# Chladni patterned surfaces

- Author:
- Roman Chijner

- Topic:
- Functions

Here is the next step from painting of implicit functions
https://www.geogebra.org/material/show/id/pRCY9r5T to Physics.
I offer You the worksheet shows "Chladni" patterned surfaces https://www.geogebra.org/material/show/id/1267579
For me,

*the***standing waves are****most amazing****topics in Physics.***Who has not admired Chladni's sound figures- Amazing Resonance Experiments? https://www.geogebra.org/m/c4NBuJnb**It is a well known equation for the zeros of the standing wave on a square Chladni plate (side length L) is given by the following:**cos(n pi x/L) cos(m pi y/L) - cos(m pi x/L)cos(n pi y/L) = 0, where n and m are integers ( http://paulbourke.net/geometry/chladni/).**I***generalised**this equation for the three-dimensional case:*cos(k*x π/L)[cos(l*y π/L) cos(m*z π/L)+s*cos(m*y π/L) cos(l*z π/L)]+**cos(l*x π/L)[cos(k*y π/L) cos(m*z π/L)+s*cos(m*y π/L) cos(k*z π/L)]+**cos(m*x π/L)[cos(k*y π/L) cos(l*z π/L)+s*cos(l*y π/L )cos(k*z π/L)]=0, where k, l and m are integers, s=∓ 1.**I managed to get not only already known 2D**Chladni patterns*: https://www.geogebra.org/material/show/id/kxXpKDaw,__https://www.geogebra.org/m/RD6tuxru__*,**but also 3D Spacial Chladni patterned surfaces.*By taking advantage of all the Geogebra*possibilities of today*, we can build*not only trace of surfaces-**https://www.geogebra.org/material/show/id/tfsu4uuW,**but also Network of rotatable implicit curves:**https://www.geogebra.org/material/show/id/PzBug5SM**https://www.geogebra.org/material/show/id/JXtDvVjc**Video:https://www.geogebra.org/m/Ayu65AEj*Pictures of spacial Chladni patterns:*https://www.geogebra.org/m/kxXpKDaw**Thanks to the Geogebra developers!*Regards, Roman Chijner