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Zeller's Congruence
Zeller's congruence is an algorithm devised by Christian Zeller in the 19th century to calculate the day of the week for any Julian calendar, Julian or Gregorian calendar date. It can be considered to be based on the conversion between Julian day and the calendar date. Formula For the Gregorian calendar, Zeller's congruence is :h = \left(q + \left\lfloor\frac\right\rfloor + K + \left\lfloor\frac\right\rfloor + \left\lfloor\frac\right\rfloor - 2J\right) \bmod 7, for the Julian calendar it is :h = \left(q + \left\lfloor\frac\right\rfloor + K + \left\lfloor\frac\right\rfloor + 5 - J\right) \bmod 7, where * ''h'' is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ..., 6 = Friday) * ''q'' is the day of the month * ''m'' is the month (3 = March, 4 = April, 5 = May, ..., 14 = February) * ''K'' the year of the century (year \bmod 100). * ''J'' is the zero-based numbering, zero-based century (actually \lfloor year/100 \rfloor) For example, the zero-based centuries for 1995 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ISO Week Date
The ISO week date system is effectively a leap week calendar system that is part of the ISO 8601 date and time standard issued by the International Organization for Standardization (ISO) since 1988 (last revised in 2019) and, before that, it was defined in ISO (R) 2015 since 1971. It is used (mainly) in government and business for fiscal years, as well as in timekeeping. This was previously known as "Industrial date coding". The system specifies a ''week year'' atop the Gregorian calendar by defining a notation for ordinal weeks of the year. The Gregorian leap cycle, which has 97 leap days spread across 400 years, contains a whole number of weeks (). In every cycle there are 71 years with an additional 53rd week (corresponding to the Gregorian years that contain 53 Thursdays). An average year is exactly 52.1775 weeks long; months ( year) average at exactly weeks. An ISO week-numbering year (also called ''ISO year'' informally) has 52 or 53 full weeks. That is 364 or 371 days i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doomsday Rule
The Doomsday rule, Doomsday algorithm or Doomsday method is an algorithm of determination of the day of the week for a given date. It provides a perpetual calendar because the Gregorian calendar moves in cycles of 400 years. The algorithm for mental calculation was devised by John Conway in 1973, drawing inspiration from Lewis Carroll's perpetual calendar algorithm. It takes advantage of each year having a certain day of the week upon which certain easy-to-remember dates, called the ''doomsdays'', fall; for example, the last day of February, 4/4, 6/6, 8/8, 10/10, and 12/12 all occur on the same day of the week in any year. Applying the Doomsday algorithm involves three steps: Determination of the anchor day for the century, calculation of the anchor day for the year from the one for the century, and selection of the closest date out of those that always fall on the doomsday, e.g., 4/4 and 6/6, and count of the number of days ( modulo 7) between that date and the date in question ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determination Of The Day Of The Week
The determination of the day of the week for any date may be performed with a variety of algorithms. In addition, perpetual calendars require no calculation by the user, and are essentially lookup tables. A typical application is to calculate the day of the week on which someone was born or a specific event occurred. Concepts In numerical calculation, the days of the week are represented as weekday numbers. If Monday is the first day of the week, the days may be coded 1 to 7, for Monday through Sunday, as is practiced in ISO 8601. The day designated with 7 may also be counted as ''0'', by applying the arithmetic modulo 7, which calculates the remainder of a number after division by 7. Thus, the number 7 is treated as 0, 8 as 1, 9 as 2, 18 as 4 and so on. If Sunday is counted as day 1, then 7 days later (i.e. day 8) is also a Sunday, and day 18 is the same as day 4, which is a Wednesday since this falls three days after Sunday. The basic approach of nearly all of the methods to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modulo Operation
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is the remainder of the Euclidean division of by , where is the dividend and is the divisor. For example, the expression "5 mod 2" would evaluate to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3. Although typically performed with and both being integers, many computing systems now allow other types of numeric operands. The range of values for an integer modulo operation of is 0 to inclusive ( mod 1 is always 0; is undefined, possibly resulting in a division by zero error in some programming languages). See Modular arithmetic for an older and related c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomical Year Numbering
