Bondi accretion: Difference between revisions

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[[File:Jordans inequality.svg|thumb|upright=1.2|[[unit circle]] with angle x and a second circle with radius <math>|EG|=\sin(x)</math> around E. <math>\begin{align}&|DE|\leq|\widehat{DC}|\leq|\widehat{DG}|\\ \Leftrightarrow &\sin(x) \leq x \leq\tfrac{\pi}{2}\sin(x)\\ \Rightarrow &\tfrac{2}{\pi}x \leq \sin(x)\leq x  \end{align}</math>]]


In mathematics, '''Jordan's inequality''', named after [[Camille Jordan]], states that


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: <math>\frac{2}{\pi}x\leq \sin{x} \leq x\text{ for }x \in \left[0,\frac{\pi}{2}\right].</math>
 
It can be proven through the [[geometry]] of [[circles]] (see drawing).<ref>http://planetmath.org/encyclopedia/ProofOfJordansInequality.html</ref>
 
==Notes==
<references/>
 
==Further reading==
*Serge Colombo: ''Holomorphic Functions of One Variable''. Taylor & Francis 1983, ISBN 0677059507, p.&nbsp;167-168 ([http://books.google.de/books?id=pFEOAAAAQAAJ&pg=PA167 online copy])
*Da-Wei Niu, Jian Cao, Feng Qi: [http://www.scientificbulletin.upb.ro/rev_docs_arhiva/full3105.pdf ''Generealizations of Jordan's Inequality and Concerned Relations'']. U.P.B. Sci. Bull., Series A, Volume 72, Issue 3, 2010, ISSN 1223-7027
*Peng Qi: [http://www.ajmaa.org/RGMIA/papers/v9n3/refine-jordan-kober.pdf ''Jordan's Inequality: Refinements, Generealizations, Applications and related Problems'']. RGMIA Res Rep Coll (2006), Volume: 9, Issue: 3, Pages: 243–259
*Meng-Kuang Kuo: [http://www.journalofinequalitiesandapplications.com/content/2011/1/130 ''Refinements of Jordan's inequality'']. Journal of Inequalities and Applications 2011, 2011:130, doi:10.1186/1029-242X-2011-130
 
==External links==
*[http://planetmath.org/encyclopedia/JordansInequality.html Jordan's inequality] at [[PlanetMath]]
*{{MathWorld|title=Jordan's inequality|urlname=JordansInequality}}
 
[[Category:Inequalities]]
 
 
{{Mathanalysis-stub}}

Revision as of 16:19, 28 November 2013

unit circle with angle x and a second circle with radius around E.

In mathematics, Jordan's inequality, named after Camille Jordan, states that

It can be proven through the geometry of circles (see drawing).[1]

Notes

  1. ↑ http://planetmath.org/encyclopedia/ProofOfJordansInequality.html

Further reading

External links

  • Jordan's inequality at PlanetMath


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