|
6174 (number)
6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule: # Take any four-digit number, using at least two different digits (leading zeros are allowed). # Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary. # Subtract the smaller number from the bigger number. # Go back to step 2 and repeat. The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations. Hanover 2017, p. 1, Overview. Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 1459: :9541 – 1459 = 8082 :8820 – 0288 = 8532 :8532 – 2358 = 6174 :7641 – 1467 = 6174 The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration. All other four-digit numbers eventually reach 6174 if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plus Magazine
''Plus Magazine'' is an online popular mathematics magazine run under the Millennium Mathematics Project at the University of Cambridge. ''Plus'' contains: * feature articles on all aspects of mathematics; * reviews of popular maths books and events; * a news section; * mathematical puzzles and games; * interviews with people in maths related careers; * ''Plus'' Podcast – Maths on the Move History ''Plus'' was initially named PASS Maths (Public Awareness and Schools Support for Maths) in 1997, when it was a project of the Interactive Courseware Research and Development Group, based jointly at the University of Cambridge and Keele University. ''Plus'' is now part of the Millennium Mathematics Project, a long term national initiative based in Cambridge and active across the UK and internationally. Authors of articles in ''Plus'' include Stephen Hawking and Marcus du Sautoy. ''Plus'' won the 2001 Webby for ''Best Science Site on the Web'', and has been described as "an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scripta Mathematica
''Scripta Mathematica'' was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics. It was said to be, at its time, "the only mathematical magazine in the world edited by specialists for laymen.". The journal was established in 1932 under the editorship of Jekuthiel Ginsburg, a professor of mathematics at Yeshiva University, and its first issue appeared in 1933 at a subscription price of three dollars per year. It ceased publication in 1973. Notable papers published in ''Scripta Mathematica'' included work by Nobelist Percy Williams Bridgman concerning the implications for physics of set-theoretic paradoxes, and Hermann Weyl's obituary of Emmy Noether Amalie Emmy NoetherEmmy is the ''Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noethe .... Some s ... [...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] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaprekar's Routine
In number theory, Kaprekar's routine is an iterative algorithm that, with each iteration, takes a natural number in a given number base, creates two new numbers by sorting the digits of its number by descending and ascending order, and subtracts the second from the first to yield the natural number for the next iteration. It is named after its inventor, the Indian mathematician D. R. Kaprekar. Kaprekar showed that in the case of four-digit numbers in base 10, if the initial number has at least two distinct digits, after seven iterations this process always yields the number 6174, which is now known as Kaprekar's constant. Definition and properties The algorithm is as follows: # Choose any natural number n in a given number base b. This is the first number of the sequence. # Create a new number \alpha by sorting the digits of n in descending order, and another new number \beta by sorting the digits of n in ascending order. These numbers may have leading zeros, which are discarded ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fixed Point (mathematics)
A fixed point (sometimes shortened to fixpoint, also known as an invariant point) is a value that does not change under a given transformation. Specifically, in mathematics, a fixed point of a function is an element that is mapped to itself by the function. In physics, the term fixed point can refer to a temperature that can be used as a reproducible reference point, usually defined by a phase change or triple point. Fixed point of a function Formally, is a fixed point of a function if belongs to both the domain and the codomain of , and . For example, if is defined on the real numbers by f(x) = x^2 - 3 x + 4, then 2 is a fixed point of , because . Not all functions have fixed points: for example, , has no fixed points, since is never equal to for any real number. In graphical terms, a fixed point means the point is on the line , or in other words the graph of has a point in common with that line. Fixed-point iteration In numerical analysis, ''fixed-point iter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repdigit
