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Mersenne
Marin Mersenne, OM (also known as Marinus Mersennus or ''le Père'' Mersenne; ; 8 September 1588 – 1 September 1648) was a French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for Mersenne prime numbers, those which can be written in the form for some integer . He also developed Mersenne's laws, which describe the harmonics of a vibrating string (such as may be found on guitars and pianos), and his seminal work on music theory, ''Harmonie universelle'', for which he is referred to as the "father of acoustics". Mersenne, an ordained Catholic priest, had many contacts in the scientific world and has been called "the center of the world of science and mathematics during the first half of the 1600s" and, because of his ability to make connections between people and ideas, "the post-box of Europe". He was also a member of the Minim religious order and wrote and lectured on theology and philosophy. Life Mersenne wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Primes
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Conjectures
In mathematics, the Mersenne conjectures concern the characterization of prime numbers of a form called Mersenne primes, meaning prime numbers that are a power of two minus one. Original Mersenne conjecture The original, called Mersenne's conjecture, was a statement by Marin Mersenne in his ''Cogitata Physico-Mathematica'' (1644; see e.g. Dickson 1919) that the numbers 2^n - 1 were prime for ''n'' = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, and were composite for all other positive integers ''n'' ≤ 257. Due to the size of these numbers, Mersenne did not and could not test all of them, nor could his peers in the 17th century. It was eventually determined, after three centuries and the availability of new techniques such as the Lucas–Lehmer test, that Mersenne's conjecture contained five errors, namely two are composite (those corresponding to the primes ''n'' = 67, 257) and three omitted primes (those corresponding to the primes ''n'' = 61, 89, 107). The correct list is: ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne's Laws
Mersenne's laws are laws describing the frequency of oscillation of a stretched string or monochord, useful in musical tuning and musical instrument construction. Overview The equation was first proposed by French mathematician and music theorist Marin Mersenne in his 1636 work ''Harmonie universelle''.Mersenne, Marin (1636)''Harmonie universelle'' Cited in, '' Wolfram.com''. Mersenne's laws govern the construction and operation of string instruments, such as pianos and harps, which must accommodate the total tension force required to keep the strings at the proper pitch. Lower strings are thicker, thus having a greater mass per length. They typically have lower tension. Guitars are a familiar exception to this: string tensions are similar, for playability, so lower string pitch is largely achieved with increased mass per length. Higher-pitched strings typically are thinner, have higher tension, and may be shorter. "This result does not differ substantially from Galileo's, yet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacques Alexandre Le Tenneur
Jacques-Alexandre Le Tenneur (1604 - 1659) was a French mathematician who defended Galileo Galilei’s ideas. He corresponded with fellow mathematicians such as Pierre Gassendi, Pierre Hérigone and Marin Mersenne. It is unclear when or where he died but he probably lived from 1610 to 1660. Biography Not much is known about Le Tenneur’s personal life and most information comes from his letters to Mersenne and Garrendi. He was mostly self-educated during his early life in Paris. By 1646 he spent a little time in Clermont in the Auvergne region of central France. and then returned to settle in Paris. Politics and background In 1651 he became King Louis XIV’s counsellor to the provincial senate of the old French province of Guyenne in Bordeaux. A civil war in France called the Fronde was going on at this time and involved Guyenne so Le Tenneur was probably involved with the political feuding of the civil war. Support of Galileo Le Tenneur was one of the few French schol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonie Universelle
''Harmonie universelle'' ("Universal Harmony"; complete title: ''Harmonie universelle, contenant la théorie et la pratique de la musique'') is a work by Marin Mersenne, published in Paris in 1636. It represented the sum of musical knowledge during his lifetime. This was a major work since it represented the most complete description of music theory near the middle of the 17th century in France. It covers all aspects including theoretical, practical, stylistic, organological, mathematical, acoustical, and theological. Content The title page specifies the scope of the topics covered by the book including the nature of sounds, movements, consonance, dissonance, genres, modes of composition, voice, singing, and all kinds of harmonic instruments. This monumental treatise is abundant in illustrations (including musical engravings), and in systematic tables. It also remains the only source of certain musical works from Jacques Mauduit, Eustache Du Caurroy, Antoine de Sewn, or Pierre de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
René Descartes
René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathematics was central to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry. Descartes spent much of his working life in the Dutch Republic, initially serving the Dutch States Army, later becoming a central intellectual of the Dutch Golden Age. Although he served a Protestant state and was later counted as a deist by critics, Descartes considered himself a devout Catholic. Many elements of Descartes' philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like Augustine. In his natural philosophy, he differed from the schools on two major points: first, he rejected the splitting of corporeal substance into mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Hobbes
Thomas Hobbes ( ; 5/15 April 1588 – 4/14 December 1679) was an English philosopher, considered to be one of the founders of modern political philosophy. Hobbes is best known for his 1651 book ''Leviathan'', in which he expounds an influential formulation of social contract theory. In addition to political philosophy, Hobbes contributed to a diverse array of other fields, including history, jurisprudence, geometry, theology, and ethics, as well as philosophy in general. Biography Early life Thomas Hobbes was born on 5 April 1588 (Old Style), in Westport, now part of Malmesbury in Wiltshire, England. Having been born prematurely when his mother heard of the coming invasion of the Spanish Armada, Hobbes later reported that "my mother gave birth to twins: myself and fear." Hobbes had a brother, Edmund, about two years older, as well as a sister named Anne. Although Thomas Hobbes's childhood is unknown to a large extent, as is his mother's name, it is known that Hobbes's fat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acoustics
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an Acoustical engineering, acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries. Hearing (sense), Hearing is one of the most crucial means of survival in the animal world and speech is one of the most distinctive characteristics of human development and culture. Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or for marking territories. Art, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minim (religious Order)
The Minims, officially known as the Order of Minims (; abbreviated OM), are a Roman Catholic religious order of friars founded by Saint Francis of Paola in fifteenth-century Italy. The order soon spread to France, Germany and Spain, and continues to exist today. Like the other mendicant orders, there are three separate components, or orders, of the movement: the friars, contemplative nuns and a Third Order of laypeople who live in the spirit of the order in their daily lives. At present there are only two fraternities of the Minim tertiaries; both are in Italy. History The founder of the Order, Saint Francis of Paola, was born in 1416 and named in honor of St. Francis of Assisi. The boy became ill when he was only one month old, and his mother prayed to St. Francis and promised that her son would spend a year in a Franciscan friary if he were healed. Francis recovered, which she believed meant that God had granted her prayer. At 13 years of age Francis fulfilled that votive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acoustics
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an Acoustical engineering, acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries. Hearing (sense), Hearing is one of the most crucial means of survival in the animal world and speech is one of the most distinctive characteristics of human development and culture. Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or for marking territories. Art, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minims (religious Order)
The Minims, officially known as the Order of Minims (; abbreviated OM), are a Roman Catholic religious order of friars founded by Saint Francis of Paola in fifteenth-century Italy. The order soon spread to France, Germany and Spain, and continues to exist today. Like the other mendicant orders, there are three separate components, or orders, of the movement: the friars, contemplative nuns and a Third Order of laypeople who live in the spirit of the order in their daily lives. At present there are only two fraternities of the Minim tertiaries; both are in Italy. History The founder of the Order, Saint Francis of Paola, was born in 1416 and named in honor of St. Francis of Assisi. The boy became ill when he was only one month old, and his mother prayed to St. Francis and promised that her son would spend a year in a Franciscan friary if he were healed. Francis recovered, which she believed meant that God had granted her prayer. At 13 years of age Francis fulfilled that vo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
