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Plato's Number
Plato's number is a number enigmatically referred to by Plato in his dialogue the ''The Republic (Plato), Republic'' (8.546b). The text is notoriously difficult to understand and its corresponding translations do not allow an unambiguous interpretation. There is no real agreement either about the meaning or the value of the number. It also has been called the "geometrical number" or the "nuptial number" (the "number of the bride"). The passage in which Plato introduced the number has been discussed ever since it was written, with no consensus in the debate. As for the number's actual value, 216 (number), 216 is the most frequently proposed value for it, but 3,600 or 12,960,000 are also commonly considered. An incomplete listfor more names and references see Dupuis J., ''Le Nombre Geometrique de Platon'', Paris: Hachette, 1885 of authors who mention or discourse about includes the names of Aristotle, Proclus for antiquity; Marsilio Ficino, Ficino and Girolamo Cardano, Cardano duri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution of higher learning on the European continent. Along with his teacher, Socrates, and his student, Aristotle, Plato is a central figure in the history of Ancient Greek philosophy and the Western and Middle Eastern philosophies descended from it. He has also shaped religion and spirituality. The so-called neoplatonism of his interpreter Plotinus greatly influenced both Christianity (through Church Fathers such as Augustine) and Islamic philosophy (through e.g. Al-Farabi). In modern times, Friedrich Nietzsche diagnosed Western culture as growing in the shadow of Plato (famously calling Christianity "Platonism for the masses"), while Alfred North Whitehead famously said: "the safest general characterization of the European philosophica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plato Number
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution of higher learning on the European continent. Along with his teacher, Socrates, and his student, Aristotle, Plato is a central figure in the history of Ancient Greek philosophy and the Western and Middle Eastern philosophies descended from it. He has also shaped religion and spirituality. The so-called neoplatonism of his interpreter Plotinus greatly influenced both Christianity (through Church Fathers such as Augustine) and Islamic philosophy (through e.g. Al-Farabi). In modern times, Friedrich Nietzsche diagnosed Western culture as growing in the shadow of Plato (famously calling Christianity "Platonism for the masses"), while Alfred North Whitehead famously said: "the safest general characterization of the European philosophical tradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integers
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Adam (classicist)
James Adam (7 April 1860 – 30 August 1907) was a Scottish classicist who taught Classics at Emmanuel College, Cambridge. Life He was born on 7 April 1860 in Kinmuck in the parish of Keithhall near Inverurie, Aberdeenshire. He was educated at the Old Grammar School in Old Aberdeen, at the University of Aberdeen where he studied under William Geddes and gained his B.A. as Senior Classic in 1884, and at Emmanuel College, Cambridge where he graduated as M.A. in 1888. In 1884 Adam was appointed Junior Fellow and soon thereafter Senior Lecturer in the Classics at Emmanuel College. In 1890, a former student of his, Adela Marion (''née'' Kensington) (1866–1944), became his wife and lifelong collaborator. Their daughter, Barbara Frances (1897–1988), was the British sociologist and criminologist Lady Barbara Wootton; one of their sons, Captain Arthur Innes Adam, was killed in France on 16 September 1916; and another son, Neil Kensington Adam, became a noted chemist. Adam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Sum Of Powers Conjecture
Euler's conjecture is a disproved conjecture in mathematics related to Fermat's Last Theorem. It was proposed by Leonhard Euler in 1769. It states that for all integers and greater than 1, if the sum of many th powers of positive integers is itself a th power, then is greater than or equal to : : ⇒ The conjecture represents an attempt to generalize Fermat's Last Theorem, which is the special case : if , then . Although the conjecture holds for the case (which follows from Fermat's Last Theorem for the third powers), it was disproved for and . It is unknown whether the conjecture fails or holds for any value . Background Euler was aware of the equality involving sums of four fourth powers; this, however, is not a counterexample because no term is isolated on one side of the equation. He also provided a complete solution to the four cubes problem as in Plato's number or the taxicab number 1729. The general solution of the equation :x_1^3+x_2^3=x_3^3+x_4^3 is :x_1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Friedrich Fries
Jakob Friedrich Fries (; 23 August 1773 – 10 August 1843) was a German post-KantianTerry Pinkard, ''German Philosophy 1760-1860: The Legacy of Idealism'', Cambridge University Press, 2002, pp. 199–212. philosopher and mathematician. Biography Fries studied theology at the academy of the Moravian Brethren at Niesky and philosophy at the Universities of Leipzig and Jena. After travelling, in 1806 he became professor of philosophy and elementary mathematics at the University of Heidelberg. Though the progress of his psychological thought compelled him to abandon the positive theology of the Moravians, he retained an appreciation of its spiritual or symbolic significance. His philosophical position with regard to his contemporaries had already been made clear in his critical work ''Reinhold, Fichte und Schelling'' (1803), and in the more systematic treatises ''System der Philosophie als evidente Wissenschaft'' (1804) and ''Wissen, Glaube und Ahnung'' (1805). Fries' most impo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Number
