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Ungula (primate Anatomy)
In solid geometry, an ungula is a region of a solid of revolution, cut off by a plane oblique to its base. A common instance is the spherical wedge. The term ''ungula'' refers to the horse hoof, hoof of a horse, an anatomical feature that defines a class of mammals called ungulates. The volume of an ungula of a cylinder was calculated by Grégoire de Saint Vincent. Two cylinders with equal radii and perpendicular axes intersect in four double ungulae.Blaise Pascal]Lettre de Dettonville a Carcavidescribes the onglet and double onglet, link from HathiTrust The bicylinder formed by the intersection had been measured by Archimedes in The Method of Mechanical Theorems, but the manuscript was lost until 1906. A historian of calculus described the role of the ungula in integral calculus: :Grégoire himself was primarily concerned to illustrate by reference to the ''ungula'' that volumetric integration could be reduced, through the Gregory of St. Vincent#Ductus plani in planum, ''ductus in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid Geometry
In mathematics, solid geometry or stereometry is the traditional name for the geometry of Three-dimensional space, three-dimensional, Euclidean spaces (i.e., 3D geometry). Stereometry deals with the measurements of volumes of various solid figures (or 3D figures), including Pyramid (geometry), pyramids, Prism (geometry), prisms and other polyhedrons; Cylinder (geometry), cylinders; cone (geometry), cones; Frustum, truncated cones; and ball (mathematics), balls bounded by spheres. History The Pythagoreanism, Pythagoreans dealt with the regular solids, but the pyramid, prism, cone and cylinder were not studied until the Platonism, Platonists. Eudoxus of Cnidus, Eudoxus established their measurement, proving the pyramid and cone to have one-third the volume of a prism and cylinder on the same base and of the same height. He was probably also the discoverer of a proof that the volume enclosed by a sphere is proportional to the cube of its radius.Paraphrased and taken in part from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Method Of Mechanical Theorems
''The Method of Mechanical Theorems'' ( el, Περὶ μηχανικῶν θεωρημάτων πρὸς Ἐρατοσθένη ἔφοδος), also referred to as ''The Method'', is one of the major surviving works of the ancient Greece, ancient Greek polymath Archimedes. ''The Method'' takes the form of a letter from Archimedes to Eratosthenes, the chief librarian at the Library of Alexandria, and contains the first attested explicit use of method of indivisibles, indivisibles (sometimes erroneously referred to as infinitesimals). The work was originally thought to be lost, but in 1906 was rediscovered in the celebrated Archimedes Palimpsest. The palimpsest includes Archimedes' account of the "mechanical method", so called because it relies on the Center of mass, center of weights of figures (centroid) and the Lever#Law of the lever, law of the lever, which were demonstrated by Archimedes in ''On the Equilibrium of Planes''. Archimedes did not admit the method of indivisibles as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Books
Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical character recognition (OCR), and stored in its digital database.The basic Google book link is found at: https://books.google.com/ . The "advanced" interface allowing more specific searches is found at: https://books.google.com/advanced_book_search Books are provided either by publishers and authors through the Google Books Partner Program, or by Google's library partners through the Library Project. Additionally, Google has partnered with a number of magazine publishers to digitize their archives. The Publisher Program was first known as Google Print when it was introduced at the Frankfurt Book Fair in October 2004. The Google Books Library Project, which scans works in the collections of library partners and adds them to the digital invent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steinmetz Solid
In geometry, a Steinmetz solid is the solid body obtained as the intersection of two or three cylinders of equal radius at right angles. Each of the curves of the intersection of two cylinders is an ellipse. The intersection of two cylinders is called a bicylinder. Topologically, it is equivalent to a square hosohedron. The intersection of three cylinders is called a tricylinder. A bisected bicylinder is called a vault, and a cloister vault in architecture has this shape. Steinmetz solids are named after mathematician Charles Proteus Steinmetz, who solved the problem of determining the volume of the intersection. However, the same problem had been solved earlier, by Archimedes in the ancient Greek world, Zu Chongzhi in ancient China, and Piero della Francesca in the early Italian Renaissance. Bicylinder A bicylinder generated by two cylinders with radius r has the ;volume :V=\frac r^3 and the ;surface area :A=16 r^2. The upper half of a bicylinder is the square ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Wedge
In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's ''base''). The angle between the radii lying within the bounding semidisks is the dihedral . If is a semidisk that forms a ball when completely revolved about the ''z''-axis, revolving only through a given produces a spherical wedge of the same angle . Beman (2008) remarks that "a spherical wedge is to the sphere of which it is a part as the angle of the wedge is to a perigon." A spherical wedge of radians (180°) is called a ''hemisphere'', while a spherical wedge of radians (360°) constitutes a complete ball. The volume of a spherical wedge can be intuitively related to the definition in that while the volume of a ball of radius is given by , the volume a spherical wedge of the same radius is given by :V = \frac \cdot \tfrac43 \pi r^3 = \tfrac23 \alpha r^3\,. Extrapolating the same principle and considering that the surface area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conical Ungula
