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Guess 2/3 of the average. In game theory, " guess 2 3 of the average " is a game that explores how a player’s strategic reasoning process takes into account the mental process of others in the game. [ 1] In this game, players simultaneously select a real number between 0 and 100, inclusive. The winner of the game is the player (s) who ...
1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. The geometric series on the real line. In mathematics, the infinite series 1 2 + 1 4 + 1 8 + 1 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation ...
Knuth's up-arrow notation. In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. [ 1] In his 1947 paper, [ 2] R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation ...
In particular concerning the large bottom trapezoid, Ahmes seems to get stuck on finding the upper base, and proposes in the original work to subtract "one tenth, equal to 1 + 1/4 + 1/8 setat plus 10 cubit strips" from a rectangle being (presumably) 4 1/2 x 3 1/2 (khet). However, even Ahmes' answer here is inconsistent with the problem's other ...
The Rhind Mathematical Papyrus, [1] [2] an ancient Egyptian mathematical work, includes a mathematical table for converting rational numbers of the form 2/ n into Egyptian fractions (sums of distinct unit fractions ), the form the Egyptians used to write fractional numbers. The text describes the representation of 50 rational numbers.
Unit fractions can also be expressed using negative exponents, as in 2 −1, which represents 1/2, and 2 −2, which represents 1/(2 2) or 1/4. A dyadic fraction is a common fraction in which the denominator is a power of two, e.g. 1 / 8 = 1 / 2 3 . In Unicode, precomposed fraction characters are in the Number Forms block.
Simpson's 1/3 rule. Simpson's 1/3 rule, also simply called Simpson's rule, is a method for numerical integration proposed by Thomas Simpson. It is based upon a quadratic interpolation and is the composite Simpson's 1/3 rule evaluated for . Simpson's 1/3 rule is as follows: where is the step size for .
Borwein and Zucker [2] have found that () can be expressed algebraically in terms of π, K(k(1)), K(k(2)), K(k(3)), and K(k(6)) where K(k(N)) is a complete elliptic integral of the first kind. This permits efficiently approximating the gamma function of rational arguments to high precision using quadratically convergent arithmetic–geometric ...