Astronomical year numbering is based on AD/ CE year numbering, but follows normal decimal integer numbering more strictly. Thus, it has a year 0; the years before that are designated with negative numbers and the years after that are designated with positive numbers. Astronomers use the Julian calendar for years before 1582, including the year 0, and the Gregorian calendar for years after 1582, as exemplified by Jacques Cassini (1740),Jacques Cassini, Tables Astronomiques' (1740), Explication et Usage pp. 5 (PA5), 7 (PA7), Tables pp. 10 (RA1-PA10), 22 (RA1-PA22), 63 (RA1-PA63), 77 (RA1-PA77), 91 (RA1-PA91), 105 (RA1-PA105), 119 (RA1-PA119). Simon Newcomb (1898) and Fred Espenak (2007).Fred EspenakPhases of the Moon: −99 to 0 (100 to 1 BCE) ''NASA Eclipse web site'' The prefix AD and the suffixes CE, BC or BCE (Common Era, Before Christ or Before Common Era) are dropped. The year 1 BC/BCE is numbered 0, the year 2 BC is numbered −1, and in general the year ''n'' BC/BCE is numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proleptic
Proleptic may refer to: * Prolepsis Prolepsis may refer to: * Prolepsis (rhetoric), a figure of speech in which the speaker raises an objection and then immediately answers it *Prolepsis (literary), anticipating action, a flash forward, see Foreshadowing * Cataphora, using an expr ..., several meanings related to foreshadowing * Proleptic calendar, a calendar that is applied to dates before its introduction * Proleptic syllogism, a class of syllogism in logic {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modulo Operation
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is the remainder of the Euclidean division of by , where is the dividend and is the divisor. For example, the expression "5 mod 2" would evaluate to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3. Although typically performed with and both being integers, many computing systems now allow other types of numeric operands. The range of values for an integer modulo operation of is 0 to inclusive ( mod 1 is always 0; is undefined, possibly resulting in a division by zero error in some programming languages). See Modular arithmetic for an older and related c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christian Zeller
Julius Christian Johannes Zeller (24 June 1822, Mühlhausen am Neckar – 31 May 1899, Cannstatt) was a German mathematician. He was born to Gottlob Zeller and Christiana Friedrike Moser.Germany Birth And Baptism Index 1558-1898 Originally trained in mathematics, geography and theology, in 1874 Zeller became Director of the Seminary in Markgröningen and a girls' orphanage. In 1882 he became a member of the Société Mathématique de France. The following year, on 16 March 1883, he delivered a short account of his congruence relation (Zeller's congruence), which was published in the society's journal. He was later awarded the Order of Friedrich, First Class, and the Ritterkreuz of Württemberg. He retired in 1898, and died in the following summer. Works On calendrical calculations Each of these four similar papers deals firstly with the day of the week and secondly with the date of Easter Sunday, for the Julian and Gregorian Calendars. * Die Grundaufgaben der Kalender ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floor Function
In mathematics and computer science, the floor function is the function that takes as input a real number , and gives as output the greatest integer less than or equal to , denoted or . Similarly, the ceiling function maps to the least integer greater than or equal to , denoted or . For example, , , , and . Historically, the floor of has been–and still is–called the integral part or integer part of , often denoted (as well as a variety of other notations). Some authors may define the integral part as if is nonnegative, and otherwise: for example, and . The operation of truncation generalizes this to a specified number of digits: truncation to zero significant digits is the same as the integer part. For an integer, . Notation The ''integral part'' or ''integer part'' of a number ( in the original) was first defined in 1798 by Adrien-Marie Legendre in his proof of the Legendre's formula. Carl Friedrich Gauss introduced the square bracket notation in hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero-based Numbering
Zero-based numbering is a way of numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in everyday ''non-mathematical'' or ''non-programming'' circumstances. Under zero-based numbering, the initial element is sometimes termed the ''zeroth'' element, rather than the ''first'' element; ''zeroth'' is a coined ordinal number corresponding to the number zero. In some cases, an object or value that does not (originally) belong to a given sequence, but which could be naturally placed before its initial element, may be termed the zeroth element. There is not wide agreement regarding the correctness of using zero as an ordinal (nor regarding the use of the term ''zeroth''), as it creates ambiguity for all subsequent elements of the sequence when lacking context. Numbering sequences starting at 0 is quite common in mathematics notation, in particular in combinatorics, though programming languages for mathematics usuall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
