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Feynman Point
A sequence of six consecutive nines occurs in the decimal representation of the number pi (), starting at the 762nd decimal place.. It has become famous because of the mathematical coincidence, and because of the idea that one could memorize the digits of up to that point, and then suggest that is rational. The earliest known mention of this idea occurs in Douglas Hofstadter's 1985 book '' Metamagical Themas'', where Hofstadter states This sequence of six nines is colloquially known as the "Feynman point", after physicist Richard Feynman, who allegedly stated this same idea in a lecture.. However it is not clear when, or even if, Feynman ever made such a statement. It is not mentioned in his memoirs and unknown to his biographer James Gleick. Related statistics is conjectured, but not known, to be a normal number. For a normal number sampled uniformly at random, the probability of a specific sequence of six digits occurring this early in the decimal representation is about ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal
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 (''decimal fractions'') 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 , w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Resolution of conjectures Proof Formal mathematics is based on ''provable'' truth. In mathematics, any number of cases supporting a universally quantified conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample could immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 101 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled ''CRC Concise Encyclopedia of Mathematics''. The free online version became only partially accessible to the public. In 1999 Weisstein we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heegner Number
In number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ..., a Heegner number (as termed by Conway and Guy) is a square-free positive integer ''d'' such that the imaginary quadratic field \Q\left sqrt\right/math> has class number 1. Equivalently, the ring of algebraic integers of \Q\left sqrt\right/math> has unique factorization. The determination of such numbers is a special case of the class number problem, and they underlie several striking results in number theory. According to the (Baker–) Stark–Heegner theorem there are precisely nine Heegner numbers: This result was conjectured by Gauss and proved up to minor flaws by Kurt Heegner in 1952. Alan Baker and Harold Stark independently proved the result in 1966, and Stark further indicated that the gap in ... [...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). Any such number can be represented as follows \underbrace_ = \frac Where nn is the concatenation of n with n. k the number of concatenated n. nn can be represented mathematically as n\cdot\left(10^+1\right) for n = 23 and k = 5, the formula will look like this \frac = \frac = \underbrace_ However, 2323232323 is not a repdigit. Also, any number can be decomposed into the sum and difference of the repdigit numbers. For example 3453455634 = 3333333333 + (111111111 + (99999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Coincidence
A mathematical coincidence is said to occur when two expressions with no direct relationship show a near-equality which has no apparent theoretical explanation. For example, there is a near-equality close to the round number 1000 between powers of 2 and powers of 10: : 2^ = 1024 \approx 1000 = 10^3. Some mathematical coincidences are used in engineering when one expression is taken as an approximation of another. Introduction A mathematical coincidence often involves an integer, and the surprising feature is the fact that a real number arising in some context is considered by some standard as a "close" approximation to a small integer or to a multiple or power of ten, or more generally, to a rational number with a small denominator. Other kinds of mathematical coincidences, such as integers simultaneously satisfying multiple seemingly unrelated criteria or coincidences regarding units of measurement, may also be considered. In the class of those coincidences that are of a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
9 (number)
9 (nine) is the natural number following and preceding . Evolution of the Hindu–Arabic digit Circa 300 BC, as part of the Brahmi numerals, various Indians wrote a digit 9 similar in shape to the modern closing question mark without the bottom dot. The Kshatrapa, Andhra and Gupta started curving the bottom vertical line coming up with a -look-alike. How the numbers got to their Gupta form is open to considerable debate. The Nagari continued the bottom stroke to make a circle and enclose the 3-look-alike, in much the same way that the sign @ encircles a lowercase ''a''. As time went on, the enclosing circle became bigger and its line continued beyond the circle downwards, as the 3-look-alike became smaller. Soon, all that was left of the 3-look-alike was a squiggle. The Arabs simply connected that squiggle to the downward stroke at the middle and subsequent European change was purely cosmetic. While the shape of the glyph for the digit 9 has an ascender in most modern typef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Number
In mathematics, a real number is said to be simply normal in an integer base b if its infinite sequence of digits is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b. A number is said to be normal in base b if, for every positive integer n, all possible strings n digits long have density b−''n''. Intuitively, a number being simply normal means that no digit occurs more frequently than any other. If a number is normal, no finite combination of digits of a given length occurs more frequently than any other combination of the same length. A normal number can be thought of as an infinite sequence of coin flips ( binary) or rolls of a die ( base 6). Even though there ''will'' be sequences such as 10, 100, or more consecutive tails (binary) or fives (base 6) or even 10, 100, or more repetitions of a sequence such as tail-head (two consecutive coin flips) or 6-1 (two consecutive rolls of a die), there will also be equally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concord Monitor
The ''Concord Monitor'' is the daily newspaper for Concord, the state capital of New Hampshire. It also covers surrounding towns in Merrimack County, most of Belknap County, as well as portions of Grafton, Rockingham and Hillsborough counties. The ''Monitor'' has several times been named as one of the best small papers in America and in April 2008, became a Pulitzer Prize winning paper, when photographer Preston Gannaway was honored for feature photography. After publishing seven days a week for decades, starting in March 2024, it ceased print publication on Sundays. History The ''Monitor'' has been published continuously since 1864, under a variety of names, including the ''Evening Monitor'', and owners. In the late 19th century it was owned by a publishing company called the Republican Press Association which also published a paper named the ''Independent Statesman''. Its masthead calls it the ''Concord Monitor and New Hampshire Patriot'', although the ''Monitor'' name ... [...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 r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Gleick
James Gleick (; born August 1, 1954) is an American author and historian of science whose work has chronicled the cultural impact of modern technology. Recognized for his writing about complex subjects through the techniques of narrative nonfiction, he has been called "one of the great science writers of all time". He is part of the inspiration for ''Jurassic Park'' character Ian Malcolm. Gleick's books include the international bestsellers '' Chaos: Making a New Science'' (1987) and '' The Information: A History, a Theory, a Flood'' (2011). Three of his books have been Pulitzer Prize and National Book Award finalists; and ''The Information'' was awarded the PEN/E. O. Wilson Literary Science Writing Award and the Royal Society Winton Prize for Science Books in 2012. His books have been translated into more than thirty languages. Per the ''Wall Street Journal'', "Some writers excel at crafting a historical narrative, others at elucidating esoteric theories, still others at huma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memoir
A memoir (; , ) is any nonfiction narrative writing based on the author's personal memories. The assertions made in the work are thus understood to be factual. While memoir has historically been defined as a subcategory of biography or autobiography since the late 20th century, the genre is differentiated in form, presenting a narrowed focus, usually a particular time phase in someone's life or career. A biography or autobiography tells the story "of a life", while a memoir often tells the story of a particular career, event, or time, such as touchstone moments and turning points in the author's life. The author of a memoir may be referred to as a memoirist or a memorialist. Early memoirs Memoirs have been written since the ancient times, as shown by Julius Caesar's '' Commentarii de Bello Gallico'', also known as ''Commentaries on the Gallic Wars''. In the work, Caesar describes the battles that took place during the nine years that he spent fighting local armies in the G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
