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Digit-reassembly Number
Digit-reassembly numbers, or Osiris numbers, are numbers that are equal to the sum of permutations of sub-samples of their own digits (compare the dismemberment and reconstruction of the god Osiris in Egyptian mythology). For example, 132 = 12 + 21 + 13 + 31 + 23 + 32.Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 138 Osiris numbers in base ten In base ten, the smallest Osiris numbers are these, with a number-length of three digits and digit-span of two for the permutated sums: :132 = 12 + 21 + 13 + 31 + 23 + 32 :264 = 24 + 42 + 26 + 62 + 46 + 64 :396 = 36 + 63 + 39 + 93 + 69 + 96 Note that all are multiples of 132. A larger Osiris number in base ten is this, with a number-length of five digits and digit-span of three for the permutated sums: :35964 = 345 + 354 + 435 + 453 + 534 + 543 + 346 + 364 + 436 + 463 + 634 + 643 + 349 + 394 + 439 + 493 + 934 + 943 + 356 + 365 + 536 + 563 + 635 + 653 + 359 + 395 + 539 + 593 + 935 + ... [...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 scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling (statistics)
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population in question. Sampling has lower costs and faster data collection than measuring the entire population and can provide insights in cases where it is infeasible to measure an entire population. Each observation measures one or more properties (such as weight, location, colour or mass) of independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population. Acceptance sampling is used to determine if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deity
A deity or god is a supernatural being who is considered divine or sacred. The ''Oxford Dictionary of English'' defines deity as a god or goddess, or anything revered as divine. C. Scott Littleton defines a deity as "a being with powers greater than those of ordinary humans, but who interacts with humans, positively or negatively, in ways that carry humans to new levels of consciousness, beyond the grounded preoccupations of ordinary life". Religions can be categorized by how many deities they worship. Monotheistic religions accept only one deity (predominantly referred to as "God"), whereas polytheistic religions accept multiple deities. Henotheistic religions accept one supreme deity without denying other deities, considering them as aspects of the same divine principle. Nontheistic religions deny any supreme eternal creator deity, but may accept a pantheon of deities which live, die and may be reborn like any other being. Although most monotheistic religions traditionall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Osiris
Osiris (, from Egyptian ''wsjr'', cop, ⲟⲩⲥⲓⲣⲉ , ; Phoenician: 𐤀𐤎𐤓, romanized: ʾsr) is the god of fertility, agriculture, the afterlife, the dead, resurrection, life, and vegetation in ancient Egyptian religion. He was classically depicted as a green-skinned deity with a pharaoh's beard, partially mummy-wrapped at the legs, wearing a distinctive atef crown, and holding a symbolic crook and flail. He was one of the first to be associated with the mummy wrap. When his brother, Set cut him up into pieces after killing him, Osiris' wife Isis found all the pieces and wrapped his body up, enabling him to return to life. Osiris was widely worshipped until the decline of ancient Egyptian religion during the rise of Christianity in the Roman Empire. Osiris was at times considered the eldest son of the earth god Geb and the sky goddess Nut, as well as being brother and husband of Isis, and brother of Set, Nephthys, and Horus the Elder, with Horus the Younger ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egyptian Mythology
Egyptian mythology is the collection of myths from ancient Egypt, which describe the actions of the Egyptian gods as a means of understanding the world around them. The beliefs that these myths express are an important part of ancient Egyptian religion. Myths appear frequently in Egyptian writings and art, particularly in short stories and in religious material such as hymns, ritual texts, funerary texts, and temple decoration. These sources rarely contain a complete account of a myth and often describe only brief fragments. Inspired by the cycles of nature, the Egyptians saw time in the present as a series of recurring patterns, whereas the earliest periods of time were linear. Myths are set in these earliest times, and myth sets the pattern for the cycles of the present. Present events repeat the events of myth, and in doing so renew ''maat'', the fundamental order of the universe. Amongst the most important episodes from the mythic past are the creation myths, in which the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Penguin Dictionary Of Curious And Interesting Numbers
''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, and a revised edition appeared in 1997 (). Contents The entries are arranged in increasing order of magnitude, with the exception of the first entry on −1 and ''i''. The book includes some irrational numbers below 10 but concentrates on integers, and has an entry for every integer up to 42. The final entry is for Graham's number. In addition to the dictionary itself, the book includes a list of mathematicians in chronological sequence (all born before 1890), a short glossary, and a brief bibliography. The back of the book contains eight short tables "for the benefit of readers who cannot wait to look for their own patterns and properties", including lists of polygonal numbers, Fibonacci numbers, prime numbers, factorials, decimal rec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal Numbers
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A ''decimal numeral'' (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , where is an integer, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero
0 (zero) is a number representing an empty quantity. In place-value notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ... such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by Multiplication, multiplying digits to the left of 0 by the radix, usually by 10. As a number, 0 fulfills a central role in mathematics as the additive identity of the integers, real numbers, and other algebraic structures. Common names for the number 0 in English are ''zero'', ''nought'', ''naught'' (), ''nil''. In contexts where at least one adjacent digit distinguishes it from the O, letter O, the number is sometimes pronounced as ''oh'' or ''o'' (). Informal or slang terms for 0 include ''zilch'' and ''zip''. Historically, ''ought'', ''aught'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems In the system with radix 13, for example, a string of digits such as 398 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship between given quantities. The plural of ''formula'' can be either ''formulas'' (from the most common English plural noun form) or, under the influence of scientific Latin, ''formulae'' (from the original Latin). In mathematics In mathematics, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems. Syntactically, a formula (often referred to as a ''well-formed formula'') is an entity which is constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brute-force Search
In computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique and algorithmic paradigm that consists of systematically enumerating all possible candidates for the solution and checking whether each candidate satisfies the problem's statement. A brute-force algorithm that finds the divisors of a natural number ''n'' would enumerate all integers from 1 to n, and check whether each of them divides ''n'' without remainder. A brute-force approach for the eight queens puzzle would examine all possible arrangements of 8 pieces on the 64-square chessboard and for each arrangement, check whether each (queen) piece can attack any other. While a brute-force search is simple to implement and will always find a solution if it exists, implementation costs are proportional to the number of candidate solutionswhich in many practical problems tends to grow very quickly as the size of the problem increases ( §Combinator ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digit Sum
In mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number 9045 would be 9 + 0 + 4 + 5 = 18. Definition Let n be a natural number. We define the digit sum for base b > 1 F_ : \mathbb \rightarrow \mathbb to be the following: :F_(n) = \sum_^ d_i where k = \lfloor \log_ \rfloor is the number of digits in the number in base b, and :d_i = \frac is the value of each digit of the number. For example, in base 10, the digit sum of 84001 is F_(84001) = 8 + 4 + 0 + 0 + 1 = 13. For any two bases 2 \leq b_1 < b_2 and for sufficiently large natural numbers , :.. The sum of the digits of the integers 0, 1, 2, ... is given by in the |
