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Daniel Shanks
Daniel Charles Shanks (January 17, 1917 – September 6, 1996) was an American mathematician who worked primarily in numerical analysis and number theory. He was the first person to compute π to 100,000 decimal places. Life and education Shanks was born on January 17, 1917, in Chicago, Illinois. He is not related to the English mathematician William Shanks, who was also known for his computation of π. He earned his Bachelor of Science degree in physics from the University of Chicago in 1937, and a Ph.D. in Mathematics from the University of Maryland in 1954. Prior to obtaining his PhD, Shanks worked at the Aberdeen Proving Ground and the Naval Ordnance Laboratory, first as a physicist and then as a mathematician. During this period he wrote his PhD thesis, which completed in 1949, despite having never taken any graduate math courses. After earning his PhD in mathematics, Shanks continued working at the Naval Ordnance Laboratory and the Naval Ship Research and Development C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chicago
Chicago is the List of municipalities in Illinois, most populous city in the U.S. state of Illinois and in the Midwestern United States. With a population of 2,746,388, as of the 2020 United States census, 2020 census, it is the List of United States cities by population, third-most populous city in the United States after New York City and Los Angeles. As the county seat, seat of Cook County, Illinois, Cook County, the List of the most populous counties in the United States, second-most populous county in the U.S., Chicago is the center of the Chicago metropolitan area, often colloquially called "Chicagoland" and home to 9.6 million residents. Located on the shore of Lake Michigan, Chicago was incorporated as a city in 1837 near a Chicago Portage, portage between the Great Lakes and the Mississippi River, Mississippi River watershed. It grew rapidly in the mid-19th century. In 1871, the Great Chicago Fire destroyed several square miles and left more than 100,000 homeless, but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bachelor Of Science
A Bachelor of Science (BS, BSc, B.S., B.Sc., SB, or ScB; from the Latin ') is a bachelor's degree that is awarded for programs that generally last three to five years. The first university to admit a student to the degree of Bachelor of Science was the University of London in 1860. In the United States, the Lawrence Scientific School first conferred the degree in 1851, followed by the University of Michigan in 1855. Nathaniel Shaler, who was Harvard's Dean of Sciences, wrote in a private letter that "the degree of Bachelor of Science came to be introduced into our system through the influence of Louis Agassiz, who had much to do in shaping the plans of this School." Whether Bachelor of Science or Bachelor of Arts degrees are awarded in particular subjects varies between universities. For example, an economics student may graduate as a Bachelor of Arts in one university but as a Bachelor of Science in another, and occasionally, both options are offered. Some universities follo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pell's Equation
Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x^2 - ny^2 = 1, where ''n'' is a given positive Square number, nonsquare integer, and integer solutions are sought for ''x'' and ''y''. In Cartesian coordinates, the equation is represented by a hyperbola; solutions occur wherever the curve passes through a point whose ''x'' and ''y'' coordinates are both integers, such as the Triviality (mathematics), trivial solution with ''x'' = 1 and ''y'' = 0. Joseph Louis Lagrange proved that, as long as ''n'' is not a square number, perfect square, Pell's equation has infinitely many distinct integer solutions. These solutions may be used to accurately Diophantine approximation, approximate the square root of ''n'' by rational numbers of the form ''x''/''y''. This equation was first studied extensively Indian mathematics, in India starting with Brahmagupta, who found an integer solution to 92x^2 + 1 = y^2 in his '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Residues
In number theory, an integer ''q'' is a quadratic residue modulo ''n'' if it is congruent to a perfect square modulo ''n''; that is, if there exists an integer ''x'' such that :x^2\equiv q \pmod. Otherwise, ''q'' is a quadratic nonresidue modulo ''n''. Quadratic residues are used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers. History, conventions, and elementary facts Fermat, Euler, Lagrange, Legendre, and other number theorists of the 17th and 18th centuries established theorems and formed conjectures about quadratic residues, but the first systematic treatment is § IV of Gauss's ''Disquisitiones Arithmeticae'' (1801). Article 95 introduces the terminology "quadratic residue" and "quadratic nonresidue", and says that if the context makes it clear, the adjective "quadratic" may be dropped. For a given ''n'', a list of the quadratic residues modulo ''n'' may be obtained by simply squaring all the numbers 0, 1, ..., . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Computation
''Mathematics of Computation'' is a bimonthly mathematics journal focused on computational mathematics. It was established in 1943 as ''Mathematical Tables and Other Aids to Computation'', obtaining its current name in 1960. Articles older than five years are available electronically free of charge. Abstracting and indexing The journal is abstracted and indexed in Mathematical Reviews, Zentralblatt MATH, Science Citation Index, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. According to the '' Journal Citation Reports'', the journal has a 2020 impact factor of 2.417. References External links * Delayed open access journals English-language journals Mathematics journals Academic journals established in 1943 American Mathematical Society academic journals Bimonthly journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IBM 7090