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit. Examples are 11, 666, 4444, and 999999. All repdigits are palindromic numbers and are multiples of repunits. Other well-known repdigits include the repunit primes and in particular the Mersenne primes (which are repdigits when represented in binary). Repdigits are the representation in base B of the number x\frac where 0 1 and ''n'', ''m'' > 2 : **(''p'', ''x'', ''y'', ''m'', ''n'') = (31, 5, 2, 3, 5) corresponding to 31 = 111112 = 1115, and, **(''p'', ''x'', ''y'', ''m'', ''n'') = (8191, 90, 2, 3, 13) corresponding to 8191 = 11111111111112 = 11190, with 11111111111 is the repunit with thirteen digits 1. *For each sequence of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
0 (number)
0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by 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 letter O, the number is sometimes pronounced as ''oh'' or ''o'' (). Informal or slang terms for 0 include ''zilch'' and ''zip''. Historically, ''ought'', ''aught'' (), and ''cipher'', have also been used. Etymology The word ''zero'' came into the English language via French from the Italian , a contraction of the Venetian form of Italian via ''ṣafira'' or ''ṣifr''. In pre-Islamic time the word (Arabic ) had the meanin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
495 (number)
495 (four hundred ndninety-five) is the natural number following 494 and preceding 496. It is a pentatope number (and so a binomial coefficient \tbinom 4 ). The maximal number of pieces that can be obtained by cutting an annulus with 30 cuts. Kaprekar transformation The Kaprekar's routine algorithm is defined as follows for three-digit numbers: # Take any three-digit number, other than repdigits such as 111. Leading zeros are allowed. # Arrange the digits in descending and then in ascending order to get two three-digit numbers, adding leading zeros if necessary. # Subtract the smaller number from the bigger number. # Go back to step 2 and repeat. Repeating this process will always reach 495 in a few steps. Once 495 is reached, the process stops because 954 – 459 = 495. Example For example, choose 495: :495 The only three-digit numbers for which this function does not work are repdigits such as 111, which give the answer 0 after a single iteration. All other three- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smooth Number
In number theory, an ''n''-smooth (or ''n''-friable) number is an integer whose prime factors are all less than or equal to ''n''. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 × 53 × 7 are both 7-smooth, while 11 and 702 = 2 × 33 × 13 are not 7-smooth. The term seems to have been coined by Leonard Adleman. Smooth numbers are especially important in cryptography, which relies on factorization of integers. The 2-smooth numbers are just the powers of 2, while 5-smooth numbers are known as regular numbers. Definition A positive integer is called B-smooth if none of its prime factors are greater than B. For example, 1,620 has prime factorization 22 × 34 × 5; therefore 1,620 is 5-smooth because none of its prime factors are greater than 5. This definition includes numbers that lack some of the smaller prime factors; for example, both 10 and 12 are 5-smooth, even though they miss out the prime factors 3 and 5, resp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brady Haran
Brady John Haran (born 18 June 1976) is an Australian-British independent filmmaker and video journalist who produces educational videos and documentary films for his YouTube channels, the most notable being ''Periodic Videos'' and ''Numberphile''. Haran is also the co-host of the'' Hello Internet'' podcast along with fellow educational YouTuber CGP Grey. On 22 August 2017, Haran launched his second podcast, called ''The Unmade Podcast'', and on 11 November 2018, he launched his third podcast, '' The Numberphile Podcast'', based on his mathematics-centered channel of the same name. Reporter and filmmaker Brady Haran studied journalism for a year before being hired by ''The Adelaide Advertiser''. In 2002, he moved from Australia to Nottingham, United Kingdom. In Nottingham, he worked for the BBC, began to work with film, and reported for ''East Midlands Today'', BBC News Online and BBC radio stations. In 2007, Haran worked as a filmmaker-in-residence for Nottingham Science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Nottingham
The University of Nottingham is a public university, public research university in Nottingham, United Kingdom. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948. The University of Nottingham belongs to the research intensive Russell Group association. Nottingham's main campus (University Park Campus, Nottingham, University Park) with Jubilee Campus and teaching hospital (Queen's Medical Centre) are located within the City of Nottingham, with a number of smaller campuses and sites elsewhere in Nottinghamshire and Derbyshire. Outside the UK, the university has campuses in Semenyih, Malaysia, and Ningbo, China. Nottingham is organised into five constituent faculties, within which there are more than 50 schools, departments, institutes and research centres. Nottingham has about 45,500 students and 7,000 staff, and had an income of £694 million in 2020–21, of which £114.9 million was from research grants and contracts. The institution's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
