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Semi-log plot of solutions of + + = for integer , , and , and .Green bands denote values of proven not to have a solution.. In the mathematics of sums of powers, it is an open problem to characterize the numbers that can be expressed as a sum of three cubes of integers, allowing both positive and negative cubes in the sum.
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [ 1 ] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences . [ 2 ]
The product and quotient of two positive numbers c and d were routinely calculated as the sum and difference of their logarithms. The product cd or quotient c/d came from looking up the antilogarithm of the sum or difference, via the same table:
In mathematics, the moving sofa problem or sofa problem is a two-dimensional idealization of real-life furniture-moving problems and asks for the rigid two-dimensional shape of the largest area that can be maneuvered through an L-shaped planar region with legs of unit width. [1] The area thus obtained is referred to as the sofa constant.
The Latin cogito, ergo sum, usually translated into English as "I think, therefore I am", [a] is the "first principle" of René Descartes's philosophy. He originally published it in French as je pense, donc je suis in his 1637 Discourse on the Method, so as to reach a wider audience than Latin would have allowed. [1]
In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete :
Smale's problems are a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975.