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Pietro Antonio Cataldi
Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems. His work included the development of continued fractions and a method for their representation. He was one of many mathematicians who attempted to prove Euclid's fifth postulate. Cataldi discovered the sixth and seventh perfect numbers by 1588.Caldwell, Chris''The largest known prime by year'' His discovery of the 6th, that corresponding to p=17 in the formula Mp=2p-1, exploded a many-times repeated number-theoretical myth that the perfect numbers had units digits that invariably alternated between 6 and 8. (Until Cataldi, 19 authors going back to Nicomachus are reported to have made the claim, with a few more repeating this afterward, according to L.E.Dickson's ''History of the Theory of Numbers''). Cataldi's discovery of the 7th (for p=19) held the record for the largest known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cataldi - Due Lettioni Date Nella Academia Erigenda Dove Si Mostra Come Si Trovi La Grandezza Delle Superficie Rettilinee, 1613 - 87568
Cataldi is an Italian surname, and may refer to: * Angelo Cataldi, American radio personality * Anna Cataldi, Italian humanitarian and journalist * Annaclara Cataldi Palau, Italian paleographer * Danilo Cataldi, Italian footballer * Lee Cataldi, Australian poet * Marianna Cataldi, Italian singer-songwriter and composer * Pietro Cataldi, Italian mathematician * Renato Cataldi Renato Cataldi (born December 25, 1909, São Paulo, Brazil; died May 29, 1981, Rio de Janeiro, Brazil) was a Brazilian painter. Cataldi is catalogued in the Julius Louzada's ''Dictionary of Arts'', and won several awards from the annual Salon ..., Brazilian painter {{surname Italian-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicomachus
Nicomachus of Gerasa ( grc-gre, Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician and music theorist, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'' in Greek. He was born in Gerasa, in the Roman province of Syria (now Jerash, Jordan). He was a Neopythagorean, who wrote about the mystical properties of numbers.Eric Temple Bell (1940), ''The development of mathematics'', page 83.Frank J. Swetz (2013), ''The European Mathematical Awakening'', page 17, Courier Life Little is known about the life of Nicomachus except that he was a Pythagorean who came from Gerasa.} Historians consider him a Neopythagorean based on his tendency to view numbers as having mystical properties. The age in which he lived (c. 100 AD) is only known because he mentions Thrasyllus in his ''Manual of Harmonics'', and because his ''Introduction to Arithmetic'' was apparently translated into Latin in the mid 2nd century by Apuleius.Henrietta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1626 Deaths
Sixteen or 16 may refer to: *16 (number), the natural number following 15 and preceding 17 *one of the years 16 BC, AD 16, 1916, 2016 Films * '' Pathinaaru'' or ''Sixteen'', a 2010 Tamil film * ''Sixteen'' (1943 film), a 1943 Argentine film directed by Carlos Hugo Christensen * ''Sixteen'' (2013 Indian film), a 2013 Hindi film * ''Sixteen'' (2013 British film), a 2013 British film by director Rob Brown Music *The Sixteen, an English choir *16 (band), a sludge metal band * Sixteen (Polish band), a Polish band Albums * ''16'' (Robin album), a 2014 album by Robin * 16 (Madhouse album), a 1987 album by Madhouse * ''Sixteen'' (album), a 1983 album by Stacy Lattisaw *''Sixteen'' , a 2005 album by Shook Ones * ''16'', a 2020 album by Wejdene Songs * "16" (Sneaky Sound System song), 2009 * "Sixteen" (Thomas Rhett song), 2017 * "Sixteen" (Ellie Goulding song), 2019 *"16", by Craig David from ''Following My Intuition'', 2016 *"16", by Green Day from ''39/Smooth'', 1990 *"16", by H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1548 Births
__NOTOC__ Year 1548 ( MDXLVIII) was a leap year starting on Sunday (link will display the full calendar) of the Julian calendar. Events January–June * February 14 – Battle of Uedahara: Firearms are used for the first time on the battlefield in Japan, and Takeda Shingen is defeated by Murakami Yoshikiyo. * April 1 – Sigismund II Augustus succeeds his father, Sigismund I the Old, as King of Poland and Grand Duke of Lithuania. * May 11 – The great fire in Brielle begins. * June ** Ming Chinese naval forces commanded by Zhu Wan destroy the pirate haven of Shuangyu, frequented by Chinese, Japanese and Portuguese smugglers. ** John Dee starts to study at the Old University of Leuven. July–December * July 7 – A marriage treaty is signed between Scotland and France, whereby five-year-old Mary, Queen of Scots, is betrothed to the future King Francis II of France. * August 7 – Mary, Queen of Scots, leaves for France. * October 20 &ndash ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2147483647
The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes. The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772. Euler used trial division, improving on Pietro Cataldi's method, so that at most 372 divisions were needed. It thus improved upon the previous record-holding prime, 6,700,417, also discovered by Euler, forty years earlier. The number 2,147,483,647 remained the largest known prime until 1867. In computing, this number is the largest value that a signed 32-bit integer field can hold. Barlow's prediction At the time of its discovery, 2,147,483,647 was the largest known prime number. In 1811, Peter Barlow, not anticipating future interest in perfect numbers, wrote (in ''An Elementary Investigation of the Theory of Numbers''): Euler ascertained that 231 − 1 = 2147483647 is a prime number; and this is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus. He introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory. Euler is held to be one of the greatest mathematicians in history and the greatest of the 18th century. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all." Carl Friedrich Gauss remarked: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it." Euler is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Largest Known Prime
