3D Implicit Surface Grapher: cos(x)+cos(y)+cos(z)=0 by Roman Chijner
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This example demonstrates the complex 3D surface formed by the implicit equation cos(x)+cos(y)+cos(z)=0. Key math concepts include implicit surfaces, 3D coordinate geometry, and trigonometric function properties. Construction highlights from the summary involve commands/objects like Textfield, g, Nn, y_max, z_max, y_min, dy2, z_min, dz2, ggb, gga, Funktion, x_max, x_min, dx2, button2, u0, Autor, multiple Textfelds, Text3, Text2, Text4, Farbe, text1, button3, and Textfeld13 for parameter control and formula display. Suitable for high school students and math enthusiasts to understand implicit surface plotting and 3D function visualization, serving as a teaching aid for calculus and analytical geometry.
GeoGebra Commands & Parameters
Textfield(x_{min}) → Textfeld1Textfield(y_{min}) → Textfeld2Textfield(z_{min}) → Textfeld3Textfield(x_{max}) → Textfeld4Textfield(y_{max}) → Textfeld5Textfield(z_{max}) → Textfeld6Textfield(Nn) → Textfeld10Textfield(g) → Textfeld13Textfield(b) → inputBox1
AI Drawing Prompt Reference
Create a 3D implicit surface defined by the equation cos(x) + cos(y) + cos(z) = 0. The surface should appear as a complex periodic wave-like structure, resembling a lattice or foam, within a three-dimensional coordinate system. Include six input fields to set the minimum and maximum values for the x, y, and z axes, controlling the displayed range. Add two more input fields for adjusting grid density and precision, and one field for color or transparency settings. Render the surface smoothly, allowing parameter changes to reveal different structural regions. This serves as an educational visualization highlighting trigonometric periodicity and implicit surface geometry.
The prompt above was compiled from the original drawing commands and is for reference only.