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, standing waves are the 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/PzBug5SMhttps://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