|
Thymaridas
Thymaridas of Paros ( el, Θυμαρίδας; c. 400 – c. 350 BCE) was an ancient Greek Mathematics, Greek mathematician and Pythagoreanism, Pythagorean noted for his work on prime numbers and simultaneous linear equations. Life and work Although little is known about the life of Thymaridas, it is believed that he was a rich man who fell into poverty. It is said that Thestor of Poseidonia traveled to Paros in order to help Thymaridas with the money that was collected for him. Iamblichus states that Thymaridas called prime numbers "rectilinear", since they can only be represented on a one-dimensional line. Non-prime numbers, on the other hand, can be represented on a two-dimensional plane as a rectangle with sides that, when multiplied, produce the non-prime number in question. He further called the number one a "limiting quantity". Iamblichus in his comments to ''Introduction to Arithmetic, Introductio arithmetica'' states that Thymaridas also worked with simultaneous linear eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paros
Paros (; el, Πάρος; Venetian: ''Paro'') is a Greek island in the central Aegean Sea. One of the Cyclades island group, it lies to the west of Naxos, from which it is separated by a channel about wide. It lies approximately south-east of Piraeus. The Municipality of Paros includes numerous uninhabited offshore islets totaling of land. Its nearest neighbor is the municipality of Antiparos, which lies to its southwest. In ancient Greece, the city-state of Paros was located on the island. Historically, Paros was known for its fine white marble, which gave rise to the term "Parian" to describe marble or china of similar qualities. Today, abandoned marble quarries and mines can be found on the island, but Paros is primarily known as a popular tourist spot. Geography Paros' geographic co-ordinates are 37° N. latitude, and 25° 10' E. longitude. The area is . Its greatest length from N.E. to S.W. is , and its greatest breadth . The island is of a round, plump-pear shape, form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Mathematics
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the grc, , máthēma , meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations. Origins of Greek mathematics The origin of Greek mathematics is not well documented. The earliest advanced civilizations in Greece and in Europe were the Minoan and later Mycenaean civilizations, both of which flourished during the 2nd millennium BCE. While these civilizations possessed writing and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the Ancient Greece, ancient Greek colony of Crotone, Kroton, in modern Calabria (Italy). Early Pythagorean communities spread throughout Magna Graecia. Pythagoras' death and disputes about his teachings led to the development of two philosophical traditions within Pythagoreanism. The ''akousmatikoi'' were superseded in the 4th century BC as a significant mendicant school of philosophy by the Cynicism (philosophy), Cynics. The ''mathēmatikoi'' philosophers were absorbed into the Platonic Academy, Platonic school in the 4th century BC. Following political instability in Magna Graecia, some Pythagorean philosophers fled to mainland Greece while others regrouped in Rhegium. By about 400 BC the majority of Pythagorean philosophers had left Italy. Pythagorean ideas exercised a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Numbers
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simultaneous Linear Equations
In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, :\begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of three equations in the three variables . A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by the ordered triple :(x,y,z)=(1,-2,-2), since it makes all three equations valid. The word "system" indicates that the equations are to be considered collectively, rather than individually. In mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject which is used in most parts of modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. A syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iamblichus
Iamblichus (; grc-gre, Ἰάμβλιχος ; Aramaic: 𐡉𐡌𐡋𐡊𐡅 ''Yamlīḵū''; ) was a Syrian neoplatonic philosopher of Arabic origin. He determined a direction later taken by neoplatonism. Iamblichus was also the biographer of the Greek mystic, philosopher, and mathematician Pythagoras. In addition to his philosophical contributions, his ''Protrepticus'' is important for the study of the sophists because it preserved about ten pages of an otherwise-unknown sophist known as the Anonymus Iamblichi. Life According to the ''Suda'' and Iamblichus' biographer, Eunapius, he was born in Chalcis in Coele Syria. The son of a wealthy, well-known family, Iamblichus was descended from the Emesene dynasty. He initially studied under Anatolius of Laodicea and later studied under Porphyry, a pupil of Plotinus (the founder of neoplatonism). Iamblichus disagreed with Porphyry about theurgy, reportedly responding to Porphyry's criticism of the practice in ''De Mysteriis Aegypt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Introduction To Arithmetic
