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Archimedes Bath
Archimedes of Syracuse ( ; ) was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, based on his surviving work, he is considered one of the leading scientists in classical antiquity, and one of the greatest mathematicians of all time. Archimedes anticipated modern calculus and analysis by applying the concept of the infinitesimals and the method of exhaustion to derive and rigorously prove many geometrical theorems, including the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral. Archimedes' other mathematical achievements include deriving an approximation of pi (), defining and investigating the Archimedean spiral, and devising a system using exponentiation for ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domenico Fetti
Domenico Fetti (also spelled Feti) ( – 16 April 1623) was an Italian Baroque painter who was active mainly in Rome, Mantua and Venice. Biography Born in Rome to a little-known painter, Pietro Fetti, Domenico is said to have apprenticed initially under Ludovico Cigoli, or his pupil Andrea Commodi in Rome from circa 1604–1613. He then worked in Mantua from 1613 to 1622, patronized by the Cardinal, later Duke Ferdinando I Gonzaga. In the Ducal Palace, he painted the ''Miracle of the Loaves and Fishes''. The series of representations of New Testament parables he carried out for his patron's '' studiolo'' gave rise to a popular speciality, and he and his studio often repeated his compositions. In August or September 1622, his feuds with some prominent Mantuans led him to move to Venice, which for the first few decades of the seventeenth century had persisted in sponsoring Mannerist styles (epitomized by Palma the Younger and the successors of Tintoretto and Veronese). In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Mathematics
Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during Classical antiquity, classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the shores of the ancient Mediterranean, from Anatolia to Italy and North Africa, but were united by Greek culture and the Ancient Greek, Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in Mathematical proof, proofs is an important difference between Greek mathematics and those of preceding civilizations. The early history of Greek mathematics is obscure, and traditional narratives of Theorem, mathematical theorems found before the fifth century BC are regarded as later inventions. It is now generally accepted that treatises of deductive mathematics written in Greek began circulating around the mid-fifth century BC, but the earliest complete work on the subje ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Area Of A Circle
In geometry, the area enclosed by a circle of radius is . Here, the Greek letter represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides. The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, , holds for a circle. Terminology Although often referred to as the area of a circle in informal contexts, strictly speaking, the term disk refers to the interior region of the circle, while circle is reserved for the boundary only, which is a curve and covers no area itself. Therefore, the area of a disk is the more precise phrase for the area enclos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorem
In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ''corollary'' for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formal system ... [...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] |
Method Of Exhaustion
The method of exhaustion () is a method of finding the area of a shape by inscribing inside it a sequence of polygons (one at a time) whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the ''n''th polygon and the containing shape will become arbitrarily small as ''n'' becomes large. As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members. The method of exhaustion typically required a form of proof by contradiction, known as ''reductio ad absurdum''. This amounts to finding an area of a region by first comparing it to the area of a second region, which can be "exhausted" so that its area becomes arbitrarily close to the true area. The proof involves assuming that the true area is greater than the second area, proving that assertion false, assuming it is less than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cavalieri's Principle
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows: * 2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in line segments of equal length, then the two regions have equal areas. * 3-dimensional case: Suppose two regions in three-space (solids) are included between two parallel planes. If every plane parallel to these two planes intersects both regions in cross section (geometry), cross-sections of equal area, then the two regions have equal volumes. Today Cavalieri's principle is seen as an early step towards integral calculus, and while it is used in some forms, such as its generalization in Fubini's theorem and layer cake representation, results using Cavalieri's principle can often be shown more directly via integration. In the other direction, Cavalieri's principle gre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous Rate of change (mathematics), rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make use of the fundamental notions of convergence (mathematics), convergence of infinite sequences and Series (mathematics), infinite series to a well-defined limit (mathematics), limit. It is the "mathematical backbone" for dealing with problems where variables change with time or another reference variable. Infinitesimal calculus was formulated separately ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Antiquity
Classical antiquity, also known as the classical era, classical period, classical age, or simply antiquity, is the period of cultural History of Europe, European history between the 8th century BC and the 5th century AD comprising the interwoven civilizations of ancient Greece and ancient Rome, Rome known together as the Greco-Roman world, centered on the Mediterranean Basin. It is the period during which ancient Greece and Rome flourished and had major influence throughout much of Europe, North Africa, and West Asia. Classical antiquity was succeeded by the period now known as late antiquity. Conventionally, it is often considered to begin with the earliest recorded Homeric Greek, Epic Greek poetry of Homer (8th–7th centuries BC) and end with the fall of the Western Roman Empire in 476 AD. Such a wide span of history and territory covers many disparate cultures and periods. ''Classical antiquity'' may also refer to an idealized vision among later people of what was, in Ed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Greek And Hellenistic Sicily
The history of Greek Sicily () began with the foundation of the first Greek Greek colonisation, colonies around the mid 8th century BC. The Greeks of Sicily were known as Siceliotes. Over the following centuries many conflicts between the city-states occurred until around 276 BC Pyrrhus of Epirus managed to conquer the whole island except Carthaginian Marsala, Lilybaeum. After the First Punic War in 241 BC the island was conquered by the Romans. Territory Cities The first Greek colonies were founded in eastern Sicily in the 8th century BC when the Chalcidian Greeks founded Zancle, Naxos (Sicily), Naxos, Leontinoi and Katane; in the south-east corner the Corinthians founded Syracuse, Sicily, Syracuse and the Megareans Megara Hyblaea, while on the western coast the Cretans and Rhodians founded Gela in 689 BC, with which the first Greek colonisation of Sicily ended. The Greek cities of Sicily were ''apoikìai'' (newly founded cities detached from their cities of origin and l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
