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One-seventh Area Triangle
In plane geometry, a triangle ''ABC'' contains a triangle having one-seventh of the area of ''ABC'', which is formed as follows: the sides of this triangle lie on cevians ''p, q, r'' where :''p'' connects ''A'' to a point on ''BC'' that is one-third the distance from ''B'' to ''C'', :''q'' connects ''B'' to a point on ''CA'' that is one-third the distance from ''C'' to ''A'', :''r'' connects ''C'' to a point on ''AB'' that is one-third the distance from ''A'' to ''B''. The proof of the existence of the one-seventh area triangle follows from the construction of six parallel lines: : two parallel to ''p'', one through ''C'', the other through ''q.r'' : two parallel to ''q'', one through ''A'', the other through ''r.p'' : two parallel to ''r'', one through ''B'', the other through ''p.q''. The suggestion of Hugo Steinhaus is that the (central) triangle with sides ''p,q,r'' be reflected in its sides and vertices. These six extra triangles partially cover ''ABC'', and leave six ove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One-seventh Area Triangle
In plane geometry, a triangle ''ABC'' contains a triangle having one-seventh of the area of ''ABC'', which is formed as follows: the sides of this triangle lie on cevians ''p, q, r'' where :''p'' connects ''A'' to a point on ''BC'' that is one-third the distance from ''B'' to ''C'', :''q'' connects ''B'' to a point on ''CA'' that is one-third the distance from ''C'' to ''A'', :''r'' connects ''C'' to a point on ''AB'' that is one-third the distance from ''A'' to ''B''. The proof of the existence of the one-seventh area triangle follows from the construction of six parallel lines: : two parallel to ''p'', one through ''C'', the other through ''q.r'' : two parallel to ''q'', one through ''A'', the other through ''r.p'' : two parallel to ''r'', one through ''B'', the other through ''p.q''. The suggestion of Hugo Steinhaus is that the (central) triangle with sides ''p,q,r'' be reflected in its sides and vertices. These six extra triangles partially cover ''ABC'', and leave six ove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and millions of books. In addition to its archiving function, the Archive is an activist organization, advocating a free and open Internet. , the Internet Archive holds over 35 million books and texts, 8.5 million movies, videos and TV shows, 894 thousand software programs, 14 million audio files, 4.4 million images, 2.4 million TV clips, 241 thousand concerts, and over 734 billion web pages in the Wayback Machine. The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Articles Containing Proofs
Article often refers to: * Article (grammar), a grammatical element used to indicate definiteness or indefiniteness * Article (publishing), a piece of nonfictional prose that is an independent part of a publication Article may also refer to: Government and law * Article (European Union), articles of treaties of the European Union * Articles of association, the regulations governing a company, used in India, the UK and other countries * Articles of clerkship, the contract accepted to become an articled clerk * Articles of Confederation, the predecessor to the current United States Constitution *Article of Impeachment, a formal document and charge used for impeachment in the United States * Articles of incorporation, for corporations, U.S. equivalent of articles of association * Articles of organization, for limited liability organizations, a U.S. equivalent of articles of association Other uses * Article, an HTML element, delimited by the tags and * Article of clothing, an ite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Objects Defined For A Triangle
Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an aim, target, or objective * Object (grammar), a sentence element, such as a direct object or an indirect object Science, technology, and mathematics Computing * 3D model, a representation of a physical object * Object (computer science), a language mechanism for binding data with methods that operate on that data ** Object-orientation, in which concepts are represented as objects *** Object-oriented programming (OOP), in which an object is an instance of a class or array ** Object (IBM i), the fundamental unit of data storage in the IBM i operating system * Object (image processing), a portion of an image interpreted as a unit * Object file, the output of a compiler or other translator program (also known as "object code") * Object, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East Orange, New Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Routh's Theorem
In geometry, Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians. The theorem states that if in triangle ABC points D, E, and F lie on segments BC, CA, and AB, then writing \tfrac = x, \tfrac = y, and \tfrac = z, the signed area of the triangle formed by the cevians AD, BE, and CF is : S_ \frac, where S_ is the area of the triangle ABC. This theorem was given by Edward John Routh on page 82 of his ''Treatise on Analytical Statics with Numerous Examples'' in 1896. The particular case x = y = z = 2 has become popularized as the one-seventh area triangle. The x = y = z = 1 case implies that the three medians are concurrent (through the centroid). Proof Suppose that the area of triangle ABC is 1. For triangle ABD and line FRC using Menelaus's theorem, We could obtain: :\frac \times \frac \times \frac = 1 Then \frac = \frac \times \frac = \frac So the area of triangle ARC is: :S_ = \frac S_ = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Gazette
''The Mathematical Gazette'' is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive areas of mathematics." It was established in 1894 by Edward Mann Langley as the successor to the Reports of the Association for the Improvement of Geometrical Teaching. Its publisher is the Mathematical Association. William John Greenstreet was its editor for more than thirty years (1897–1930). Since 2000, the editor is Gerry Leversha. Editors * Edward Mann Langley: 1894-1896 * Francis Sowerby Macaulay: 1896-1897 * William John Greenstreet: 1897-1930 * Alan Broadbent: 1930-1955 * Reuben Goodstein: 1956-1962 * Edwin A. Maxwell: 1962-1971 * Douglas Quadling Douglas Arthur Quadling (1926–2015) was an English mathematician, school master and educationalist who was one of the four drivers behind the School Mathematics Project (SMP) i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Feynman
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, as well as his work in particle physics for which he proposed the parton model. For contributions to the development of quantum electrodynamics, Feynman received the Nobel Prize in Physics in 1965 jointly with Julian Schwinger and Shin'ichirō Tomonaga. Feynman developed a widely used pictorial representation scheme for the mathematical expressions describing the behavior of subatomic particles, which later became known as Feynman diagrams. During his lifetime, Feynman became one of the best-known scientists in the world. In a 1999 poll of 130 leading physicists worldwide by the British journal ''Physics World'', he was ranked the seventh-greatest physicist of all time. He assisted in the development o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logical system in which each result is '' proved'' from axioms and previously proved theorems. The ''Elements'' begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called algebra and number theory, explained in geometrical language. For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Randi
James Randi (born Randall James Hamilton Zwinge; August 7, 1928 – October 20, 2020) was a Canadian-American stage magician, author and scientific skeptic who extensively challenged paranormal and pseudoscientific claims. Rodrigues 2010p. 271/ref> He was the co-founder of the Committee for Skeptical Inquiry (CSI), and founder of the James Randi Educational Foundation (JREF). Randi began his career as a magician under the stage name The Amazing Randi and later chose to devote most of his time to investigating paranormal, occult, and supernatural claims, which he collectively called "woo-woo". Randi retired from practicing magic at age 60, and from his foundation at 87. Although often referred to as a "debunker", Randi said he disliked the term's connotations and preferred to describe himself as an "investigator". He wrote about paranormal phenomena, skepticism, and the history of magic. He was a frequent guest on ''The Tonight Show Starring Johnny Carson'', famously expo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was also a leading authority on Lewis Carroll. ''The Annotated Alice'', which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematicsand by extension, mathematics in generalthroughout the latter half of the 20th century, principally through his "Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