The book ''Introduction to Arithmetic'' ( grc-gre, Ἀριθμητικὴ εἰσαγωγή, ''Arithmetike eisagoge'') is the only extant work on mathematics by Nicomachus (60–120 AD). Summary The work contains both philosophical prose and basic mathematical ideas. Nicomachus refers to Plato quite often, and writes that philosophy can only be possible if one knows enough about mathematics. Nicomachus also describes how natural numbers and basic mathematical ideas are eternal and unchanging, and in an abstract realm. It consists of two books, twenty-three and twenty-nine chapters, respectively. Although he was preceded by the Babylonians and the Chinese, Nicomachus provided one of the earliest Greco-Roman multiplication tables, whereas the oldest extant Greek multiplication table is found on a wax tablet dated to the 1st century AD (now found in the British Museum). Influence The ''Introduction to Arithmetic'' of Nicomachus was a standard textbook in Neoplatonic schools an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek Mathematicians
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the grc, , máthēma , meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations. Origins of Greek mathematics The origin of Greek mathematics is not well documented. The earliest advanced civilizations in Greece and in Europe were the Minoan and later Mycenaean civilizations, both of which flourished during the 2nd millennium BCE. While these civilizations possessed writing an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4th-century BC Deaths
The 4th century (per the Julian calendar and Anno Domini/Common era) was the time period which lasted from 301 ( CCCI) through 400 ( CD). In the West, the early part of the century was shaped by Constantine the Great, who became the first Roman emperor to adopt Christianity. Gaining sole reign of the empire, he is also noted for re-establishing a single imperial capital, choosing the site of ancient Byzantium in 330 (over the current capitals, which had effectively been changed by Diocletian's reforms to Milan in the West, and Nicomedeia in the East) to build the city soon called Nova Roma (New Rome); it was later renamed Constantinople in his honor. The last emperor to control both the eastern and western halves of the empire was Theodosius I. As the century progressed after his death, it became increasingly apparent that the empire had changed in many ways since the time of Augustus. The two emperor system originally established by Diocletian in the previous century fell int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4th-century BC Greek People
The 4th century (per the Julian calendar and Anno Domini/Common era) was the time period which lasted from 301 ( CCCI) through 400 ( CD). In the West, the early part of the century was shaped by Constantine the Great, who became the first Roman emperor to adopt Christianity. Gaining sole reign of the empire, he is also noted for re-establishing a single imperial capital, choosing the site of ancient Byzantium in 330 (over the current capitals, which had effectively been changed by Diocletian's reforms to Milan in the West, and Nicomedeia in the East) to build the city soon called Nova Roma (New Rome); it was later renamed Constantinople in his honor. The last emperor to control both the eastern and western halves of the empire was Theodosius I. As the century progressed after his death, it became increasingly apparent that the empire had changed in many ways since the time of Augustus. The two emperor system originally established by Diocletian in the previous century fell in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Parians
Ancient history is a time period from the beginning of writing and recorded human history to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian cuneiform script. Ancient history covers all continents inhabited by humans in the period 3000 BCAD 500. The three-age system periodizes ancient history into the Stone Age, the Bronze Age, and the Iron Age, with recorded history generally considered to begin with the Bronze Age. The start and end of the three ages varies between world regions. In many regions the Bronze Age is generally considered to begin a few centuries prior to 3000 BC, while the end of the Iron Age varies from the early first millennium BC in some regions to the late first millennium AD in others. During the time period of ancient history, the world population was already exponentially increasing due to the Neolithic Revolution, which was in full progress. While in 10,000 BC, the world population stood a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