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. Depending on the author, the base may be restricted to be a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a solid object; otherwise it is a two-dimensional object in three-dimensional space. In the case of a solid object, the boundary formed by these lines or partial lines is called the ''lateral surface''; if the lateral surface is unbounded, it is a conical surface. In the case of line segments, the cone does not extend beyond the base, while in the case of half-lines, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shell Integration
Shell integration (the shell method in integral calculus) is a method for calculating the volume of a solid of revolution, when integrating along an axis ''perpendicular to'' the axis of revolution. This is in contrast to disc integration which integrates along the axis ''parallel'' to the axis of revolution. Definition The shell method goes as follows: Consider a volume in three dimensions obtained by rotating a cross-section in the -plane around the -axis. Suppose the cross-section is defined by the graph of the positive function on the interval . Then the formula for the volume will be: :2 \pi \int_a^b x f(x)\, dx If the function is of the coordinate and the axis of rotation is the -axis then the formula becomes: :2 \pi \int_a^b y f(y)\, dy If the function is rotating around the line then the formula becomes: :\begin \displaystyle 2 \pi \int_a^b (x-h) f(x)\,dx, & \text\ h \le a < b\\ \displaystyle 2 \pi \int_a^b (h-x) f(x)\,dx, & \text\ a < b \le h, \end and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cylindrical Ungula
A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in ball and sphere)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces. In the literature the unadorned term cylinder could refer to either of these or to an even more specialized object, the ''right circular cylinder''. Types The definitions and results in this section are taken from the 1913 text ''Plane and Solid Geometry'' by George Wentworth and David Eugene Smith . A ' is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elsevier
Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell'', the ScienceDirect collection of electronic journals, '' Trends'', the '' Current Opinion'' series, the online citation database Scopus, the SciVal tool for measuring research performance, the ClinicalKey search engine for clinicians, and the ClinicalPath evidence-based cancer care service. Elsevier's products and services also include digital tools for data management, instruction, research analytics and assessment. Elsevier is part of the RELX Group (known until 2015 as Reed Elsevier), a publicly traded company. According to RELX reports, in 2021 Elsevier published more than 600,000 articles annually in over 2,700 journals; as of 2018 its archives contained over 17 million documents and 40,000 e-books, with over one billion annual downloads. Researchers have criticized Elsevier for its high profit marg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pergamon Press
Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, that published scientific and medical books and journals. Originally called Butterworth-Springer, it is now an imprint of Elsevier. History The core company, Butterworth-Springer, started in 1948 to bring the "Springer know-how and techniques of aggressive publishing in science"Joe Haines (1988) ''Maxwell'', Houghton Mifflin, p. 137. to Britain. Paul Rosbaud was the man with the knowledge. When Maxwell acquired the company in 1951, Rosbaud held a one-quarter share. They changed the house name to Pergamon Press, using a logo that was a reproduction of a Greek coin from Pergamon. Maxwell and Rosbaud worked together growing the company until May 1956, when, according to Joe Haines, Rosbaud was sacked. When Pergamon Press started it had only six serials and two books. Initially the company headquarters was in Fitzroy Square in West End of London. In 1959, the company moved into Headingt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Margaret Baron
Margaret E. Baron (1915 – 16 August 1996) was a British mathematics educator and historian of mathematics known for her book on the history of calculus. Life Baron was originally from Gateshead, in northeastern England, and earned a bachelor's degree from Durham University through King's College, Newcastle, which later became Newcastle University. She worked for a year as an English teacher in Frankfurt, and in 1938 became a mathematics teacher at the Bede School for Girls, later to become part of Sunderland College. Because she married George Baron, a teacher at the corresponding boys' school, she was dismissed as a teacher in 1940. She took two more teaching posts, at the Royal Grammar School, Newcastle upon Tyne and the High Storrs School in Sheffield, before leaving work to raise her family in Gateshead. Her husband returned from war service in 1946, and they moved to London. Eventually she returned to teaching, at Goldsmiths' College and then, in 1957, as head of mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral Calculus
In mathematics, an integral assigns numbers to Function (mathematics), functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Derivative, differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are posi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
