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Apollonius Of Perga
Apollonius of Perga ( ; ) was an ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the earlier contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. With his predecessors Euclid and Archimedes, Apollonius is generally considered among the greatest mathematicians of antiquity. Aside from geometry, Apollonius worked on numerous other topics, including astronomy. Most of this work has not survived, where exceptions are typically fragments referenced by other authors like Pappus of Alexandria. His hypothesis of eccentric orbits to explain the apparently aberrant motion of the planets, commonly believed until the Middle Ages, was superseded during the Renaissance. The Apollonius crater on the Moon is named in his honor. Life Despite his momentous contributions to the field of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Eccentricity
In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit (or capture orbit), and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the Galaxy. Definition In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit. The eccentricity of this Kepler orbit is a non-negative number that defines its shape. The eccentricity may take the following values: * Circular orbit: * Elliptic orbit: * Parabolic trajectory: * Hyperbolic trajectory: The eccentricity is given by e = \sqrt where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anatolia
Anatolia (), also known as Asia Minor, is a peninsula in West Asia that makes up the majority of the land area of Turkey. It is the westernmost protrusion of Asia and is geographically bounded by the Mediterranean Sea to the south, the Aegean Sea to the west, the Turkish Straits to the northwest, and the Black Sea to the north. The eastern and southeastern limits have been expanded either to the entirety of Asiatic Turkey or to an imprecise line from the Black Sea to the Gulf of Alexandretta. Topographically, the Sea of Marmara connects the Black Sea with the Aegean Sea through the Bosporus and the Dardanelles, and separates Anatolia from Thrace in Southeast Europe. During the Neolithic, Anatolia was an early centre for the development of farming after it originated in the adjacent Fertile Crescent. Beginning around 9,000 years ago, there was a major migration of Anatolian Neolithic Farmers into Neolithic Europe, Europe, with their descendants coming to dominate the continent a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pamphylia
Pamphylia (; , ''Pamphylía'' ) was a region in the south of Anatolia, Asia Minor, between Lycia and Cilicia, extending from the Mediterranean Sea, Mediterranean to Mount Taurus (all in modern-day Antalya province, Turkey). It was bounded on the north by Pisidia and was therefore a country of small extent, having a coast-line of only about 120 km (75 miles) with a breadth of about 50 km (30 miles). Under the Roman administration the term Pamphylia was extended so as to include Pisidia and the whole tract up to the frontiers of Phrygia and Lycaonia, and in this wider sense it is employed by Ptolemy. Name The name ''Pamphylia'' comes from the Greek language, Greek Παμφυλία, itself from (''pamphylos''), literally "of mingled tribes or races", a compound of πᾶν (''pan''), neuter of πᾶς (''pas'') "all" + φυλή (''phylē''), "race, tribe". Herodotus derived its etymology from a Dorians, Dorian tribe, the Pamphyloi (Πάμφυλοι), who were said to hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perga
Perga or Perge ( Hittite: ''Parha'', ''Perge'', ) was originally an ancient Lycian settlement that later became a Greek city in Pamphylia. It was the capital of the Roman province of Pamphylia Secunda, now located in Antalya Province on the southwestern Mediterranean coast of Turkey. Today its ruins lie east of Antalya. It was the birthplace of Apollonius of Perga, one of the most notable ancient Greek mathematicians for his work on conic sections. A unique and prominent feature for a Roman city was the long central water channel in the centre of the main street which contained a series of cascading pools and which would have been remarkable even today in a semi-arid area where summer temperatures reach over 30 degrees Celsius. History Perge was situated on the coastal plain between the Rivers Catarrhactes (Düden Nehri) and Cestrus (Aksu), about 11 km from the mouth of the latter. Early Bronze The history of the city dates back to the Late Chalcolitic Era or Ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hellenistic Period
