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Golden Ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \frac = \frac = \varphi, where the Greek letter Phi (letter), phi ( or ) denotes the golden ratio. The constant satisfies the quadratic equation 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; it also goes by 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 Straightedge and compass construction, construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phyllotaxis
In botany, phyllotaxis () or phyllotaxy is the arrangement of leaf, leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature. Leaf arrangement The basic leaf#Arrangement on the stem, arrangements of leaves on a stem are opposite and alternate (also known as spiral). Leaves may also be Whorl (botany), whorled if several leaves arise, or appear to arise, from the same level (at the same Node (botany), node) on a stem. With an opposite leaf arrangement, two leaves arise from the stem at the same level (at the same Node (botany), 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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greece
Ancient Greece () was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity (), that comprised a loose collection of culturally and linguistically related city-states and communities. Prior to the Roman period, most of these regions were officially unified only once under the Kingdom of Macedon from 338 to 323 BC. In Western history, the era of classical antiquity was immediately followed by the Early Middle Ages and the Byzantine period. Three centuries after the decline of Mycenaean Greece during the Bronze Age collapse, Greek urban poleis began to form in the 8th century BC, ushering in the Archaic period and the colonization of the Mediterranean Basin. This was followed by the age of Classical Greece, from the Greco-Persian Wars to the death of Alexander the Great in 323 BC, and which included the Golden Age of Athens and the Peloponnesian War. The u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roger Penrose
Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, 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 physical cosmology, 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 the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity". He won the Royal Society Prizes for Science Books, Royal Society Science Books Prize for ''The Emperor's New Mind'' (1989), which outlines his views on physics and con ... [...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 philosophy, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his Kepler's laws of planetary motion, laws of planetary motion, and his books ''Astronomia nova'', ''Harmonice Mundi'', and ''Epitome Astronomiae Copernicanae'', influencing among others Isaac Newton, providing one of the foundations for his theory of Newton's law of universal gravitation, universal gravitation. The variety and impact of his work made Kepler one of the founders and fathers of modern astronomy, the scientific method, Natural science, natural and modern science. He has been described as the "father of science fiction" for his novel ''Somnium (novel), Somnium''. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Hans Ulrich von Eggenberg, Prince Hans Ulrich von Eggenberg. Lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci
Leonardo Bonacci ( – ), commonly known as Fibonacci, was an Italians, 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'', is first found in a modern source in a 1838 text by the Franco-Italian mathematician Guglielmo Libri Carucci dalla Sommaja, Guglielmo Libri and is short for ('son of Bonacci'). However, even as early as 1506, Perizolo, a notary of the Holy Roman Empire, mentions him as "Lionardo Fibonacci". Fibonacci popularized the Hindu–Arabic numeral system, Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of (''Book of Calculation'') and also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in . Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official who directed a trading post in Béjaïa, Bugia, modern-day Béjaïa, Algeria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greece
Ancient Greece () was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity (), that comprised a loose collection of culturally and linguistically related city-states and communities. Prior to the Roman period, most of these regions were officially unified only once under the Kingdom of Macedon from 338 to 323 BC. In Western history, the era of classical antiquity was immediately followed by the Early Middle Ages and the Byzantine period. Three centuries after the decline of Mycenaean Greece during the Bronze Age collapse, Greek urban poleis began to form in the 8th century BC, ushering in the Archaic period and the colonization of the Mediterranean Basin. This was followed by the age of Classical Greece, from the Greco-Persian Wars to the death of Alexander the Great in 323 BC, and which included the Golden Age of Athens and the Peloponnesian War. The u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagoras
Pythagoras of Samos (; BC) was an ancient Ionian Greek philosopher, polymath, 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, Western philosophy. Modern scholars disagree regarding Pythagoras's education and influences, but most agree that he travelled to Croton in southern Italy around 530 BC, where he founded a school in which initiates were allegedly sworn to secrecy and lived a communal, ascetic lifestyle. In antiquity, Pythagoras was credited with mathematical and scientific discoveries, such as the Pythagorean theorem, Pythagorean tuning, the five regular solids, the theory of proportions, the sphericity of the Earth, the identity of the morning and evening stars as the planet Venus, and the division of the globe into five climatic zones. He was reputedly the first man to call himself a philosopher ("lover of wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mario Livio
Mario Livio (born June 19, 1945) is an astrophysics, 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 ''Golden ratio, 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 has focused much of his research on supernova explosions and their use in determining the Metric expansion of space, rate of expansion of the universe. He has also studied so-called dark energy, black holes, and the formation of planetary systems around young stars. He has contributed to hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Formula
In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations, such as completing the square, yield the same solutions. Given a general quadratic equation of the form , with representing an unknown, and coefficients , , and representing known real number, real or complex number, complex numbers with , the values of satisfying the equation, called the Zero of a function, ''roots'' or ''zeros'', can be found using the quadratic formula, x = \frac, where the plus–minus sign, plus–minus symbol "" indicates that the equation has two roots. Written separately, these are: x_1 = \frac, \qquad x_2 = \frac. The quantity is known as the discriminant of the quadratic equation. If the coefficients , , and are real numbers then when , the equation has two distinct real number, real roots; when , the equation has one repeated root, repeated real root; and when , the equation h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aesthetics
Aesthetics (also spelled esthetics) is the branch of philosophy concerned with the nature of beauty and taste (sociology), taste, which in a broad sense incorporates the philosophy of art.Slater, B. H.Aesthetics ''Internet Encyclopedia of Philosophy,'' , accessed on 15 September 2024. Aesthetics examines values about, and Critical thinking, critical judgments of, artistic taste and preference. It thus studies how Artist, artists imagine, create, and perform works of art, as well as how people use, enjoy, and criticize art. Aesthetics considers why people consider certain things beautiful and not others, as well as how objects of beauty and art can affect our moods and our beliefs. Aesthetics tries to find answers to what exactly is art and what makes good art. It considers what happens in our minds when we view Visual arts, visual art, listen to music, read poetry, enjoy delicious food, and engage in large artistic projects like creating and experiencing plays, fashion shows ... [...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), known as Salvador Dalí ( ; ; ), was a Spanish Surrealism, surrealist artist renowned for his technical skill, precise draftsmanship, and the striking and bizarre images in his work. Born in Figueres in Catalonia, Dalí received his formal education in fine arts in Madrid. Influenced by Impressionism and the Renaissance art, 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. 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 fai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
