The chord length distribution function of a non-convex hexagon

Bäsel, Uwe; Bonanzinga, Vittoria; Duma, Andrei

doi:10.1515/caim-2018-0002

Abstract

In this paper we obtain the chord length distribution function of a non-convex equilateral hexagon and then derive the associated density function. Finally, we calculate the expected value of the chord length.

References

1. Uwe Bäsel, Andrei Duma: Verteilungsfunktionen der Sehnenlänge eines nichtkonvexen Polygons, Fernuniversität Hagen: Seminarberichte aus der Fakultät für Mathematik und Informatik, 84 (2011), 141-151. https://www.fernuni-hagen.de/imperia/md/content/fakultaetfuermathematikundinformatik/forschung/berichtemathematik/berichteband84.pdf
Search in Google Scholar Back to article
2. Uwe Bäsel: Random chords and point distances in regular polygons, Acta Math. Univ. Comenianae, 83, 1 (2014), 1-18. http://www.emis.de/journals/AMUC/vol-83/no1/baesel/baeselrea.pdf
Search in Google Scholar Back to article
3. Salvino Ciccariello: The isotropic correlation function of plane figures: the triangle case, Journal of Physics: Conference Series 24 (2010) 012014, XIV International Conference on Small-Angle Scattering (SAS09), 1-10. http://iopscience.iop.org/article/10.1088/1742-6596/247/1/012014/pdf10.1088/1742-6596/247/1/012014
Search in Google Scholar Back to article
4. Vincenzo Conserva, Andrei Duma: Schnitte eine regulären Hexagons im Bufion- und Laplace-Gitter, Fernuniversität Hagen: Seminarberichte aus der Fakultät für Mathematik und Informatik, 78 (2007), 29-36.
Search in Google Scholar Back to article
5. Andrei Duma, Sebastiano Rizzo: Chord length distribution functions for an arbitrary triangle, Rend. Circ. Mat. Palermo, Serie II, Suppl. 81 (2009), 141-157. http://math.unipa.it/ficircmat/Suppl%2081%20PDF.pdf
Search in Google Scholar Back to article
6. Andrei Duma, Sebastiano Rizzo: La funzione di distribuzione di una corda in un trapezio rettangolo, Rend. Circ. Mat. Palermo, Serie II, Suppl. 83 (2011), 147-160. http://math.unipa.it/ficircmat/Supplemento83.pdf
Search in Google Scholar Back to article
7. John Gates: Some properties of chord length distributions, J. Appl. Prob., 24 (1987), 863-874. https://www.jstor.org/stable/321421110.1017/S0021900200116742
Search in Google Scholar Back to article
8. Wilfried Gille: Chord length distributions and small-angle scattering, Eur. Phys. J. B, 17 (2000), 371-383. https://link.springer.com/content/pdf/10.1007%2Fs100510070116.pdf10.1007/s100510070116
Search in Google Scholar Back to article
9. Wilfried Gille: Particle and Particle Systems Characterization: Small-Angle Scattering (SAS) Applications, CRC Press, Boca Raton/London/New York, 2014.
Search in Google Scholar Back to article
10. H. S. Harutyunyan: Chord length distribution function for regular hexagon, Uchenie Zapiski, Yerevan State University, 1 (2007), 17-24. http://www.ysu.am/files/2.CHORD%20LENGTH%20DISTRIBUTION%20FUNCTION.pdf
Search in Google Scholar Back to article
11. H. S. Harutyunyan, V. K. Ohanyan: The chord length distribution function for regular polygons, Adv. Appl. Prob. (SGSA), 41 (2009), 358-366. https://www.jstor.org/stable/2779388210.1239/aap/1246886615
Search in Google Scholar Back to article
12. C. L. Mallows, J. M. C. Clark: Linear-intercept distributions do not characterize plane sets, J. Appl. Prob., 7 (1970), 240-244.10.2307/3212164
Search in Google Scholar Back to article
13. Arakaparampil M. Mathai: An Introduction to Geometrical Probability, Gordon and Breach, Australia, 1999.
Search in Google Scholar Back to article
14. Alain Mazzolo, Benoît Roesslinger, Wilfried Gille: Properties of chord length distributions of nonconvex bodies, Journal of Mathematical Physics, 44, 12 (2003), 6195-6208. http://aip.scitation.org/doi/abs/10.1063/1.1622446710.1063/1.16224467
Open DOI Search in Google Scholar Back to article
15. Luis A. Santalfio: Integral Geometry and Geometric Probability, Addison- Wesley, London, 1976.
Search in Google Scholar Back to article
16. Loredana Sorrenti: Chord length distribution functions for an isosceles trapezium, General Mathematics, 20, 1 (2012), 9-24. http://depmath.ulbsibiu.ro/genmath/gm/vol20nr1/02Sorrenti/02Sorrenti.pdf
Search in Google Scholar Back to article
17. Rolf Sulanke: Die Verteilung der Sehnenlängen an ebenen und räumlichen Figuren, Math. Nachr., 23 (1961), 51-74. http://onlinelibrary.wiley.com/doi/10.1002/mana.19610230104/epdf10.1002/mana.19610230104/epdf
Open DOI Search in Google Scholar Back to article

The chord length distribution function of a non-convex hexagon

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