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| The '''Ragsdale conjecture''' is a [[mathematics|mathematical]] [[conjecture]] that concerns the possible arrangements of real [[algebraic curves]] embedded in the [[projective plane]]. It was proposed by [[Virginia Ragsdale]] several years after 1900 and was disproved in 1979.<ref>{{cite journal| last=Viro | first=Oleg Ya. | authorlink=Oleg Viro | year=1980 | title=Кривые степени 7, кривые степени 8 и гипотеза Рэгсдейл | trans_title=Curves of degree 7, curves of degree 8 and the hypothesis of Ragsdale | journal=[[Doklady Akademii Nauk SSSR]] | volume=254 | issue=6 | pages=1306–1309}} Translated in {{cite journal| journal=Soviet Mathematics - Doklady | volume=22 | pages=566–570 | year=1980}}</ref>
| | Nice to meet you, I am Marvella Shryock. Years ago we moved to North Dakota and I adore every day residing right here. She is a librarian but she's always needed her own business. One of the issues he loves most is ice skating but he is having difficulties to discover time for it.<br><br>My weblog: at home std testing; [http://muzikoman.com/profile-682/info/ published here], |
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| ==Background==
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| Her dissertation dealt with [[Hilbert's sixteenth problem]], which was proposed in the year 1900, along with [[Hilbert's problems|22 other unsolved problems of the 19th century]]. Ragsdale conjectured a particular upper bound on the number of topological circles of a certain type, along with the basis of evidence. The conjecture was held of high importance in the field of real algebraic geometry for nearly a century. Later [[Oleg Viro]] and [[Ilya Itenberg]] produced [[counterexamples]] to the Ragsdale conjecture, although the problem of finding a sharp upper bound remains unsolved.
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| ==Conjecture==
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| Ragsdale's main conjecture is as follows.
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| Assume that an [[algebraic curve]] of degree 2''k'' contains ''p'' even and ''n'' odd ovals. Ragsdale conjectured that
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| :<math> p \le \tfrac32 k(k-1) + 1 \quad\text{and}\quad n \le \tfrac32 k(k-1). </math>
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| She also posed the inequality
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| :<math> | 2(p-n)-1 | \le 3k^2 - 3k + 1, </math> | |
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| and showed that the inequality could not be further improved. This inequality was later proved by [[Ivan Petrovsky|Petrovsky]].
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| ==Notes==
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| <references/>
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| ==References==
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| * {{cite web |url=http://www.agnesscott.edu/LRiddle/women/ragsdale.htm |title=Virginia Ragsdale |accessdate=2007-03-09 |last=De Loera |first=Jesús |coauthors=Frederick J. Wicklin |year=2006 |work=Biographies of Women Mathematicians }}
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| [[Category:Conjectures]]
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| [[Category:Real algebraic geometry]]
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Revision as of 17:32, 23 February 2014
Nice to meet you, I am Marvella Shryock. Years ago we moved to North Dakota and I adore every day residing right here. She is a librarian but she's always needed her own business. One of the issues he loves most is ice skating but he is having difficulties to discover time for it.
My weblog: at home std testing; published here,