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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] |
Richard Feynman
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist. He is best 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, and in particle physics, for which he proposed the parton model. For his 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 pictorial representation scheme for the mathematical expressions describing the behavior of subatomic particles, which later became known as Feynman diagrams and is widely used. 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 Manhatt ... [...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(s) may also refer to: Government and law * Elements of treaties of the European Union * Articles of association, the regulations governing a company, used in India, the UK and other countries; called articles of incorporation in the US * 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 * Article of manufacture, in the United States patent law, a category of things that may be patented * Articles of organization, for limited liability organizations, a US equivalent of articles of association Other uses * Article element , in HTML * "Articles", a song ... [...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 (other), 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 file, the output of a compiler or other translator program (also known as "object code") * HTML object element Mathematics * Object (mathematics), an abstrac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American Multinational corporation, multinational Publishing, publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, Academic journal, 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, Technology, technical, and engineering subject areas, abandoning its literary interests. Wiley's son Joh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marion Walter
Marion Walter (July 30, 1928 – May 9, 2021) was an internationally-known mathematics educator and professor of mathematics at the University of Oregon in Eugene, Oregon. There is a theorem named after her, called Marion Walter's Theorem or just Marion's Theorem as it is affectionately known. Early life Marion Walter was born in Berlin, Germany in 1928 to Erna and Willy Walter. Her father was a prosperous merchant who specialized in costume jewelry. In 1936, when the Nazis were gaining strength in Germany and it was no longer possible for Jews to attend public school, she and her sister, Ellen, were sent to a Jewish boarding school called Landschulheim Herrlingen in the village of Herrlingen, a suburb of Ulm. The book ''Education towards spiritual resistance: The Jewish Landschulheim Herrlingen, 1933 to 1939'' by Lucie Schachne documents this remarkable school, which was closed in 1939. On March 15, 1939, Marion and Ellen Walter were sent on a ''Kindertransport'' to England ... [...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, Menelaus's theorem implies :\frac \times \frac \times \frac = -1. Then \frac = \frac \times \frac = \frac. Thus the area of triangle ARC is :S_ = \frac S_ = \frac \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Gazette
''The Mathematical Gazette'' is a triannual peer-reviewed academic journal published by Cambridge University Press on behalf of the Mathematical Association. It covers mathematics education with a focus on the 15–20 years age range. The journal was established in 1894 by Edward Mann Langley as the successor to the ''Reports of the Association for the Improvement of Geometrical Teaching''. William John Greenstreet was its editor-in-chief for more than thirty years (1897–1930). Since 2000, the editor is Gerry Leversha. Editors-in-chief The following persons are or have been editor-in-chief: Abstracting and indexing The journal is abstracted and indexed in EBSCO databases, Emerging Sources Citation Index, Scopus Scopus is a scientific abstract and citation database, launched by the academic publisher Elsevier as a competitor to older Web of Science in 2004. The ensuing competition between the two databases has been characterized as "intense" and is c ..., and zbMA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including websites, Application software, software applications, music, audiovisual, and print materials. The Archive also advocates a Information wants to be free, free and open Internet. Its mission is committing to provide "universal access to all knowledge". 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 hundreds of billions of web captures. The Archive also oversees numerous Internet Archive#Book collections, book digitization projects, collectively one of the world's largest book digitization efforts. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. One of those is the parallel postulate which relates to parallel lines on a Euclidean plane. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logic, logical system in which each result is ''mathematical proof, 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 ... [...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, Rodrigues 2010p. 271 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. 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 exposing fraudulent faith healer Peter Pop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
