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Pietro 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 simple 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 lar ... [...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. Notable people with the surname include: * Angelo Cataldi (born 1951), American radio personality * Anna Cataldi (1939–2021), Italian humanitarian and journalist * Annaclara Cataldi Palau, Italian paleographer * Danilo Cataldi (born 1994), Italian footballer * Lee Cataldi (born 1942), Australian poet * Marianna Cataldi (born 1976), Italian singer-songwriter and composer * Pietro Cataldi (1548–1626), Italian mathematician * Renato Cataldi Renato Cataldi (born December 25, 1909, São Paulo, Brazil; died May 29, 1981, Rio de Janeiro Rio de Janeiro, or simply Rio, is the capital of the Rio de Janeiro (state), state of Rio de Janeiro. It is the List of cities in Brazil by popul ... (1909–1981), Brazilian painter {{surname Italian-language surnames ... [...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''. The L. E. Dickson instructorships at the University of Chicago Department of Mathematics are named after him. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
16th-century Italian Mathematicians
The 16th century began with the Julian year 1501 (represented by the Roman numerals MDI) and ended with either the Julian or the Gregorian year 1600 (MDC), depending on the reckoning used (the Gregorian calendar introduced a lapse of 10 days in October 1582). The Renaissance in Italy and Europe saw the emergence of important artists, authors and scientists, and led to the foundation of important subjects which include accounting and political science. Copernicus proposed the heliocentric universe, which was met with strong resistance, and Tycho Brahe refuted the theory of celestial spheres through observational measurement of the 1572 appearance of a Milky Way supernova. These events directly challenged the long-held notion of an immutable universe supported by Ptolemy and Aristotle, and led to major revolutions in astronomy and science. Galileo Galilei became a champion of the new sciences, invented the first thermometer and made substantial contributions in the fields of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1626 Deaths
Events January–March * January 7 – Polish-Swedish War: Battle of Wallhof in Latvia – Gustavus Adolphus, King of Sweden, defeats a Polish army. * January 9 – Peter Minuit sails from Texel Island for America's New Netherland colony, with two ships of Dutch emigrants. * February 2 – King Charles I of England is crowned, but without his wife, Henrietta Maria, who declines to participate in a non-Catholic ceremony. * February 5 – The Huguenot rebels and the French government sign the Treaty of Paris, ending the second Huguenot rebellion. * February 10 – Battle of Ningyuan: In Xingcheng in China, after an 8-day battle, Ming dynasty commander Yuan Chonghuan defeats the much larger force of Manchu leader Nurhaci, who dies soon after and is succeeded by Huang Taiji. * February 11 – Emperor Susenyos of Ethiopia and Patriarch Afonso Mendes declare the primacy of the Roman See over the Ethiopian Church, and Roman Catholicism ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1548 Births
Year 1548 ( MDXLVIII) was a leap year starting on Sunday of the Julian calendar. Events January–March * January 5 – Abu al-Abbas Ahmad III, ruler of the Hafsid Sultanate in what is now Tunisia in northern Africa, renews the 1547 treaty of friendship with Spain that had been signed by representatives of his father. * January 19 – Three ships from the Portuguese Navy arrive at the port of Aden to assist Mohammed bin Ali al-Tawlaki, who has been defending the city against an attack by the Ottoman Navy. The Portuguese ships are forced to retreat to Zeila in Somalia, where 120 survivors are captured and their ships are burned. * January 27 – King Henri II of France makes the Châtillon agreement, a contract for betrothal for an arranged marriage between his four year old son, Prince Francois, to the five year old Mary, Queen of Scots, to take place in 1558. * January 28 – (Tenbun 17, 30th day of 12th month) Nagao Kagetora (later Uesugi Kenshin) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ibn Fallus
Shams ad-Dīn Abû’t-Tāhir Ismāʽīl ibn-Ibrāhīm ibn-Ġāzī ibn-ʽAlī ibn Muhammad al-Ḥanafī al-Māridīnī (1194–1252), often called Ismāʽīl ibn-Fullūs or Ibn Fallus, was an Arab Egyptian mathematician of the Islamic Golden Age. Whilst on pilgrimage to Mecca, he tells of an epitome he wrote on number theory (extant in manuscript), which building on the work of Nicomachus, added three new perfect numbers (33,550,336; 8,589,869,056; and 137,438,691,328) to the four already discovered by the Greeks. His table also included seven other supposed perfect numbers which are now known to be incorrect. Roshdi Rashed believes the errors emerged from over-reliance on Nicomachus' method. This work did not reach Europe, and the three perfect numbers were only rediscovered there during the Renaissance, including by Pietro Cataldi.Scott, Paul"Just Perfect, part 2" ''The Australian Mathematics Teacher'', vol. 63, no. 2. p. 3. Further reading * Ismāʽīl ibn-FullūsIʽdād a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2147483647
The number 2147483647 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 wrote (in ''An Elementary Investigation of the Theory of Numbers''): Euler ascertained that 231 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, conse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonhard Euler
Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus. He also introduced much of modern mathematical terminology and Mathematical notation, notation, including the notion of a mathematical function. He is known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory. Euler has been called a "universal genius" who "was fully equipped with almost unlimited powers of imagination, intellectual gifts and extraordinary memory". He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Kingdom of Prussia, Prussia. Euler is credited for popularizing the Greek letter \pi (lowercase Pi (letter), pi) to denote Pi, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Largest Known Prime
The largest known prime number is , a number which has 41,024,320 digits when written in the decimal system. It was found on October 12, 2024, on a cloud-based virtual machine volunteered by Luke Durant, a 36-year-old researcher from San Jose, California, to the Great Internet Mersenne Prime Search (GIMPS). A prime number is a natural number greater than 1 with no divisors other than 1 and itself. Euclid's theorem proves that for any given prime number, there will always be a higher one, and thus there are infinitely many; 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 utilize a specialized primality test that is faster than the general one. , the seven largest known primes are Mersenne primes. The last eighteen record primes were Mersenne primes. The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2''k'' − 1 is simply ''k'' ones. ... [...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 Leonard Eugene 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 In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a ''Multiple (mathematics), multiple'' of m. An integer n is divis ... and Primality - 486 pages * Volume 2 - Diophantine Analysis - 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 Nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicomachus
Nicomachus of Gerasa (; ) was an Ancient Greek Neopythagorean philosopher from Gerasa, in the Roman province of Syria (now Jerash, Jordan). Like many Pythagoreans, Nicomachus wrote about the mystical properties of numbers, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'', which are an important resource on Ancient Greek mathematics and Ancient Greek music in the Roman period. Nicomachus' work on arithmetic became a standard text for Neoplatonic education in Late antiquity, with philosophers such as Iamblichus and John Philoponus writing commentaries on it. A Latin paraphrase by Boethius of Nicomachus's works on arithmetic and music became standard textbooks in medieval education. Life Little is known about the life of Nicomachus except that he was a Pythagorean who came from Gerasa. His ''Manual of Harmonics'' was addressed to a lady of noble birth, at whose request Nicomachus wrote the book, which suggests that he was a respected schola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bologna
Bologna ( , , ; ; ) is the capital and largest city of the Emilia-Romagna region in northern Italy. It is the List of cities in Italy, seventh most populous city in Italy, with about 400,000 inhabitants and 150 different nationalities. Its Metropolitan City of Bologna, metropolitan province is home to more than 1 million people. Bologna is most famous for being the home to the List of oldest universities in continuous operation, oldest university in continuous operation,Top Universities ''World University Rankings'' Retrieved 6 January 2010Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hilde [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
