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On Growth And Form
''On Growth and Form'' is a book by the Scottish mathematical biologist D'Arcy Wentworth Thompson (1860–1948). The book is long – 793 pages in the first edition of 1917, 1116 pages in the second edition of 1942. The book covers many topics including the effects of scale on the shape of animals and plants, large ones necessarily being relatively thick in shape; the effects of surface tension in shaping soap films and similar structures such as cells; the logarithmic spiral as seen in mollusc shells and ruminant horns; the arrangement of leaves and other plant parts (phyllotaxis); and Thompson's own method of transformations, showing the changes in shape of animal skulls and other structures on a Cartesian grid. The work is widely admired by biologists, anthropologists and architects among others, but less often read than cited. Peter Medawar explains this as being because it clearly pioneered the use of mathematics in biology, and helped to defeat mystical ideas of vitali ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Arcy Wentworth Thompson
Sir D'Arcy Wentworth Thompson CB FRS FRSE (2 May 1860 – 21 June 1948) was a Scottish biologist, mathematician and classics scholar. He was a pioneer of mathematical and theoretical biology, travelled on expeditions to the Bering Strait and held the position of Professor of Natural History at University College, Dundee for 32 years, then at St Andrews for 31 years. He was elected a Fellow of the Royal Society, was knighted, and received the Darwin Medal and the Daniel Giraud Elliot Medal. Thompson is remembered as the author of the 1917 book ''On Growth and Form'', which led the way for the scientific explanation of morphogenesis, the process by which patterns and body structures are formed in plants and animals. Thompson's description of the mathematical beauty of nature, and the mathematical basis of the forms of animals and plants, stimulated thinkers as diverse as Julian Huxley, C. H. Waddington, Alan Turing, René Thom, Claude Lévi-Strauss, Eduardo Paolozzi, Le Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Darwinism
Darwinism is a scientific theory, theory of Biology, biological evolution developed by the English naturalist Charles Darwin (1809–1882) and others, stating that all species of organisms arise and develop through the natural selection of small, inherited variations that increase the individual's ability to compete, survive, and reproduction, reproduce. Also called Darwinian theory, it originally included the broad concepts of transmutation of species or of evolution which gained general scientific acceptance after Darwin published ''On the Origin of Species'' in 1859, including concepts which predated Darwin's theories. English biologist Thomas Henry Huxley coined the term ''Darwinism'' in April 1860. Terminology Darwinism subsequently referred to the specific concepts of natural selection, the Weismann barrier, or the central dogma of molecular biology. Though the term usually refers strictly to biological evolution, creationism, creationists have appropriated it to refer to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a Chemical reaction, reaction with other Chemical substance, substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both Basic research, basic and Applied science, applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the properties ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Tyler Bonner
John Tyler Bonner (May 12, 1920 – February 7, 2019) was an American biologist who was a professor in the Ecology and evolutionary biology, Department of Ecology and Evolutionary Biology at Princeton University. He was a pioneer in the use of cellular slime molds to understand evolution and development over a career of 40 years and was one of the world's leading experts on cellular slime moulds. Arizona State University says that the establishment and growth of developmental-evolutionary biology owes a great debt to the work of Bonner's studies. His work is highly readable and unusually clearly written and his contributions have made many complicated ideas of biology accessible to a wide audience. Career Bonner was the George M. Moffett Professor Emeritus of Biology at Princeton University. He was trained at Harvard University between 1937 and 1947, aside from a stint in the United States Army Air Forces from 1942 to 1946. He soon joined the faculty of Princeton University, becom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholars, including J. Robert Oppenheimer, Albert Einstein, Hermann Weyl, John von Neumann, and Kurt Gödel, many of whom had emigrated from Europe to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Despite collaborative ties and neighboring geographic location, the institute, being independent, has "no formal links" with Princeton University. The institute does not charge tuition or fees. Flexner's guiding principle in founding the institute was the pursuit of knowledge for its own sake.Jogalekar. The faculty have no classes to teach. There are no degree programs or experimental facilities at the institute. Research is never contracted or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transformation (mathematics)
