|
History Of Calculus
Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series. Many elements of calculus appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India. Infinitesimal calculus was developed in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz independently of each other. An argument over priority led to the Leibniz–Newton calculus controversy which continued until the death of Leibniz in 1716. The development of calculus and its uses within the sciences have continued to the present. Etymology In mathematics education, ''calculus'' denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. The word ''calculus'' is Latin for "small pebble" (the diminutive of '' calx,'' meaning "stone"), a meaning which still persists in medicine. Because such pebbles 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] |
Abacus
An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. An abacus consists of a two-dimensional array of Sliding (motion), slidable beads (or similar objects). In their earliest designs, the beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation. Each rod typically represents one Numerical digit, digit of a multi-digit number laid out using a positional numeral system such as base ten (though some cultures used different numerical bases). Roman Empire, Roman and East Asian abacuses use a system resembling bi-quinary coded decimal, with a top deck (containing one or two beads) representing fives and a bottom deck (containing four or five beads) representing ones. Natural numbers are normally use ... [...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] |
Eudoxus Of Cnidus
Eudoxus of Cnidus (; , ''Eúdoxos ho Knídios''; ) was an Ancient Greece, ancient Greek Ancient Greek astronomy, astronomer, Greek mathematics, mathematician, doctor, and lawmaker. He was a student of Archytas and Plato. All of his original works are lost, though some fragments are preserved in Hipparchus' ''Commentaries on the Phenomena of Aratus and Eudoxus''. ''Theodosius' Spherics, Spherics'' by Theodosius of Bithynia may be based on a work by Eudoxus. Life Eudoxus, son of Aeschines, was born and died in Cnidus (also transliterated Knidos), a city on the southwest coast of Anatolia. The years of Eudoxus' birth and death are not fully known but Diogenes Laertius, Diogenes Laërtius gave several biographical details, mentioned that Apollodorus of Athens, Apollodorus said he reached his wikt:acme#English, acme in the 103rd Olympiad (368–), and claimed he died in his 53rd year. From this 19th century mathematical historians reconstructed dates of 408–, but 20th century schola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Segment And Inscribed Triangle
Parabolic usually refers to something in a shape of a parabola, but may also refer to a parable. Parabolic may refer to: *In mathematics: **In elementary mathematics, especially elementary geometry: **Parabolic coordinates **Parabolic cylindrical coordinates ** parabolic Möbius transformation ** Parabolic geometry (other) ** Parabolic spiral ** Parabolic line **In advanced mathematics: *** Parabolic cylinder function *** Parabolic induction *** Parabolic Lie algebra ***Parabolic partial differential equation *In physics: **Parabolic trajectory *In technology: **Parabolic antenna ** Parabolic microphone **Parabolic reflector **Parabolic trough - a type of solar thermal energy collector ** Parabolic flight - a way of achieving weightlessness ** Parabolic action, or parabolic bending curve - a term often used to refer to a progressive bending curve in fishing rods. *In commodities and stock markets: ** Parabolic SAR - a chart pattern in which prices rise or fall with an incre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science (journal)
''Science'' is the peer review, peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. ''Science'' is based in Washington, D.C., United States, with a second office in Cambridge, UK. Contents The major focus of the journal is publishing important original scientific research and research reviews, but ''Science'' also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, ''Science'' and its rival ''Nature (journal), Nature'' cover the full range of List of academ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jupiter
Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a Jupiter mass, mass more than 2.5 times that of all the other planets in the Solar System combined and slightly less than one-thousandth the mass of the Sun. Its diameter is 11 times that of Earth and a tenth that of the Sun. Jupiter orbits the Sun at a distance of , with an orbital period of . It is the List of brightest natural objects in the sky, third-brightest natural object in the Earth's night sky, after the Moon and Venus, and has been observed since prehistoric times. Its name derives from that of Jupiter (god), Jupiter, the chief deity of ancient Roman religion. Jupiter was the first of the Sun's planets to form, and its inward migration during the primordial phase of the Solar System affected much of the formation history of the other planets. Jupiter's atmosphere consists of 76% hydrogen and 24% helium by mass, with a denser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trapezoidal Rule
