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Golden Section
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( or \phi) denotes the golden ratio. The constant \varphi satisfies the quadratic equation \varphi^2 = \varphi + 1 and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of \varphi—may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phyllotaxis
In botany, phyllotaxis () or phyllotaxy is the arrangement of leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature. Leaf arrangement The basic arrangements of leaves on a stem are opposite and alternate (also known as spiral). Leaves may also be whorled if several leaves arise, or appear to arise, from the same level (at the same node) on a stem. With an opposite leaf arrangement, two leaves arise from the stem at the same level (at the same node), on opposite sides of the stem. An opposite leaf pair can be thought of as a whorl of two leaves. With an alternate (spiral) pattern, each leaf arises at a different point (node) on the stem. Distichous phyllotaxis, also called "two-ranked leaf arrangement" is a special case of either opposite or alternate leaf arrangement where the leaves on a stem are arranged in two vertical columns on opposite sides of the stem. Examples include various bulbous plants such as '' Boophone''. It also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean Sea, Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of Classical Antiquity, classical antiquity ( AD 600), that comprised a loose collection of culturally and linguistically related polis, city-states and other territories. Most of these regions were officially unified only once, for 13 years, under Alexander the Great's Macedonian empire, empire from 336 to 323 BC (though this excludes a number of Greek city-states free from Alexander's jurisdiction in the western Mediterranean, around the Black Sea, Cyprus, and Cyrenaica). In Western history, the era of classical antiquity was immediately followed by the Early Middle Ages and the Byzantine period. Roughly three centuries after the Late Bronze Age collapse of Mycenaean Greece, Greek urban poleis began to form in the 8th century BC, ushering in the Archaic Greece, Archaic period and Greek colonis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roger Penrose
Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fellow of Wadham College, Oxford, and an honorary fellow of St John's College, Cambridge and University College London. Penrose has contributed to the mathematical physics of general relativity and cosmology. He has received several prizes and awards, including the 1988 Wolf Prize in Physics, which he shared with Stephen Hawking for the Penrose–Hawking singularity theorems, and one half of the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity". He is regarded as one of the greatest living physicists, mathematicians and scientists, and is particularly noted for the breadth and depth of his work in both natural and formal sciences. Early life and education ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books '' Astronomia nova'', '' Harmonice Mundi'', and '' Epitome Astronomiae Copernicanae''. These works also provided one of the foundations for Newton's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci'', was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for ('son of Bonacci'). However, even earlier in 1506 a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci". Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of '' Liber Abaci'' (''Book of Calculation''). He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in ''Liber Abaci''. Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in Bugia (Béjaïa) in mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean Sea, Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of Classical Antiquity, classical antiquity ( AD 600), that comprised a loose collection of culturally and linguistically related polis, city-states and other territories. Most of these regions were officially unified only once, for 13 years, under Alexander the Great's Macedonian empire, empire from 336 to 323 BC (though this excludes a number of Greek city-states free from Alexander's jurisdiction in the western Mediterranean, around the Black Sea, Cyprus, and Cyrenaica). In Western history, the era of classical antiquity was immediately followed by the Early Middle Ages and the Byzantine period. Roughly three centuries after the Late Bronze Age collapse of Mycenaean Greece, Greek urban poleis began to form in the 8th century BC, ushering in the Archaic Greece, Archaic period and Greek colonis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagoras
Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samian, or simply ; in Ionian Greek; ) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in general. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although modern scholars doubt that he ever advocated complete vegetarianism. The t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mario Livio
Mario Livio (born June 19, 1945) is an Israeli-American astrophysicist and an author of works that popularize science and mathematics. For 24 years (1991-2015) he was an astrophysicist at the Space Telescope Science Institute, which operates the Hubble Space Telescope. He has published more than 400 scientific articles on topics including cosmology, supernova explosions, black holes, extrasolar planets, and the emergence of life in the universHis book on the irrational number ''phi'', ''The Golden Ratio: The Story of Phi, the World's Most Astonishing Number'' (2002), won the Peano Prize and the International Pythagoras Prize for popular books on mathematics. Scientific career Livio earned a Bachelor of Science degree in physics and mathematics at the Hebrew University of Jerusalem, a Master of Science degree in theoretical particle physics at the Weizmann Institute, and a Ph.D. in theoretical astrophysics at Tel Aviv University. He was a professor of physics at the Technion � ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Formula
In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others. Given a general quadratic equation of the form :ax^2+bx+c=0 with representing an unknown, with , and representing constants, and with , the quadratic formula is: :x = \frac where the plus–minus symbol "±" indicates that the quadratic equation has two solutions. Written separately, they become: : x_1=\frac\quad\text\quad x_2=\frac Each of these two solutions is also called a root (or zero) of the quadratic equation. Geometrically, these roots represent the -values at which ''any'' parabola, explicitly given as , crosses the -axis. As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aesthetics
Aesthetics, or esthetics, is a branch of philosophy that deals with the nature of beauty and taste, as well as the philosophy of art (its own area of philosophy that comes out of aesthetics). It examines aesthetic values, often expressed through judgments of taste. Aesthetics covers both natural and artificial sources of experiences and how we form a judgment about those sources. It considers what happens in our minds when we engage with objects or environments such as viewing visual art, listening to music, reading poetry, experiencing a play, watching a fashion show, movie, sports or even exploring various aspects of nature. The philosophy of art specifically studies how artists imagine, create, and perform works of art, as well as how people use, enjoy, and criticize art. Aesthetics considers why people like some works of art and not others, as well as how art can affect moods or even our beliefs. Both aesthetics and the philosophy of art try to find answers for what exa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salvador Dalí
Salvador Domingo Felipe Jacinto Dalí i Domènech, Marquess of Dalí of Púbol (; ; ; 11 May 190423 January 1989) was a Spanish surrealist artist renowned for his technical skill, precise draftsmanship, and the striking and bizarre images in his work. Born in Figueres, Catalonia, Spain, Dalí received his formal education in fine arts in Madrid. Influenced by Impressionism and the Renaissance masters from a young age he became increasingly attracted to Cubism and avant-garde movements. He moved closer to Surrealism in the late 1920s and joined the Surrealist group in 1929, soon becoming one of its leading exponents. His best-known work, '' The Persistence of Memory'', was completed in August 1931, and is one of the most famous Surrealist paintings. Dalí lived in France throughout the Spanish Civil War (1936 to 1939) before leaving for the United States in 1940 where he achieved commercial success. He returned to Spain in 1948 where he announced his return to the Catholic fait ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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