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Hardy-Ramanujan Journal
1729 is the natural number following 1728 and preceding 1730. It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation: The two different ways are: : 1729 = 13 + 123 = 93 + 103 The quotation is sometimes expressed using the term "positive cubes", since allowing negative perfect cubes (the cube of a negative integer) gives the smallest solution as 91 (which is a divisor of 1729; 1991 = 1729). :91 = 63 + (−5)3 = 43 + 33 Numbers that are the smallest number that can be expressed as the sum of two cubes in ''n'' distinct ways have been dubbed " taxicab numbers". The number was also found in one of Ramanujan's notebooks dated years before the incident, and was noted by Frénicle de Bessy in 1657. A commemorative plaque now appears at the site of the Ramanujan-Hardy in ... [...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] |
Centered Cube Number
A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with points on the square faces of the th layer. Equivalently, it is the number of points in a body-centered cubic pattern within a cube that has points along each of its edges. The first few centered cube numbers are : 1, 9, 35, 91, 189, 341, 559, 855, 1241, 1729, 2331, 3059, 3925, 4941, 6119, 7471, 9009, ... . Formulas The centered cube number for a pattern with concentric layers around the central point is given by the formula :n^3 + (n + 1)^3 = (2n+1)\left(n^2+n+1\right). The same number can also be expressed as a trapezoidal number (difference of two triangular numbers), or a sum of consecutive numbers, as :\binom-\binom = (n^2+1)+(n^2+2)+\cdots+(n+1)^2. Properties Because of the factorization , it is impossible for a centered cube number to be a prime number. The only centered ... [...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] |
4104 (number)
4104 (four thousand one hundred ndfour) is the natural number following 4103 and preceding 4105. It is the second positive integer which can be expressed as the sum of two positive cubes in two different ways. The first such number, 1729, is called the "Ramanujan–Hardy number". 4104 is the sum of 4096 + 8 (that is, 163 + 23), and also the sum of 3375 + 729 (that is, 153 + 93). See also * Taxicab number In mathematics, the ''n''th taxicab number, typically denoted Ta(''n'') or Taxicab(''n''), also called the ''n''th Hardy–Ramanujan number, is defined as the smallest integer that can be expressed as a sum of two ''positive'' integer cubes in ... * 1729 External links MathWorld: Hardy–Ramanujan Number {{DEFAULTSORT:4104 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interesting Number Paradox
The interesting number paradox is a humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting. The "proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a contradiction. "Interestingness" concerning numbers is not a formal concept in normal terms, but an innate notion of "interestingness" seems to run among some number theorists. Famously, in a discussion between the mathematicians G. H. Hardy and Srinivasa Ramanujan about interesting and uninteresting numbers, Hardy remarked that the number 1729 of the taxicab he had ridden seemed "rather a dull one", and Ramanujan immediately answered that it is interesting, being the smallest number tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Disappearing Number
''A Disappearing Number'' is a 2007 play co-written and devised by the Théâtre de Complicité company and directed and conceived by English playwright Simon McBurney. It was inspired by the collaboration during the 1910s between the pure mathematicians Srinivasa Ramanujan from India, and the Cambridge University don G.H. Hardy. It was a co-production between the UK-based theatre company Complicite and Theatre Royal, Plymouth, and Ruhrfestspiele, Wiener Festwochen, and the Holland Festival. ''A Disappearing Number'' premiered in Plymouth in March 2007, toured internationally, and played at The Barbican Centre in Autumn 2007 and 2008 and at Lincoln Center in July 2010. It was directed by Simon McBurney with music by Nitin Sawhney. The production is 110 minutes with no intermission. The piece was co-devised and written by the cast and company. The cast in order of appearance: Firdous Bamji, Saskia Reeves, David Annen, Paul Bhattacharjee, Shane Shambu, Divya Kasturi and Chetna P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galactic Algorithm
A galactic algorithm is one that outperforms any other algorithm for problems that are sufficiently large, but where "sufficiently large" is so big that the algorithm is never used in practice. Galactic algorithms were so named by Richard Lipton and Ken Regan, because they will never be used on any data sets on Earth. Possible use cases Even if they are never used in practice, galactic algorithms may still contribute to computer science: * An algorithm, even if impractical, may show new techniques that may eventually be used to create practical algorithms. * Available computational power may catch up to the crossover point, so that a previously impractical algorithm becomes practical. * An impractical algorithm can still demonstrate that conjectured bounds can be achieved, or that proposed bounds are wrong, and hence advance the theory of algorithms. As Lipton states: Similarly, a hypothetical large but polynomial O\bigl(n^\bigr) algorithm for the Boolean satisfiability problem, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication Algorithm
A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Efficient multiplication algorithms have existed since the advent of the decimal system. Long multiplication If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results. It requires memorization of the multiplication table for single digits. This is the usual algorithm for multiplying larger numbers by hand in base 10. A person doing long multiplication on paper will write down all the products and then add them together; an abacus-user will sum the products as soon as each one is computed. Example This example uses ''long multiplication'' to multiply 23,958 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discriminant
In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number theory, and algebraic geometry. The discriminant of the quadratic polynomial ax^2+bx+c is :b^2-4ac, the quantity which appears under the square root in the quadratic formula. If a\ne 0, this discriminant is zero if and only if the polynomial has a double root. In the case of real coefficients, it is positive if the polynomial has two distinct real roots, and negative if it has two distinct complex conjugate roots. Similarly, the discriminant of a cubic polynomial is zero if and only if the polynomial has a multiple root. In the case of a cubic with real coefficients, the discriminant is positive if the polynomial has three distinct real roots, and negative i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Form
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong to a fixed field , such as the real or complex numbers, and one speaks of a quadratic form over . If K=\mathbb R, and the quadratic form takes zero only when all variables are simultaneously zero, then it is a definite quadratic form, otherwise it is an isotropic quadratic form. Quadratic forms occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory (orthogonal group), differential geometry (Riemannian metric, second fundamental form), differential topology ( intersection forms of four-manifolds), and Lie theory (the Killing form). Quadratic forms are not to be confused with a quadratic equation, which has only one variable and includes terms of degree two or less. A quadratic form is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
