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Kenneth Appel
Kenneth Ira Appel (October 8, 1932 – April 19, 2013) was an American mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana–Champaign, solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color. Biography Appel was born in Brooklyn, New York, on October 8, 1932. He grew up in Queens, New York, and was the son of a Jewish couple, Irwin Appel and Lillian Sender Appel. He worked as an actuary for a brief time and then served in the U.S. Army for two years at Fort Benning, Georgia, and in Baumholder, Germany. In 1959, he finished his doctoral program at the University of Michigan, and he also married Carole S. Stein in Philadelphia. The couple moved to Princeton, New Jersey, where Appel worked for the Institute for Defense Analyses from 1959 to 1961. His mai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brooklyn
Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York (state), New York. Kings County is the most populous Administrative divisions of New York (state)#County, county in the State of New York, and the County statistics of the United States#Most densely populated, second-most densely populated county in the United States, behind New York County (Manhattan). Brooklyn is also New York City's most populous borough,2010 Gazetteer for New York State United States Census Bureau. Retrieved September 18, 2016. with 2,736,074 residents in 2020. Named after the Dutch village of Breukelen, Brooklyn is located on the western portion of Long Island and shares a border with the borough of Queens. It has several bridge an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Koch
John Koch (August 18, 1909 — April 19, 1978), (pronounced "KŌK") was an American painter and teacher, and an important figure in 20th century Realism. He is best known for his light-filled paintings of urban interiors, often featuring classical allusions, many set in his own Manhattan apartment. His work is in the collections of prominent American museums, including the Metropolitan Museum of Art, the Smithsonian American Art Museum, the Whitney Museum of American Art, the Brooklyn Museum, the Museum of Fine Arts, Boston, and many others. Life and career He was born in Toledo, Ohio, to Marian Joan and Edward John Koch, and grew up mostly in Ann Arbor, Michigan. During his high school years he spent two summers at an artists' colony in Provincetown, Massachusetts. He moved to New York City in 1928, where he met and became friends with Dora Zaslavsky, a talented piano teacher, four years his senior.Grady Turner, "Enigmatic Intimacy: The Interior World of John Koch", catalo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baumholder, Germany
Baumholder () is a town in the Birkenfeld district in Rhineland-Palatinate, Germany, in the Westrich, an historic region that encompasses areas in both Germany and France. The town of Baumholder is the administrative seat of the like-named ''Verbandsgemeinde'', a state-recognised tourism resort and, according to state planning, a middle centre. Geography Location Baumholder lies between the Hunsrück to the north and the North Palatine Uplands to the south, right on a height that marks the latter's northern boundary. This area is also known as the Westrich. Baumholder lies roughly 10 km south of Idar-Oberstein. The countryside around Baumholder is marked by many meadows, fields and woodlands, both broadleaf and mixed. A great part of the Baumholder Troop Drilling Ground abutting the town serves as a refuge for many plant and animal species that have become rare, for example the common kingfisher, the lynx and the badger, some of which are on the IUCN Red List. Climate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Actuary
An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms. While the concept of insurance dates to antiquity, the concepts needed to scientifically measure and mitigate risks have their origins in the 17th century studies of probability and annuities. Actuaries of the 21st century require analytical skills, business knowledge, and an understanding of human behavior and information systems to design and manage programs that control risk. The actual steps needed to become an actuary are usually country-specific; however, almost all processes share a rigorous schooling or examination structure and take many yea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Queens, New York
Queens is a borough of New York City, coextensive with Queens County, in the U.S. state of New York. Located on Long Island, it is the largest New York City borough by area. It is bordered by the borough of Brooklyn at the western tip of Long Island to its west, and Nassau County to its east. Queens also shares water borders with the boroughs of Manhattan, the Bronx, and Staten Island (via the Rockaways). With a population of 2,405,464 as of the 2020 census, Queens is the second most populous county in the State of New York, behind Kings County (Brooklyn), and is therefore also the second most populous of the five New York City boroughs. If Queens became a city, it would rank as the fifth most-populous in the U.S. after New York City, Los Angeles, Chicago, and Houston. Approximately 47% of the residents of Queens are foreign-born. Queens is the most linguistically diverse place on Earth and is one of the most ethnically diverse counties in the United States. Queens was establ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brooklyn, New York
Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, behind New York County (Manhattan). Brooklyn is also New York City's most populous borough,2010 Gazetteer for New York State United States Census Bureau. Retrieved September 18, 2016. with 2,736,074 residents in 2020. Named after the Dutch village of Breukelen, Brooklyn is located on the western portion of Long Island and shares a border with the borough of Queens. It has several bridge and tunnel connections to the borough of |
Four-color Theorem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet. It was the first major theorem to be proved using a computer. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. The proof has gained wide acceptance since then, although some doubters remain. The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken after many false proofs and counterexamples (unlike the five color theorem, proved in the 1800s, which states that five colors are enough to color a map). To dispel any remaining doubts about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Americans
Americans are the citizens and nationals of the United States of America.; ; Although direct citizens and nationals make up the majority of Americans, many dual citizens, expatriates, and permanent residents could also legally claim American nationality. The United States is home to people of many racial and ethnic origins; consequently, American culture and law do not equate nationality with race or ethnicity, but with citizenship and an oath of permanent allegiance. Overview The majority of Americans or their ancestors immigrated to the United States or are descended from people who were brought as slaves within the past five centuries, with the exception of the Native American population and people from Hawaii, Puerto Rico, Guam, and the Philippine Islands, who became American through expansion of the country in the 19th century, additionally America expanded into American Samoa, the U.S. Virgin Islands and Northern Mariana Islands in the 20th century. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter H
Peter may refer to: People * List of people named Peter, a list of people and fictional characters with the given name * Peter (given name) ** Saint Peter (died 60s), apostle of Jesus, leader of the early Christian Church * Peter (surname), a surname (including a list of people with the name) Culture * Peter (actor) (born 1952), stage name Shinnosuke Ikehata, Japanese dancer and actor * ''Peter'' (album), a 1993 EP by Canadian band Eric's Trip * ''Peter'' (1934 film), a 1934 film directed by Henry Koster * ''Peter'' (2021 film), Marathi language film * "Peter" (''Fringe'' episode), an episode of the television series ''Fringe'' * ''Peter'' (novel), a 1908 book by Francis Hopkinson Smith * "Peter" (short story), an 1892 short story by Willa Cather Animals * Peter, the Lord's cat, cat at Lord's Cricket Ground in London * Peter (chief mouser), Chief Mouser between 1929 and 1946 * Peter II (cat), Chief Mouser between 1946 and 1947 * Peter III (cat), Chief Mouser between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew Appel
Andrew Wilson Appel (born 1960) is the Eugene Higgins Professor of computer science at Princeton University. He is especially well-known because of his compiler books, the ''Modern Compiler Implementation in ML'' () series, as well as ''Compiling With Continuations'' (). He is also a major contributor to the Standard ML of New Jersey compiler, along with David MacQueen, John H. Reppy, Matthias Blume and others and one of the authors of '' Rog-O-Matic''. Biography Andrew Appel is the son of mathematician Kenneth Appel, who proved the Four-Color Theorem in 1976. Appel graduated summa cum laude with an A.B. in physics from Princeton University in 1981 after completing a senior thesis, titled "Investigation of galaxy clustering using an asymptotically fast N-body algorithm", under the supervision of Nobel laureate James Peebles. He later received a Ph.D. (computer science) at Carnegie-Mellon University, in 1985. He became an ACM Fellow in 1998, due to his research of programmin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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