The IBM 7090 is a second-generation Transistor computer, transistorized version of the earlier IBM 709 vacuum tube mainframe computer that was designed for "large-scale scientific and technological applications". The 7090 is the fourth member of the IBM 700/7000 series#Scientific Architecture, IBM 700/7000 series scientific computers. The first 7090 installation was in December 1959. In 1960, a typical system sold for $2.9 million (equivalent to $ million in ) or could be rented for $63,500 a month (). The 7090 uses a 36-bit word length, with an address space of 32,768 words (15-bit addresses). It operates with a basic memory cycle of 2.18 μs, using the IBM 7302 Core Storage Magnetic-core memory, core memory technology from the IBM 7030 (Stretch) project. With a processing speed of around 100 FLOPS, Kflop/s, the 7090 is six times faster than the 709, and could be rented for half the price. An upgraded version, the 7094, was up to twice as fast. Both the 7090 and the 7094 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wrench
John William Wrench, Jr. (October 13, 1911 – February 27, 2009) was an American mathematician who worked primarily in numerical analysis. He was a pioneer in using computers for mathematical calculations, and is noted for work done with Daniel Shanks to calculate the mathematical constant pi to 100,000 decimal places. Life and education Wrench was born on October 13, 1911, in Westfield, New York, and grew up in Hamburg, New York. He received a BA summa cum laude in mathematics in 1933 and an MA in mathematics in 1935, both from the University at Buffalo. He received his PhD in mathematics in 1938 from Yale University. His thesis was titled ''The derivation of arctangent relations''. Wrench died on February 27, 2009, of pneumonia in Frederick, Maryland. Career Wrench started his career teaching at George Washington University, but switched to doing research for the United States Navy during World War II. His specialty for the Navy was developing high-speed computation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epstein Zeta Function
In mathematics, the simplest real analytic Eisenstein series is a special function of two variables. It is used in the representation theory of SL(2,R) and in analytic number theory. It is closely related to the Epstein zeta function. There are many generalizations associated to more complicated groups. Definition The Eisenstein series ''E''(''z'', ''s'') for ''z'' = ''x'' + ''iy'' in the upper half-plane is defined by :E(z,s) =\sum_ for Re(''s'') > 1, and by analytic continuation for other values of the complex number ''s''. The sum is over all pairs of coprime integers. There are several other slightly different definitions. Some authors omit the factor of , and some sum over all pairs of integers that are not both zero; which changes the function by a factor of ζ(2''s''). Properties As a function on ''z'' Viewed as a function of ''z'', ''E''(''z'',''s'') is a real-analytic eigenfunction of the Laplace operator on H with the eigenvalue ''s''(''s''-1). In other words, it sat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Identities
In mathematics, an identity is an equality relating one mathematical expression ''A'' to another mathematical expression ''B'', such that ''A'' and ''B'' (which might contain some variables) produce the same value for all values of the variables within a certain domain of discourse. In other words, ''A'' = ''B'' is an identity if ''A'' and ''B'' define the same functions, and an identity is an equality between functions that are differently defined. For example, (a+b)^2 = a^2 + 2ab + b^2 and \cos^2\theta + \sin^2\theta =1 are identities. Identities are sometimes indicated by the triple bar symbol instead of , the equals sign. Formally, an identity is a universally quantified equality. Common identities Algebraic identities Certain identities, such as a+0=a and a+(-a)=0, form the basis of algebra, while other identities, such as (a+b)^2 = a^2 + 2ab +b^2 and a^2 - b^2 = (a+b)(a-b), can be useful in simplifying algebraic expressions and expanding th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ballistics
Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially weapon munitions such as bullets, unguided bombs, rockets and the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance. A ballistic body is a free-moving body with momentum, which can be subject to forces such as those exerted by pressurized gases from a gun barrel or a propelling nozzle, normal force by rifling, and gravity and air drag during flight. A ballistic missile is a missile that is missile guidance, guided only during the relatively brief initial phase of powered flight, with the trajectory subsequently governed by the laws of classical mechanics, in contrast to (for example) a cruise missile, which is aerodynamics, aerodynamically guided in powered flight like a fixed-wing aircraft. History and prehistory The earliest known ballistic projectiles were stones, spears, and the throwing s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Body
A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The radiation emitted by a black body in thermal equilibrium with its environment is called ''black-body radiation''. The name "black body" is given because it absorbs all colors of light. In contrast, a white body is one with a "rough surface that reflects all incident rays completely and uniformly in all directions." A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic black-body radiation. The radiation is emitted according to Planck's law, meaning that it has a spectrum that is determined by the temperature alone (see figure at right), not by the body's shape or composition. An ideal black body in thermal equilibrium has two main properties: #It is an ideal emitter: at every frequency, it emits as much or more thermal radiative energy as any other body at the same temperature. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Bureau Of Standards
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical science laboratory programs that include nanoscale science and technology, engineering, information technology, neutron research, material measurement, and physical measurement. From 1901 to 1988, the agency was named the National Bureau of Standards. History Background The Articles of Confederation, ratified by the colonies in 1781, provided: The United States in Congress assembled shall also have the sole and exclusive right and power of regulating the alloy and value of coin struck by their own authority, or by that of the respective states—fixing the standards of weights and measures throughout the United States. Article 1, section 8, of the Constitution of the United States, ratified in 1789, granted these powers to the new Con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
