[color=#0000ff] Here is the next step from painting of implicit functions[br][/color][url=https://www.geogebra.org/material/show/id/pRCY9r5T]https://www.geogebra.org/material/show/id/pRCY9r5T[/url][color=#0000ff] to Physics.[/color][br][br][color=#0000ff]I offer You the worksheet shows "Chladni" patterned surfaces [/color][url=https://www.geogebra.org/material/show/id/1267579]https://www.geogebra.org/material/show/id/1267579[/url][br][color=#0000ff]For me, [/color][i][b]standing waves are [/b][/i][color=#0000ff]the [/color][i][b]most amazing[/b][/i][i][b] topics in Physics. [/b][/i][i][color=#0000ff]Who has not admired Chladni's sound figures- Amazing Resonance Experiments?[br][/color][url=https://www.geogebra.org/m/c4NBuJnb]https://www.geogebra.org/m/c4NBuJnb[/url][/i][br][color=#ff3333][i][br]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: [/i][/color][br][i][color=#ff3333] 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 ( [/color][url=http://paulbourke.net/geometry/chladni/]http://paulbourke.net/geometry/chladni/[/url][color=#ff3333]).[br] [/color][/i][color=#ff3333][i]I [b]generalised[/b] this equation for the three-dimensional case:[/i][/color][br][color=#ff3333][i] 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)]+[/i][/color][br][color=#ff3333][i] 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)]+[/i][/color][br][i][color=#ff3333] 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.[br][/color][/i][i][color=#0000ff]I managed to get not only already known 2D[/color][i] [color=#0000ff]Chladni patterns[/color][/i][color=#0000ff]: [/color][url=https://www.geogebra.org/material/show/id/kxXpKDaw][color=#0000ff]h[/color]ttps://www.geogebra.org/material/show/id/kxXpKDaw[/url][color=#0000ff], [br][/color][i][u][url=https://www.geogebra.org/m/RD6tuxru]https://www.geogebra.org/m/RD6tuxru[/url][/u][/i][/i][i][color=#000000],[br][/color][/i][i][color=#0000ff]but also 3D Spacial Chladni patterned surfaces.[/color] [/i][color=#0000ff]By taking advantage of all the Geogebra [i]possibilities of today[/i], we can build [/color][i][color=#0000ff]not only trace of surfaces-[/color][br][/i][i][url=https://www.geogebra.org/material/show/id/tfsu4uuW]https://www.geogebra.org/material/show/id/tfsu4uuW[/url][color=#6600cc],[br][/color][/i][i][color=#0000ff]but also Network of rotatable implicit curves:[/color][/i][br][i][url=https://www.geogebra.org/material/show/id/PzBug5SM]https://www.geogebra.org/material/show/id/PzBug5SM[/url][/i][i][url=https://www.geogebra.org/material/show/id/JXtDvVjc]https://www.geogebra.org/material/show/id/JXtDvVjc[/url][/i][br][i][color=#0000ff]Video:[/color][url=https://www.geogebra.org/m/Ayu65AEj]https://www.geogebra.org/m/Ayu65AEj[/url][/i][br][color=#0000ff]Pictures of spacial Chladni patterns:[/color][br][i][color=#000000][url=https://www.geogebra.org/m/kxXpKDaw]https://www.geogebra.org/m/kxXpKDaw[/url][/color][/i][br][i][color=#0000ff]Thanks to the Geogebra developers![br][/color][/i][color=#0000ff]Regards,[br]Roman Chijner[br][/color][br][br][br][br][br]