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Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2.Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5).
The arithmetic mean, or less precisely the average, of a list of n numbers x 1, x 2, . . . , x n is the sum of the numbers divided by n: + + +. The geometric mean is similar, except that it is only defined for a list of nonnegative real numbers, and uses multiplication and a root in place of addition and division:
Fermat's Last Theorem, formulated in 1637, states that no three positive integers a, b, and c can satisfy the equation + = if n is an integer greater than two (n > 2).. Over time, this simple assertion became one of the most famous unproved claims in mathematics.
This is an accepted version of this page This is the latest accepted revision, reviewed on 13 January 2025. Educational assessment For other uses, see Exam (disambiguation) and Examination (disambiguation). Cambodian students taking an exam in order to apply for the Don Bosco Technical School of Sihanoukville in 2008 American students in a computer fundamentals class taking an online test in ...
A little mathematics of the multiplication-table type is enough to show that in the next generation the numbers will be as (p + q) 2:2(p + q)(q + r):(q + r) 2, or as p 1:2q 1:r 1, say. The interesting question is: in what circumstances will this distribution be the same as that in the generation before?
Solution of this equation is far from straightforward. Debye and Hückel expanded the exponential as a truncated Taylor series to first order. The zeroth order term vanishes because the solution is on average electrically neutral (so that Σ n i z i = 0), which leaves us with only the first order term. The result has the form of the Helmholtz ...
[5] [6] By 1803, he had observed changes in the relative positions in a number of double stars over the course of 25 years, and concluded that, instead of showing parallax changes, they seemed to be orbiting each other in binary systems. [7] The first orbit of a binary star was computed in 1827, when Félix Savary computed the orbit of Xi Ursae ...
This is an accepted version of this page This is the latest accepted revision, reviewed on 17 January 2025. Civil services examination in India This article is about the examination in India. For civil service examinations in general, see civil service entrance examination. This article may need to be rewritten to comply with Wikipedia's quality standards. You can help. The talk page may ...