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Geminus
Geminus of Rhodes (), was a Greek astronomer and mathematician, who flourished in the 1st century BC. An astronomy work of his, the ''Introduction to the Phenomena'', still survives; it was intended as an introductory astronomy book for students. He also wrote a work on mathematics, of which only fragments quoted by later authors survive. Life Nothing is known about the life of Geminus. It is not even certain that he was born in Rhodes, but references to mountains on Rhodes in his astronomical works suggests that he worked there. His dates are not known with any certainty either. A passage in his works referring to the ''Annus Vagus'' (Wandering Year) of the Egyptian calendar of 120 years before his own time, has been used to imply a date of c. 70 BC for the time of writing, which would be consistent with the idea that he may have been a pupil of Posidonius, but a date as late as 50 AD has also been suggested. The crater Geminus on the Moon is named after him. Astronomy The ...
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Geminus (crater)
Geminus is a lunar impact crater that is located near the northeast limb of the visible Moon. In this position the crater appears oval in shape due to foreshortening, but it is actually more nearly circular in form. It was named by the IAU in 1935. The circular rim of Geminus contain a number of outward notches, particularly to the north and east. The crater ejecta is still visible in the rough surroundings beyond the rim, but any rays deposited during the impact have long since been worn away by space weathering. The inner wall is wide and extensively terraced, although these features are now somewhat muted due to impact erosion. There are no notable impacts on the interior floor, but there is a long, slender central ridge located at the midpoint and a pair of readily observed clefts. Notable nearby craters include Messala to the northeast, Bernoulli due east, and Burckhardt and Cleomedes Cleomedes () was a Greek astronomer who is known chiefly for his book ''On the C ...
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Zodiac
The zodiac is a belt-shaped region of the sky that extends approximately 8° north and south celestial latitude of the ecliptic – the apparent path of the Sun across the celestial sphere over the course of the year. Within this zodiac belt appear the Moon and the brightest planets, along their orbital planes. The zodiac is divided along the ecliptic into 12 equal parts, called " signs", each occupying 30° of celestial longitude. These signs roughly correspond to the astronomical constellations with the following modern names: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. The signs have been used to determine the time of the year by identifying each sign with the days of the year the Sun is in the respective sign. In Western astrology, and formerly astronomy, the time of each sign is associated with different attributes. The zodiacal system and its angular measurement in 360 sexagesimal degree ...
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Rhodes
Rhodes (; ) is the largest of the Dodecanese islands of Greece and is their historical capital; it is the List of islands in the Mediterranean#By area, ninth largest island in the Mediterranean Sea. Administratively, the island forms a separate municipality within the Rhodes (regional unit), Rhodes regional unit, which is part of the South Aegean Administrative regions of Greece, administrative region. The principal town of the island and seat of the municipality is the Rhodes (city), city of Rhodes, which had 50,636 inhabitants in 2011. In 2022, the island had a population of 125,113 people. It is located northeast of Crete and southeast of Athens. Rhodes has several nicknames, such as "Island of the Sun" due to its patron sun god Helios, "The Pearl Island", and "The Island of the Knights", named after the Knights Hospitaller, Knights of Saint John of Jerusalem, who ruled the island from 1310 to 1522. Historically, Rhodes was famous for the Colossus of Rhodes, one of the Sev ...
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Posidonius
Posidonius (; , "of Poseidon") "of Apameia" (ὁ Ἀπαμεύς) or "of Rhodes" (ὁ Ῥόδιος) (), was a Greeks, Greek politician, astronomer, astrologer, geographer, historian, mathematician, and teacher native to Apamea (Syria), Apamea, Syria. He was considered the most learned man of his time and, possibly, of the entire Stoicism, Stoic school. After a period learning Stoicism, Stoic philosophy from Panaetius in Athens, he spent many years in travel and scientific researches in Spain, Africa, Italy, Gaul, Liguria, Sicily and on the eastern shores of the Adriatic. He settled as a teacher at Rhodes where his fame attracted numerous scholars. Next to Panaetius he did most, by writings and personal lectures, to spread Stoicism to the Roman world, and he became well known to many leading men, including Pompey and Cicero. His works are now lost, but they proved a mine of information to later writers. The titles and subjects of more than twenty of them are known. In common w ...
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Proclus
Proclus Lycius (; 8 February 412 – 17 April 485), called Proclus the Successor (, ''Próklos ho Diádokhos''), was a Greek Neoplatonist philosopher, one of the last major classical philosophers of late antiquity. He set forth one of the most elaborate and fully developed systems of Neoplatonism and, through later interpreters and translators, exerted an influence on Byzantine philosophy, early Islamic philosophy, scholastic philosophy, and German idealism, especially G. W. F. Hegel, who called Proclus's ''Platonic Theology'' "the true turning point or transition from ancient to modern times, from ancient philosophy to Christianity." Biography The primary source for the life of Proclus is the eulogy ''Proclus'', ''or On Happiness'' that was written for him upon his death by his successor, Marinus, Marinus' biography set out to prove that Proclus reached the peak of virtue and attained eudaimonia. There are also a few details about the time in which he lived in the ...
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Eutocius
Eutocius of Ascalon (; ; 480s – 520s) was a Greek mathematician who wrote commentaries on several Archimedean treatises and on the Apollonian ''Conics''. Life and work Little is known about the life of Eutocius. He was born in Ascalon, then in Palestina Prima and lived during the reign of Justinian. Eutocius probably became the head of the Alexandrian school following Ammonius, and he was succeeded in this position by Olympiodorus, possibly as early as 525. From his testimony, it seems he traveled to other cultural centers of his time to find missing manuscripts. Eutocius wrote commentaries on Apollonius and on Archimedes. The surviving commentaries are: *A Commentary on the first four books of the '' Conics'' of Apollonius. *Commentaries on Archimedes' work: **''On the Sphere and Cylinder'' I-II. **''Measurement of the Circle'' (Latin: ''In Archimedis Dimensionem Circuli''). ** ''On the Equilibrium'' ''of Planes'' I-II. *An introduction to Book I of Ptolemy's ''Alma ...
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Pure Mathematics
Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but pure mathematicians are not primarily motivated by such applications. Instead, the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles. While pure mathematics has existed as an activity since at least ancient Greece, the concept was elaborated upon around the year 1900, after the introduction of theories with counter-intuitive properties (such as non-Euclidean geometries and Cantor's theory of infinite sets), and the discovery of apparent paradoxes (such as continuous functions that are nowhere differentiable, and Russell's paradox). This introduced the need to renew the concept of mathematical rigor and rewrite all mathematics accordingly, with a ...
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Applied Mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the profession, professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of Mathematical analysis, applied analysis, most notably differential equations; approximation theory (broadly construed, ...
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Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ...
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Arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the ...
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Simplicius Of Cilicia
Simplicius of Cilicia (; ; – c. 540) was a disciple of Ammonius Hermiae and Damascius, and was one of the last of the Neoplatonists. He was among the pagan philosophers persecuted by Justinian in the early 6th century, and was forced for a time to seek refuge in the Persian court, before being allowed back into the empire. He wrote extensively on the works of Aristotle. Although his writings are all commentaries on Aristotle and other authors, rather than original compositions, his intelligent and prodigious learning makes him the last great philosopher of pagan antiquity. His works have preserved much information about earlier philosophers which would have otherwise been lost. Life Little is known about Simplicius' life. Based on his education, it's likely he was born some time around 480. His commentary on Aristotle's On the Heavens can be definitively dated to 538, which is the latest known definitive evidence for his life, making it likely he died some time around 5 ...
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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, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ...
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