Chladni Figures Revisited: A Peek Into The Third Dimension
Inhaltsverzeichnis
Reference
Martin Skrodzki, Ulrich Reitebuch and Konrad Polthier: Chladni Figures Revisited: A Peek Into The Third Dimension. In: Bridges 2016, Pages 481–484.
DOI
Abstract
In his 1802 book ”Acoustics”, Ernst Florens Friedrich Chladni describes how to visualize different vibration modes using sand, a metal plate, and a violin bow. We will review the underlying physical and mathematical formulations and lift them to the third dimension. Finally, we present some of the resulting three dimensional Chladni figures.
Extended Abstract
Bibtex
@inproceedings{bridges2016:481,
author = {Martin Skrodzki, Ulrich Reitebuch and Konrad Polthier},
title = {Chladni Figures Revisited: A Peek Into The Third Dimension},
pages = {481--484},
booktitle = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},
year = {2016},
editor = {Eve Torrence, Bruce Torrence, Carlo S\'equin, Douglas McKenna, Krist\'of Fenyvesi and Reza Sarhangi},
isbn = {978-1-938664-19-9},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
url = {http://de.evo-art.org/index.php?title=Chladni_Figures_Revisited:_A_Peek_Into_The_Third_Dimension },
note = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-481.html}}
}
Used References
[1] Jaime Arango and Carlos Reyes. Stochastic models for chladni figures. Proceedings of the Edinburgh Mathematical Society, pages 1–14, 2015.
[2] Frank Findeiß. Die Entdeckung der Chladnischen Klangfiguren. Urspr¨unge undWeiterentwicklung im historischen Kontext. Leuphana Universit¨at L¨uneburg, Germany, 2015.
[3] Martin J. Gander and Felix Kwok. Chladni figures and the tacoma bridge: motivating pde eigenvalue problems via vibrating plates. SIAM Review, 54(3):573–596, 2012.
[4] Bruno L´evy and Hao Richard Zhang. Spectral mesh processing. In ACM SIGGRAPH 2010 Courses, page 8. ACM, 2010.
[5] Persistence of Vision Pty. Ltd. Raytracer (version 3.7). http://http://www.povray.org/. Accessed: 2016- 04-19.
[6] Herbert John Pain. The physics of vibrations and waves. John Wiley, 2005.
[7] Oscar Sol. 3d chladni patterns. https://www.flickr.com/photos/oscarsol/sets/72157641551929843. Accessed: 2016-03-15.
[8] William Henry Stone. Elementary Lessons on Sound. Macmillan & Company, 1879.
Links
Full Text
http://archive.bridgesmathart.org/2016/bridges2016-481.pdf
