Search results
Results from the WOW.Com Content Network
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]
[2] Of the cleanly formulated Hilbert problems, numbers 3, 7, 10, 14, 17, 18, 19, 21, and 20 have resolutions that are accepted by consensus of the mathematical community. Problems 1, 2, 5, 6, [ a ] 9, 11, 12, 15, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems.
[2] The seven problems were officially announced by John Tate and Michael Atiyah during a ceremony held on May 24, 2000 (at the amphithéâtre Marguerite de Navarre) in the Collège de France in Paris. [3] Grigori Perelman, who had begun work on the Poincaré conjecture in the 1990s, released his proof in 2002 and 2003. His refusal of the Clay ...
Its run-time complexity, when using Fibonacci heaps, is (+ ), [2] where m is a number of edges. This is currently the fastest run-time of a strongly polynomial algorithm for this problem. If all weights are integers, then the run-time can be improved to O ( m n + n 2 log log n ) {\displaystyle O(mn+n^{2}\log \log n)} , but the ...
Erdős, Paul; Rényi, Alfréd (1961), "On a classical problem of probability theory" (PDF), Magyar Tudományos Akadémia Matematikai Kutató Intézetének Közleményei, 6: 215– 220, MR 0150807. Laplace, Pierre-Simon (1812), Théorie analytique des probabilités , pp. 194– 195 .
[2] What is now called the Kepler problem was first discussed by Isaac Newton as a major part of his Principia. His "Theorema I" begins with the first two of his three axioms or laws of motion and results in Kepler's second law of planetary motion. Next Newton proves his "Theorema II" which shows that if Kepler's second law results, then the ...
Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, [1] to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equal area.
The art gallery problem or museum problem is a well-studied visibility problem in computational geometry.It originates from the following real-world problem: "In an art gallery, what is the minimum number of guards who together can observe the whole gallery?"