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Garfield's Proof Of The Pythagorean Theorem
Garfield's proof of the Pythagorean theorem is an original proof of the Pythagorean theorem discovered by James A. Garfield (November 19, 1831 – September 19, 1881), the 20th president of the United States. The proof appeared in print in the ''Journal of Education, New-England Journal of Education'' (Vol. 3, No.14, April 1, 1876). At the time of the publication of the proof Garfield was a Congressman from Ohio. He assumed the office of President on March 4, 1881, and served in that position only for a brief period up to September 19, 1881 when he died following his assassination in July. Garfield was the only President of the United States to have contributed anything original to mathematics. The proof is nontrivial and, according to the historian of mathematics William Dunham (mathematician), William Dunham, "Garfield's is really a very clever proof." The proof appears as the 231st proof in ''The Pythagorean Proposition'', a compendium of 370 different proofs of the Pythagorean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Abram Garfield, Photo Portrait Seated
James may refer to: People * James (given name) * James (surname) * James (musician), aka Faruq Mahfuz Anam James, (born 1964), Bollywood musician * James, brother of Jesus * King James (other), various kings named James * Prince James (other) * Saint James (other) Places Canada * James Bay, a large body of water * James, Ontario United Kingdom * James College, a college of the University of York United States * James, Georgia, an unincorporated community * James, Iowa, an unincorporated community * James City, North Carolina * James City County, Virginia ** James City (Virginia Company) ** James City Shire * James City, Pennsylvania * St. James City, Florida Film and television * ''James'' (2005 film), a Bollywood film * ''James'' (2008 film), an Irish short film * ''James'' (2022 film), an Indian Kannada-language film * "James", a television episode of ''Adventure Time'' Music * James (band), a band from Manchester ** ''James'', US ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The theorem can be written as an equation relating the lengths of the sides , and the hypotenuse , sometimes called the Pythagorean equation: :a^2 + b^2 = c^2 . The theorem is named for the Ancient Greece, Greek philosopher Pythagoras, born around 570 BC. The theorem has been Mathematical proof, proved numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both Geometry, geometric proofs and Algebra, algebraic proofs, with some dating back thousands of years. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James A
James may refer to: People * James (given name) * James (surname) * James (musician), aka Faruq Mahfuz Anam James, (born 1964), Bollywood musician * James, brother of Jesus * King James (other), various kings named James * Prince James (other) * Saint James (other) Places Canada * James Bay, a large body of water * James, Ontario United Kingdom * James College, York, James College, a college of the University of York United States * James, Georgia, an unincorporated community * James, Iowa, an unincorporated community * James City, North Carolina * James City County, Virginia ** James City (Virginia Company) ** James City Shire * James City, Pennsylvania * St. James City, Florida Film and television * James (2005 film), ''James'' (2005 film), a Bollywood film * James (2008 film), ''James'' (2008 film), an Irish short film * James (2022 film), ''James'' (2022 film), an Indian Kannada-language film * "James", a television Adventure Time (season 5)#ep42, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
President Of The United States
The president of the United States (POTUS) is the head of state and head of government of the United States. The president directs the Federal government of the United States#Executive branch, executive branch of the Federal government of the United States, federal government and is the Powers of the president of the United States#Commander-in-chief, commander-in-chief of the United States Armed Forces. The power of the presidency has grown since the first president, George Washington, took office in 1789. While presidential power has ebbed and flowed over time, the presidency has played an increasing role in American political life since the beginning of the 20th century, carrying over into the 21st century with some expansions during the presidencies of Presidency of Franklin D. Roosevelt, Franklin D. Roosevelt and Presidency of George W. Bush, George W. Bush. In modern times, the president is one of the world's most powerful political figures and the leader of the world's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Education
The Journal of Education () is an academic journal, published by SAGE Publishing on behalf of the Boston University Wheelock College of Education & Human Development, with Hardin Coleman as its editor-in-chief. It bills itself as "the oldest educational publication in the country". History The ''Journal of Education'' was formed in 1875 by the union of the ''Maine Journal of Education'', the ''Massachusetts Teacher'', the ''Rhode Island Schoolmaster'', the ''Connecticut School Journal'', and the ''College Courant''. The oldest of these, the ''Connecticut School Journal'', had been published under various names since 1838. The merged journal was originally called the ''New England Journal of Education'' from 1875 to 1880 and (after several additional mergers) became the ''Journal of Education'' by 1892. The Boston University School of Education took over as its publisher in 1953. By the early 1970s, the relevance of the journal had lagged, and the school revitalized it by turni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Dunham (mathematician)
William Wade Dunham (born 1947) is an American writer who was originally trained in topology but became interested in the history of mathematics and specializes in Leonhard Euler. He has received several awards for writing and teaching on this subject. Education Dunham received his BS from the University of Pittsburgh in 1969, his MS from Ohio State in 1970, and his PhD from the same institution in 1974. Writings Dunham won the American Association of Publishers' award for writing the Best Mathematics Book of 1994 for his book ''The Mathematical Universe''. In his book ''Euler: The Master of Us All'', he examines Leonhard Euler's impressive mathematical work. He received a Lester R. Ford Award in 2006 for his expository article ''Touring the Calculus'', and the Chauvenet Prize in 2022 for his article ''The Early (and Peculiar) History of the Möbius Function''. In 2007, Dunham gave a lecture about Euler's product-sum formula and its relationship to analytic number theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Garfield Proof
''Garfield'' is an American comic strip created by Jim Davis. Originally published locally as ''Jon'' in 1976 (later changed to ''Garfield'' in 1977), then in nationwide syndication from 1978, it chronicles the life of the title character Garfield the cat, Odie the dog, and their owner Jon Arbuckle. As of 2013, it was syndicated in roughly 2,580 newspapers and journals; the comic held the Guinness World Record for being the world's most widely syndicated comic strip. Though its setting is rarely mentioned in print, ''Garfield'' takes place in Davis's hometown of Muncie, Indiana, according to the television special ''Happy Birthday, Garfield''. Common themes in the strip include Garfield's laziness, obsessive eating, love of coffee and lasagna, disdain of Mondays, and dieting. Garfield is also shown to manipulate people to get whatever he wants. The strip's focus is mostly on the interactions among Garfield, Jon, and Odie, but other recurring characters appear as well. ''Ga ... [...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] |
Pythagoras
Pythagoras of Samos (; BC) was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Modern scholars disagree regarding Pythagoras's education and influences, but most agree that he travelled to Croton in southern Italy around 530 BC, where he founded a school in which initiates were allegedly sworn to secrecy and lived a communal, ascetic lifestyle. In antiquity, Pythagoras was credited with mathematical and scientific discoveries, such as the Pythagorean theorem, Pythagorean tuning, the five regular solids, the theory of proportions, the sphericity of the Earth, the identity of the morning and evening stars as the planet Venus, and the division of the globe into five climatic zones. He was reputedly the first man to call himself a philosopher ("lover of wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Plane Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, '' 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 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 thous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Geometry
Geometry (from the ; '' geo-'' "earth", '' -metron'' "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, '' The Elements'' is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century. In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See Areas of mathematics and Algebraic geometry.) Early geometry The earliest recorded beg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorems In Plane Geometry
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ''corollary'' for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasonin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
