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Elevator Paradox
The elevator paradox is a paradox first noted by Marvin Stern and George Gamow, physicists who had offices on different floors of a multi-story building. Gamow, who had an office near the bottom of the building noticed that the first elevator to stop at his floor was most often going down, while Stern, who had an office near the top, noticed that the first elevator to stop at his floor was most often going up. This creates the false impression that elevator cars are more likely to be going in one direction than the other depending on which floor the observer is on. Modeling the elevator problem Several attempts (beginning with Gamow and Stern) were made to analyze the reason for this phenomenon: the basic analysis is simple, while detailed analysis is more difficult than it would at first appear. Simply, if one is on the top floor of a building, ''all'' elevators will come from below (none can come from above), and then depart going down, while if one is on the second fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paradox
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites". In logic, many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Gamow
George Gamow (March 4, 1904 – August 19, 1968), born Georgiy Antonovich Gamov ( uk, Георгій Антонович Гамов, russian: Георгий Антонович Гамов), was a Russian-born Soviet and American polymath, theoretical physicist and cosmologist. He was an early advocate and developer of Lemaître's Big Bang theory. He discovered a theoretical explanation of alpha decay by quantum tunneling, invented the liquid drop model and the first mathematical model of the atomic nucleus, and worked on radioactive decay, star formation, stellar nucleosynthesis and Big Bang nucleosynthesis (which he collectively called nucleocosmogenesis), and molecular genetics. In his middle and late career, Gamow directed much of his attention to teaching and wrote popular books on science, including '' One Two Three... Infinity'' and the ''Mr Tompkins'' series of books (1939–1967). Some of his books are still in print more than a half-century after their original publicat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, through biological physics, to cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: experimental physicists who specialize in the observation of natural phenomena and the development and analysis of experiments, and theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies (also known as applie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elevator
An elevator or lift is a wire rope, cable-assisted, hydraulic cylinder-assisted, or roller-track assisted machine that vertically transports people or freight between floors, levels, or deck (building), decks of a building, watercraft, vessel, or other structure. They are typically powered by electric motors that drive traction cables and counterweight systems such as a hoist (device), hoist, although some pump hydraulic fluid to raise a cylindrical piston like a hydraulic jack, jack. In agriculture and manufacturing, an elevator is any type of conveyor device used to lift materials in a continuous stream into bins or silos. Several types exist, such as the chain and bucket elevator, grain auger screw conveyor using the principle of Archimedes' screw, or the chain and paddles or forks of hay elevators. Languages other than English, such as Japanese, may refer to elevators by loanwords based on either ''elevator'' or ''lift''. Due to wheelchair access laws, elevators are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elevator Paradox-compat
An elevator or lift is a cable-assisted, hydraulic cylinder-assisted, or roller-track assisted machine that vertically transports people or freight between floors, levels, or decks of a building, vessel, or other structure. They are typically powered by electric motors that drive traction cables and counterweight systems such as a hoist, although some pump hydraulic fluid to raise a cylindrical piston like a jack. In agriculture and manufacturing, an elevator is any type of conveyor device used to lift materials in a continuous stream into bins or silos. Several types exist, such as the chain and bucket elevator, grain auger screw conveyor using the principle of Archimedes' screw, or the chain and paddles or forks of hay elevators. Languages other than English, such as Japanese, may refer to elevators by loanwords based on either ''elevator'' or ''lift''. Due to wheelchair access laws, elevators are often a legal requirement in new multistory buildings, esp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle Wave
A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square wave, the triangle wave contains only odd harmonics. However, the higher harmonics roll-off, roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse). Definitions Definition A triangle wave of period ''p'' that spans the range [0,1] is defined as: x(t)= 2 \left, \frac - \left \lfloor \frac + \frac \right \rfloor \ where \lfloor\,\ \rfloor is the Floor and ceiling functions, floor function. This can be seen to be the absolute value of a shifted sawtooth wave. For a triangle wave spanning the range the expression becomes: x(t)= 2 \left , 2 \left ( \frac - \left \lfloor + \right \rfloor \right) \right , - 1. A more general equation for a triangle wave with amplitude a and period p using the modulo operation and absol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Recreational Mathematics
The ''Journal of Recreational Mathematics'' was an American journal dedicated to recreational mathematics, started in 1968. It had generally been published quarterly by the Baywood Publishing Company, until it ceased publication with the last issue (volume 38, number 2) published in 2014. The initial publisher (of volumes 1–5) was Greenwood Periodicals. Harry L. Nelson was primary editor for five years (volumes 9 through 13, excepting volume 13, number 4, when the initial editor returned as lead) and Joseph Madachy, the initial lead editor and editor of a predecessor called ''Recreational Mathematics Magazine'' which ran during the years 1961 to 1964, was the editor for many years. Charles Ashbacher and Colin Singleton took over as editors when Madachy retired (volume 30 number 1). The final editors were Ashbacher and Lamarr Widmer. The journal has from its inception also listed associate editors, one of whom was Leo Moser. The journal contains: # Original articles # Book rev ... [...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] |
Statistical Paradoxes
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An expe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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