very challenging to find, with only about 100 known. Definition Let n be a natural number, let k = \lfloor \log_ \rfloor + 1 be the number of digits in the number in base b, and let :d_i = \frac be the value of each digit of the number. We define a linear recurrence relation. S(i) such that for 0 \leq i bool: """Determine if a number in a particular base is a Keith number.""" if x 0: return True sequence = [] y = x while y > 0: sequence.append(y % b) y = y // b digit_count = len(sequence) sequence.reverse() while ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Padovan Sequence
In number theory, the Padovan sequence is the sequence of integers ''P''(''n'') defined. by the initial values :P(0)=P(1)=P(2)=1, and the recurrence relation :P(n)=P(n-2)+P(n-3). The first few values of ''P''(''n'') are :1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, ... A Padovan prime is a Padovan number that's also prime. The first Padovan primes are: :2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, 3093215881333057, 1363005552434666078217421284621279933627102780881053358473, 1558877695141608507751098941899265975115403618621811951868598809164180630185566719, ... . The Padovan sequence is named after Richard Padovan who attributed its discovery to Netherlands, Dutch architect Hans van der Laan in his 1994 essay ''Dom. Hans van der Laan : Modern Primitive''.Richard Padovan. ''Dom Hans van der Laan: modern primitive'': Architectura & Natura Press, . The sequence was described by Ian Stewart (mathematician), Ian Stewart in his Scientific Ame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Nonagonal Number
A centered nonagonal number (or centered enneagonal number) is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers. The centered nonagonal number for ''n'' layers is given by the formula :Nc(n) = \frac. Multiplying the (''n'' - 1)th triangular number by 9 and then adding 1 yields the ''n''th centered nonagonal number, but centered nonagonal numbers have an even simpler relation to triangular numbers: every third triangular number (the 1st, 4th, 7th, etc.) is also a centered nonagonal number. Thus, the first few centered nonagonal numbers are : 1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946. The list above includes the perfect numbers 28 and 496. All even perfect numbers are triangular numbers whose index is an odd Mersenne prime. Since every Mersenne prime greater than 3 is congruent to 1 modulo 3, it follows that every even perfect nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leyland Number
In number theory, a Leyland number is a number of the form :x^y + y^x where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are : 8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124 . The requirement that ''x'' and ''y'' both be greater than 1 is important, since without it every positive integer would be a Leyland number of the form ''x''1 + 1''x''. Also, because of the commutative property of addition, the condition ''x'' ≥ ''y'' is usually added to avoid double-covering the set of Leyland numbers (so we have 1 References External links * {{DEFAULTSORT:Leyland Number Integer sequences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Number
A hexagonal number is a figurate number. The ''n''th hexagonal number ''h''''n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex. The formula for the ''n''th hexagonal number :h_n= 2n^2-n = n(2n-1) = \frac. The first few hexagonal numbers are: : 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946... Every hexagonal number is a triangular number, but only every ''other'' triangular number (the 1st, 3rd, 5th, 7th, etc.) is a hexagonal number. Like a triangular number, the digital root in base 10 of a hexagonal number can only be 1, 3, 6, or 9. The digital root pattern, repeating every nine terms, is "1 6 6 1 9 3 1 3 9". Every even perfect number is hexagonal, given by the formula :M_p 2^ = M_p \frac = h_=h_ :where ''M''''p'' is a Mersenne prime. No odd perfect numbers are known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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