In calculus, the trapezoidal rule (or trapezium rule in British English) is a technique for numerical integration, i.e., approximating the definite integral: \int_a^b f(x) \, dx. The trapezoidal rule works by approximating the region under the graph of the function f(x) as a trapezoid and calculating its area. It follows that \int_^ f(x) \, dx \approx (b-a) \cdot \tfrac(f(a)+f(b)). The integral can be even better approximated by Partition of an interval, partitioning the integration interval, applying the trapezoidal rule to each subinterval, and summing the results. In practice, this "chained" (or "composite") trapezoidal rule is usually what is meant by "integrating with the trapezoidal rule". Let \ be a partition of [a,b] such that a=x_0 < x_1 < \cdots < x_ < x_N = b and be the length of the -th subinterval (that is, ), then |
Babylon
Babylon ( ) was an ancient city located on the lower Euphrates river in southern Mesopotamia, within modern-day Hillah, Iraq, about south of modern-day Baghdad. Babylon functioned as the main cultural and political centre of the Akkadian-speaking region of Babylonia. Its rulers established two important empires in antiquity, the 19th–16th century BC Old Babylonian Empire, and the 7th–6th century BC Neo-Babylonian Empire. Babylon was also used as a regional capital of other empires, such as the Achaemenid Empire. Babylon was one of the most important urban centres of the ancient Near East, until its decline during the Hellenistic period. Nearby ancient sites are Kish, Borsippa, Dilbat, and Kutha. The earliest known mention of Babylon as a small town appears on a clay tablet from the reign of Shar-Kali-Sharri (2217–2193 BC), of the Akkadian Empire. Babylon was merely a religious and cultural centre at this point and neither an independent state nor a large city, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow Mathematical Papyrus
The Moscow Mathematical Papyrus, also named the Golenishchev Mathematical Papyrus after its first non-Egyptian owner, Egyptologist Vladimir Golenishchev, is an ancient Egyptian mathematical papyrus containing several problems in arithmetic, geometry, and algebra. Golenishchev bought the papyrus in 1892 or 1893 in Thebes. It later entered the collection of the Pushkin State Museum of Fine Arts in Moscow, where it remains today. Based on the palaeography and orthography of the hieratic text, the text was most likely written down in the 13th Dynasty and based on older material probably dating to the Twelfth Dynasty of Egypt, roughly 1850 BC.Clagett, Marshall. 1999. Ancient Egyptian Science: A Source Book. Volume 3: Ancient Egyptian Mathematics. Memoirs of the American Philosophical Society 232. Philadelphia: American Philosophical Society. Approximately 5.5 m (18 ft) long and varying between wide, its format was divided by the Soviet Orientalist Vasily Vasilievic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedes Pi
Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenistic Sicily, 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 mathematical analysis, analysis by applying the concept of the Cavalieri's principle, infinitesimals and the method of exhaustion to derive and rigorously prove many geometry, geometrical theorem, 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 math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felicific Calculus
The felicific calculus is an algorithm formulated by utilitarianism, utilitarian philosopher Jeremy Bentham (1748–1832) for calculating the degree or amount of pleasure that a specific action is likely to induce. Bentham, an ethics, ethical hedonist, believed the moral rightness or wrongness of an action to be a function of the amount of pleasure or pain that it produced. The felicific calculus could in principle, at least, determine the moral status of any considered act. The algorithm is also known as the utility calculus, the hedonistic calculus and the hedonic calculus. To be included in this calculation are several Variable (math), variables (or vector space, vectors), which Bentham called "circumstances". These are: # Intensity: How strong is the pleasure? # Time, Duration: How long will the pleasure last? # Certainty or uncertainty: How likely or unlikely is it that the pleasure will occur? # Propinquity or remoteness: How soon will the pleasure occur? # Fecundity: The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
