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Golden Rectangle
In geometry, a golden rectangle is a rectangle with side lengths in golden ratio \tfrac :1, or with approximately equal to or Golden rectangles exhibit a special form of self-similarity: if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well. Construction Owing to the Pythagorean theorem, the diagonal dividing one half of a square equals the radius of a circle whose outermost point is the corner of a golden rectangle added to the square. Thus, a golden rectangle can be Straightedge and compass construction, constructed with only a straightedge and compass in four steps: # Draw a square # Draw a line from the midpoint of one side of the square to an opposite corner # Use that line as the radius to draw an arc that defines the height of the rectangle # Complete the golden rectangle A distinctive feature of this shape is that when a square (geometry), square section is added—or removed—the product is another golden re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mice Problem
In mathematics, the mice problem is a continuous pursuit–evasion problem in which a number of mice (or insects, dogs, missiles, etc.) are considered to be placed at the corners of a regular polygon. In the classic setup, each then begins to move towards its immediate neighbour (clockwise or anticlockwise). The goal is often to find out at what time the mice meet. The most common version has the mice starting at the corners of a unit square, moving at unit speed. In this case they meet after a time of one unit, because the distance between two neighboring mice always decreases at a speed of one unit. More generally, for a regular polygon of n unit-length sides, the distance between neighboring mice decreases at a speed of 1 - \cos(2\pi/n), so they meet after a time of 1/\bigl(1 - \cos(2\pi/n)\bigr). Path of the mice For all regular polygons, each mouse traces out a pursuit curve in the shape of a logarithmic spiral A logarithmic spiral, equiangular spiral, or growth spira ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Le Corbusier
Charles-Édouard Jeanneret (6 October 188727 August 1965), known as Le Corbusier ( , ; ), was a Swiss-French architectural designer, painter, urban planner and writer, who was one of the pioneers of what is now regarded as modern architecture. He was born in Switzerland to French speaking Swiss parents, and acquired French nationality by naturalization on 19 September 1930. His career spanned five decades, in which he designed buildings in Europe, Japan, India, as well as North and South America. He considered that "the roots of modern architecture are to be found in Viollet-le-Duc." Dedicated to providing better living conditions for the residents of crowded cities, Le Corbusier was influential in urban planning, and was a founding member of the (CIAM). Le Corbusier prepared the master plan for the city of Chandigarh in India, and contributed specific designs for several buildings there, especially the government buildings. On 17 July 2016, seventeen projects by Le Corbusie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Villa Stein
Villa Stein is a building designed by Le Corbusier between 1926 and 1928 at Garches, France. The building is also known as Villa Garches, Villa de Monzie, and Villa Stein-de Monzie. Located at 17 Rue de professeur Victor Pauchet, the villa was built for Gabrielle Colaco-Osorio de Monzie (1882–1961) and Sarah Stein, sister-in-law of American writer Gertrude Stein, between 1926 and 1928.Friedman References * External links Villa Stein - Le Corbusier - Great Buildings OnlineVilla Stein - de Monzie - wikiarquitectura.com Villas in France, Stein Le Corbusier buildings in France Houses completed in 1927 20th-century architecture in France {{France-struct-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random House
Random House is an imprint and publishing group of Penguin Random House. Founded in 1927 by businessmen Bennett Cerf and Donald Klopfer as an imprint of Modern Library, it quickly overtook Modern Library as the parent imprint. Over the following decades, a series of acquisitions made it into one of the largest publishers in the United States. In 2013, it was merged with Penguin Group to form Penguin Random House, which is owned by the Germany-based media conglomerate Bertelsmann. Penguin Random House uses its brand for Random House Publishing Group and Random House Children's Books, as well as several imprints. Company history 20th century Random House was founded in 1927 by Bennett Cerf and Donald Klopfer, two years after they acquired the Modern Library imprint from publisher Horace Liveright, which reprints classic works of literature. Cerf is quoted as saying, "We just said we were going to publish a few books on the side at random", which suggested the name Random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divina Proportione