In mathematics, a transformation is a function ''f'', usually with some geometrical underpinning, that maps a set ''X'' to itself, i.e. . Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations. Partial transformations While it is common to use the term transformation for any function of a set into itself (especially in terms like "transformation semigroup" and similar), there exists an alternative form of terminological convention in which the term "transformation" is reserved only for bijections. When such a narrow notion of transformation is generalized to partial functions, then a partial transformation is a function ''f'': ''A'' → ''B'', where both ''A'' and ''B'' are subsets of some set ''X''. Algebraic structures The set of all transformations on a given base set, together with function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albrecht Dürer
Albrecht Dürer (; ; hu, Ajtósi Adalbert; 21 May 1471 – 6 April 1528),Müller, Peter O. (1993) ''Substantiv-Derivation in Den Schriften Albrecht Dürers'', Walter de Gruyter. . sometimes spelled in English as Durer (without an umlaut) or Duerer, was a German painter, printmaker, and theorist of the German Renaissance. Born in Nuremberg, Dürer established his reputation and influence across Europe in his twenties due to his high-quality woodcut prints. He was in contact with the major Italian artists of his time, including Raphael, Giovanni Bellini, and Leonardo da Vinci, and from 1512 was patronized by Emperor Maximilian I. Dürer's vast body of work includes engravings, his preferred technique in his later prints, altarpieces, portraits and self-portraits, watercolours and books. The woodcuts series are more Gothic than the rest of his work. His well-known engravings include the three '' Meisterstiche'' (master prints) ''Knight, Death and the Devil'' (1513), '' Sain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engraving
Engraving is the practice of incising a design onto a hard, usually flat surface by cutting grooves into it with a Burin (engraving), burin. The result may be a decorated object in itself, as when silver, gold, steel, or Glass engraving, glass are engraved, or may provide an Intaglio (printmaking), intaglio printing plate, of copper or another metal, for printing images on paper as prints or illustrations; these images are also called "engravings". Engraving is one of the oldest and most important techniques in printmaking. Wood engraving is a form of relief printing and is not covered in this article, same with rock engravings like petroglyphs. Engraving was a historically important method of producing images on paper in artistic printmaking, in mapmaking, and also for commercial reproductions and illustrations for books and magazines. It has long been replaced by various photographic processes in its commercial applications and, partly because of the difficulty of learning th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Allometry
Allometry is the study of the relationship of body size to shape, anatomy, physiology and finally behaviour, first outlined by Otto Snell in 1892, by D'Arcy Thompson in 1917 in ''On Growth and Form'' and by Julian Huxley in 1932. Overview Allometry is a well-known study, particularly in statistical shape analysis for its theoretical developments, as well as in biology for practical applications to the differential growth rates of the parts of a living organism's body. One application is in the study of various insect species (e.g., Hercules beetles), where a small change in overall body size can lead to an enormous and disproportionate increase in the dimensions of appendages such as legs, antennae, or horns The relationship between the two measured quantities is often expressed as a power law equation (Allometric equation) which expresses a remarkable scale symmetry: : y = kx^a \,\! or in a logarithmic form: : \log y = a \log x + \log k\,\! or similarly \ln y = a \ln x ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book ''Liber Abaci''. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Applications of Fibonacci numbers include co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truss
A truss is an assembly of ''members'' such as beams, connected by ''nodes'', that creates a rigid structure. In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object". A "two-force member" is a structural component where force is applied to only two points. Although this rigorous definition allows the members to have any shape connected in any stable configuration, trusses typically comprise five or more triangular units constructed with straight members whose ends are connected at joints referred to as ''nodes''. In this typical context, external forces and reactions to those forces are considered to act only at the nodes and result in forces in the members that are either tensile or compressive. For straight members, moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes, as is necessary for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
