|
Wheat And Chessboard Problem
The wheat and chessboard problem (sometimes expressed in terms of rice grains) is a mathematical problem expressed in word problem (mathematics education), textual form as: The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: and so forth for the 64 squares. The total number of grains can be shown to be 264−1 or 18,446,744,073,709,551,615 (eighteen Names of large numbers#Standard dictionary numbers, quintillion, four hundred forty-six quadrillion, seven hundred forty-four trillion, seventy-three billion, seven hundred nine million, five hundred fifty-one thousand, six hundred and fifteen, over 1.4 trillion metric tons), which is over 2,000 times the annual world production of wheat. This exercise can be used to demonstrate how quickly exponential sequences grow, as well as to introduce exponents, zero power, capital-sigma notation and geometric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wheat And Chessboard Problem
The wheat and chessboard problem (sometimes expressed in terms of rice grains) is a mathematical problem expressed in word problem (mathematics education), textual form as: The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: and so forth for the 64 squares. The total number of grains can be shown to be 264−1 or 18,446,744,073,709,551,615 (eighteen Names of large numbers#Standard dictionary numbers, quintillion, four hundred forty-six quadrillion, seven hundred forty-four trillion, seventy-three billion, seven hundred nine million, five hundred fifty-one thousand, six hundred and fifteen, over 1.4 trillion metric tons), which is over 2,000 times the annual world production of wheat. This exercise can be used to demonstrate how quickly exponential sequences grow, as well as to introduce exponents, zero power, capital-sigma notation and geometric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing exponential decay instead. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression. The formula for exponential growth of a variable at the growth rate , as time goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is x_t = x_0(1+r)^t where is the value of at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moore's Law
Moore's law is the observation that the number of transistors in a dense integrated circuit (IC) doubles about every two years. Moore's law is an observation and projection of a historical trend. Rather than a law of physics, it is an empirical relationship linked to gains from experience in production. The observation is named after Gordon Moore, the co-founder of Fairchild Semiconductor and Intel (and former CEO of the latter), who in 1965 posited a doubling every year in the number of components per integrated circuit, and projected this rate of growth would continue for at least another decade. In 1975, looking forward to the next decade, he revised the forecast to doubling every two years, a compound annual growth rate (CAGR) of 41%. While Moore did not use empirical evidence in forecasting that the historical trend would continue, his prediction held since 1975 and has since become known as a "law". Moore's prediction has been used in the semiconductor industry to g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Malthusian Growth Model
A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote ''An Essay on the Principle of Population'' (1798), one of the earliest and most influential books on population."Malthus, An Essay on the Principle of Population: Library of Economics" Malthusian models have the following form: : P(t) = P_0e^ where * ''P''0 = ''P''(0) is the initial population size, * ''r'' = the population growth rate, which Ronald Fisher called the ''Malthusian parameter of population growth'' in The Genetical Theory of Natural Selection, and Alfred J. Lotka called the ''intrinsic rate of increase'', * ''t'' = time. The model can also been written in the form of a differential equation: : \frac = rP with initial condition: P(0)= P0 This model is often referred to as the ''exponential law''. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ambalappuzha Sri Krishna Temple
Ambalappuzha Sree Krishna Swamy Temple is an Indian Hindu temple dedicated to Krishna at Ambalappuzha in Alappuzha district of Kerala. The temple is believed to have been built during 15th century AD by the local ruler Chembakasserry Pooradam Thirunal-Devanarayanan Thampuran. It is one of the seven greatest temples in Travancore. The idol at Ambalappuzha is likened to Parthasarthi form of Vishnu, holding a whip in his right hand and a conch in his left. During the raids of Tipu Sultan in 1789, the idol of Sri Krishna from the Guruvayoor Temple was brought to the Ambalappuzha Temple for safe keeping for three years. ''Payasam'', a sweet pudding made of rice and milk is served in the temple and is believed that the Lord Guruvayoorappan visits the temple daily to accept the offering. Legend According to the legend, the god Krishna once appeared in the form of a sage in the court of the king who ruled the region and challenged him for a game of chess (or '' chaturanga''). The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Limits To Growth
''The Limits to Growth'' (''LTG'') is a 1972 report that discussed the possibility of exponential economic and population growth with finite supply of resources, studied by computer simulation. The study used the World3 computer model to simulate the consequence of interactions between the earth and human systems. The model was based on the work of Jay Forrester of MIT, as described in his book ''World Dynamics''. Commissioned by the Club of Rome, the findings of the study were first presented at international gatherings in Moscow and Rio de Janeiro in the summer of 1971. The report's authors are Donella H. Meadows, Dennis L. Meadows, Jørgen Randers, and William W. Behrens III, representing a team of 17 researchers. The report concludes that, without substantial changes in resource consumption, "the most probable result will be a rather sudden and uncontrollable decline in both population and industrial capacity". Although its methods and premises were heavily challenged on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Billions And Billions
''Billions and Billions: Thoughts on Life and Death at the Brink of the Millennium'' is a 1997 book by the American astronomer and science popularizer Carl Sagan. The last book written by Sagan before his death in 1996, it was published by Random House. Overview The book is a collection of essays Sagan wrote covering diverse topics such as global warming, the population explosion, extraterrestrial life, morality, and the abortion debate. The last chapter is an account of his struggle with myelodysplasia, the disease which finally took his life in December 1996. Sagan's wife, Ann Druyan, wrote the epilogue of the book after his death. "Billions and billions" To help viewers of ''Cosmos'' distinguish between "millions" and "billions", Sagan stressed the "b". Sagan never did, however, say "billions and billions". The public's association of the phrase and Sagan came from a ''Tonight Show'' skit. Parodying Sagan's affect, Johnny Carson quipped "billions and billions". [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