''Divina proportione'' (15th century Italian for ''Divine proportion''), later also called ''De divina proportione'' (converting the Italian title into a Latin one) is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, completed by February 9th, 1498 in Milan and first printed in 1509. Its subject was mathematical proportions (the title refers to the golden ratio) and their applications to geometry, to visual art through perspective, and to architecture. The clarity of the written material and Leonardo's excellent diagrams helped the book to achieve an impact beyond mathematical circles, popularizing contemporary geometric concepts and images. Some of its content was plagiarised from an earlier book by Piero della Francesca, '' De quinque corporibus regularibus''. Contents of the book The book consists of three separate manuscripts, which Pacioli worked on between 1496 and 1498. He credits Fibonacci as the main source for the mathematics he p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luca Pacioli
Luca Bartolomeo de Pacioli, O.F.M. (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting. He is referred to as the father of accounting and bookkeeping and he was the first person to publish a work on the double-entry system of book-keeping on the continent. He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany. Life Luca Pacioli was born between 1446 and 1448 in the Tuscan town of Sansepolcro where he received an abbaco education. This was education in the vernacular (''i.e.'', the local tongue) rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli; however, Luca Pacioli was said to have lived with the Befolci family as a child in his birth town Sansepolcro. He moved to Venice around 1464, where he continued his own education while working ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greeks
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 unificati ... [...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] |
Tablet Of Shamash
The Tablet of Shamash (also known as the Sun God Tablet or the Nabuapaliddina Tablet) is a stele recovered from the ancient Babylonian city of Sippar in southern Iraq in 1881; it is now a major piece in the British Museum's ancient Middle East collection and is a visual attestation of Ancient near eastern cosmology, Babylonian cosmology. It is dated to the reign of King Nabu-apla-iddina ca. 888 – 855 Before Christ, BC. Discovery The tablet was discovered during excavations by Hormuzd Rassam between 1878 and 1883. The tablet was found complete but broken into two large and six small pieces. By the time of King Nabopolassar, between 625 and 605 BC, it had broken into four parts and been repaired. The terracotta coffer also contained two clay impressions of the tablets presentation scene. The coffer was sealed under an Bitumen, asphalt temple floor. It has been suggested that the coffer also contained a second tablet as well as a third clay impression (now in the Istanbul Museu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Babylonia
Babylonia (; , ) was an Ancient history, ancient Akkadian language, Akkadian-speaking state and cultural area based in the city of Babylon in central-southern Mesopotamia (present-day Iraq and parts of Kuwait, Syria and Iran). It emerged as an Akkadian-populated but Amorites, Amorite-ruled state . During the reign of Hammurabi and afterwards, Babylonia was retrospectively called "the country of Akkad" ( in Akkadian), a deliberate archaism in reference to the previous glory of the Akkadian Empire. It was often involved in rivalry with the older ethno-linguistically related state of Assyria in the north of Mesopotamia and Elam to the east in Ancient Iran. Babylonia briefly became the major power in the region after Hammurabi (floruit, fl. –1752 BC middle chronology, or –1654 BC, short chronology timeline, short chronology) created a short-lived empire, succeeding the earlier Akkadian Empire, Third Dynasty of Ur, and Old Assyrian Empire. The Babylonian Empire rapidly fell apar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Rhombus
In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio: : = \varphi = \approx 1.618~034 Equivalently, it is the Varignon parallelogram formed from the edge midpoints of a golden rectangle. Rhombi with this shape form the faces of several notable polyhedra. The golden rhombus should be distinguished from the two rhombi of the Penrose tiling, which are both related in other ways to the golden ratio but have different shapes than the golden rhombus. Angles (See the characterizations and the basic properties of the general rhombus for angle properties.) The internal supplementary angles of the golden rhombus are:. See in particular table 1, p. 188. *Acute angle: \alpha=2\arctan ; :by using the arctangent addition formula (see inverse trigonometric functions): :\alpha=\arctan=\arctan=\arctan2\approx63.43495^\circ. : *Obtuse angle: \beta=2\arctan\varphi=\pi-\arctan2\approx116.56505^\circ, :which is also the dihedral angle of the dodecahedron. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