The largest known prime number () is , a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. A prime number is a positive integer, excluding 1, with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so there is no largest prime. Many of the largest known primes are Mersenne primes, numbers that are one less than a power of two, because they can utilise a specialised primality test that is faster than the general one. , the eight largest known primes are Mersenne primes. The last seventeen record primes were Mersenne primes. The binary representation of any Mersenne prime is composed of all 1's, since the binary form of 2''k'' − 1 is simply ''k'' 1's. Current record The record is currently held by with 24,862,048 digits, found by GIMPS in December 2018. The first and last 120 digits of its val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of The Theory Of Numbers
''History of the Theory of Numbers'' is a three-volume work by L. E. Dickson summarizing work in number theory up to about 1920. The style is unusual in that Dickson mostly just lists results by various authors, with little further discussion. The central topic of quadratic reciprocity and higher reciprocity laws is barely mentioned; this was apparently going to be the topic of a fourth volume that was never written . Volumes * Volume 1 - Divisibility and Primality - 486 pages * Volume 2 - Diophantine Analysis In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ... - 803 pages * Volume 3 - Quadratic and Higher Forms - 313 pages References * * * * * * * * * * * * External links History of the Theory of Numbers - Volume 1at the Internet Archive. History of the Theory of Numbers - Volu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonard Eugene Dickson
Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also remembered for a three-volume history of number theory, ''History of the Theory of Numbers''. Life Dickson considered himself a Texan by virtue of having grown up in Cleburne, where his father was a banker, merchant, and real estate investor. He attended the University of Texas at Austin, where George Bruce Halsted encouraged his study of mathematics. Dickson earned a B.S. in 1893 and an M.S. in 1894, under Halsted's supervision. Dickson first specialised in Halsted's own specialty, geometry.A. A. Albert (1955Leonard Eugene Dickson 1874–1954from National Academy of Sciences Both the University of Chicago and Harvard University welcomed Dickson as a Ph.D. student, and Dickson initially accepted Harvard's offer, but chose to attend Chicago in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Units Digit
A numerical digit (often shortened to just digit) is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits (Latin ''digiti'' meaning fingers) of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal (ancient Latin adjective ''decem'' meaning ten) digits. For a given numeral system with an integer base, the number of different digits required is given by the absolute value of the base. For example, the decimal system (base 10) requires ten digits (0 through to 9), whereas the binary system (base 2) requires two digits (0 and 1). Overview In a basic digital system, a numeral is a sequence of digits, which may be of arbitrary length. Each position in the sequence has a place value, and each digit has a value. The value of the numeral is computed by multiplying each digit in the sequence by its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bologna
Bologna (, , ; egl, label= Emilian, Bulåggna ; lat, Bononia) is the capital and largest city of the Emilia-Romagna region in Northern Italy. It is the seventh most populous city in Italy with about 400,000 inhabitants and 150 different nationalities. Its metropolitan area is home to more than 1,000,000 people. It is known as the Fat City for its rich cuisine, and the Red City for its Spanish-style red tiled rooftops and, more recently, its leftist politics. It is also called the Learned City because it is home to the oldest university in the world. Originally Etruscan, the city has been an important urban center for centuries, first under the Etruscans (who called it ''Felsina''), then under the Celts as ''Bona'', later under the Romans (''Bonōnia''), then again in the Middle Ages, as a free municipality and later ''signoria'', when it was among the largest European cities by population. Famous for its towers, churches and lengthy porticoes, Bologna has a well-preserved ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Myth
Myth is a folklore genre consisting of Narrative, narratives that play a fundamental role in a society, such as foundational tales or Origin myth, origin myths. Since "myth" is widely used to imply that a story is not Objectivity (philosophy), objectively true, the identification of a narrative as a myth can be highly controversial. Many adherents of religions view their own religions' stories as truth and so object to their characterization as myth, the way they see the stories of other religions. As such, some scholars label all religious narratives "myths" for practical reasons, such as to avoid depreciating any one tradition because cultures interpret each other differently relative to one another. Other scholars avoid using the term "myth" altogether and instead use different terms like "sacred history", "holy story", or simply "history" to avoid placing pejorative overtones on any sacred narrative. Myths are often endorsed by secular and religious authorities and are close ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