In classical antiquity, the Hellenistic period covers the time in Greek history after Classical Greece, between the death of Alexander the Great in 323 BC and the death of Cleopatra VII in 30 BC, which was followed by the ascendancy of the Roman Empire, as signified by the Battle of Actium in 31 BC and the Roman conquest of Ptolemaic Egypt the following year, which eliminated the last major Hellenistic kingdom. Its name stems from the Ancient Greek word ''Hellas'' (, ''Hellás''), which was gradually recognized as the name for Greece, from which the modern historiographical term ''Hellenistic'' was derived. The term "Hellenistic" is to be distinguished from "Hellenic" in that the latter refers to Greece itself, while the former encompasses all the ancient territories of the period that had come under significant Greek influence, particularly the Hellenized Middle East, after the conquests of Alexander the Great. After the Macedonian conquest of the Achaemenid Empire in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pompeii
Pompeii ( ; ) was a city in what is now the municipality of Pompei, near Naples, in the Campania region of Italy. Along with Herculaneum, Stabiae, and Villa Boscoreale, many surrounding villas, the city was buried under of volcanic ash and pumice in the eruption of Mount Vesuvius in 79 AD. Largely preserved under the ash, Pompeii offers a unique snapshot of Culture of ancient Rome, Roman life, frozen at the moment it was buried, as well as insight into ancient urban planning. It was a wealthy town of 10,000 to 20,000 residents at the time it was destroyed. It hosted many fine public buildings and luxurious private houses with lavish decorations, furnishings and artworks, which were the main attractions for early excavators; subsequent excavations have found hundreds of private homes and businesses reflecting various architectural styles and social classes, as well as numerous public buildings. Organic remains, including wooden objects and human bodies, were interred in the as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy III Euergetes
Ptolemy III Euergetes (, "Ptolemy the Euergetes, Benefactor"; c. 280 – November/December 222 BC) was the third pharaoh of the Ptolemaic dynasty in Egypt from 246 to 222 BC. The Ptolemaic Kingdom reached the height of its military and economic power during his kingship, as initiated by his father Ptolemy II Philadelphus. Ptolemy III was the eldest son of Ptolemy II and Arsinoe I. When Ptolemy III was young, his mother was disgraced and he was removed from the succession. He was restored as heir to the throne in the late 250s BC and succeeded his father as king without issue in 246 BC. On his succession, Ptolemy III married Berenice II, reigning queen of Cyrenaica, thereby bringing her territory into the Ptolemaic realm. In the Third Syrian War (246–241 BC), Ptolemy III invaded the Seleucid empire and won a near total victory, but was forced to abandon the campaign as a result of an uprising in Egypt. In the aftermath of this rebellion, Ptolemy forged a closer bond with the Egy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eutocius Of Ascalon
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 '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moon
The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar day) that is synchronized to its orbital period (Lunar month#Synodic month, lunar month) of 29.5 Earth days. This is the product of Earth's gravitation having tidal forces, tidally pulled on the Moon until one part of it stopped rotating away from the near side of the Moon, near side, making always the same lunar surface face Earth. Conversley, the gravitational pull of the Moon, on Earth, is the main driver of Earth's tides. In geophysical definition of planet, geophysical terms, the Moon is a planetary-mass object or satellite planet. Its mass is 1.2% that of the Earth, and its diameter is , roughly one-quarter of Earth's (about as wide as the contiguous United States). Within the Solar System, it is the List of Solar System objects by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apollonius (crater)
Apollonius is a lunar impact crater located near the eastern limb of the Moon. It lies in the region of uplands to the west of Mare Undarum and northeast of the Sinus Successus on the Mare Fecunditatis. It was named after Greek mathematician Apollonius of Perga. It is southwest of the crater Firmicus, and north of Condon. The outer rim of Apollonius is somewhat worn and is overlain by a pair of small craters (including Apollonius E) across the western wall. The nearly flat interior floor has a low albedo and has been covered by lava. It lacks a central peak or notable small craters across the bottom. Satellite craters By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint that is closest to Apollonius. The following craters have been renamed by the IAU. * Apollonius C — ''See'' Ameghino (crater). * Apollonius D — ''See'' Cartan (crater). * Apollonius G — ''See'' Townley (crater). * Apollonius ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
