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2 + 2 = 5 or two plus two equals five is a mathematical falsehood which is used as an example of a simple logical error that is obvious to anyone familiar with basic arithmetic. The phrase has been used in various contexts since 1728, and is best known from the 1949 dystopian novel Nineteen Eighty-Four by George Orwell .
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In an enthralling new book about this little-known chapter in American theater history, Shakespeare scholar James Shapiro examines the short, tragic life of the Federal Theatre Project.
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Statement of the inequality. Suppose is a natural number and are positive numbers and: Then the Shapiro inequality states that. where and . For greater values of the inequality does not hold, and the strict lower bound is with . The initial proofs of the inequality in the pivotal cases [2] and [3] rely on numerical computations.
In mathematics, the Shapiro polynomials are a sequence of polynomials which were first studied by Harold S. Shapiro in 1951 when considering the magnitude of specific trigonometric sums. In signal processing , the Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. [2]