In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols, \sigma_1(n)=2n where \sigma_1 is the sum-of-divisors function. For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 = 28. This definition is ancient, appearing as early as Euclid's ''Elements'' (VII.22) where it is called (''perfect'', ''ideal'', or ''complete number''). Euclid also proved a formation rule (IX.36) whereby q(q+1)/2 is an even perfect number whenever q is a prime of the form 2^p-1 for positive integer p—what is now called a Mersenne prime. Two millenni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metonic Cycle
The Metonic cycle or enneadecaeteris (from grc, ἐννεακαιδεκαετηρίς, from ἐννεακαίδεκα, "nineteen") is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 synodic months is just 2 hours, 4 minutes and 58 seconds longer than 19 tropical years. Meton of Athens, in the 5th century BC, judged the cycle to be a whole number of days, 6,940. Using these whole numbers facilitates the construction of a lunisolar calendar. A tropical year is longer than 12 lunar months and shorter than 13 of them. The arithmetic identity 12×12 + 7×13 = 235 shows that a combination of 12 "short" years (12 months) and 7 "long" years (13 months) will be almost exactly equal to 19 solar years. Application in traditional calendars In the Babylonian and Hebrew lunisolar calendars, the years 3, 6, 8, 11, 14, 17, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Triple
A Pythagorean triple consists of three positive integers , , and , such that . Such a triple is commonly written , and a well-known example is . If is a Pythagorean triple, then so is for any positive integer . A primitive Pythagorean triple is one in which , and are coprime (that is, they have no common divisor larger than 1). For example, is a primitive Pythagorean triple whereas is not. A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle, and is necessarily a right triangle. The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a^2+b^2=c^2; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples. For instance, the triangle with sides a=b=1 and c=\sqrt2 is a right triangle, but (1,1,\sqrt2) is not a Pythagorean triple because \sqrt2 is not an integer. Moreover, 1 and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Babylon
''Bābili(m)'' * sux, 𒆍𒀭𒊏𒆠 * arc, 𐡁𐡁𐡋 ''Bāḇel'' * syc, ܒܒܠ ''Bāḇel'' * grc-gre, Βαβυλών ''Babylṓn'' * he, בָּבֶל ''Bāvel'' * peo, 𐎲𐎠𐎲𐎡𐎽𐎢 ''Bābiru'' * elx, 𒀸𒁀𒉿𒇷 ''Babili'' * Kassite: ''Karanduniash'', ''Karduniash'' , image = Street in Babylon.jpg , image_size=250px , alt = A partial view of the ruins of Babylon , caption = A partial view of the ruins of Babylon , map_type = Near East#West Asia#Iraq , relief = yes , map_alt = Babylon lies in the center of Iraq , coordinates = , location = Hillah, Babil Governorate, Iraq , region = Mesopotamia , type = Settlement , part_of = Babylonia , length = , width = , area = , height = , builder = , material = , built = , abandoned = , epochs = , cultures = Sumerian, Akkadian, Amorite, Kassite, Assyrian, Chaldean, Achaemenid, Hellenistic, Parthian, Sasanian, Muslim , dependency_of = , occupants = , event = , excavations = , archaeologists = Hormuzd Rassam, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Victor Cousin
Victor Cousin (; 28 November 179214 January 1867) was a French philosopher. He was the founder of " eclecticism", a briefly influential school of French philosophy that combined elements of German idealism and Scottish Common Sense Realism. As the administrator of public instruction for over a decade, Cousin also had an important influence on French educational policy. Biography Early years The son of a watchmaker, he was born in Paris, in the Quartier Saint-Antoine. At the age of ten he was sent to the local grammar school, the Lycée Charlemagne, where he studied until he was eighteen. ''Lycées'' being organically linked to the University of France and its Faculties since their Napoleonic institution (the ''baccalauréat'' was awarded by juries made of university professors) Cousin was "crowned" in the ancient hall of the Sorbonne for a Latin oration he wrote which owned him a first prize at the ''concours général'', a competition between the best pupils at ''lycé ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renaissance
The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ideas and achievements of classical antiquity. It occurred after the Crisis of the Late Middle Ages and was associated with great social change. In addition to the standard periodization, proponents of a "long Renaissance" may put its beginning in the 14th century and its end in the 17th century. The traditional view focuses more on the early modern aspects of the Renaissance and argues that it was a break from the past, but many historians today focus more on its medieval aspects and argue that it was an extension of the Middle Ages. However, the beginnings of the period – the early Renaissance of the 15th century and the Italian Proto-Renaissance from around 1250 or 1300 – overlap considerably with the Late Middle Ages, conventi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
