Boy Surface Coloring
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This example demonstrates the coloring of the Boy surface, a significant example in topology. Using the Surface command in GeoGebra, we can construct the Boy surface and enhance its visual effect through color changes. The construction involves the use of the Surface command and parameters u and v. This example is suitable for teaching topology and calculus in university-level mathematics courses.
GeoGebra Commands & Parameters
Surface(((2 / 3 * ((cos(u) * cos((2 * v))) + ((sqrt(2) * sin(u)) * cos(v)))) * cos(u) / (sqrt(2) - (sin((2 * u)) * sin((3 * v))))), ((2 / 3 * ((cos(u) * sin((2 * v))) - ((sqrt(2) * sin(u)) * sin(v)))) * cos(u) / (sqrt(2) - (sin((2 * u)) * sin((3 * v))))), ((sqrt(2) * cos(u)) * cos(u) / (sqrt(2) - (sin((2 * u)) * sin((3 * v))))), u, 0, 3.141592653589793, v, 0, 3.141592653589793) → aSurface(((2 / 3 * ((cos(u) * cos((2 * v))) + ((sqrt(2) * sin(u)) * cos(v)))) * cos(u) / (sqrt(2) - (sin((2 * u)) * sin((3 * v))))), ((2 / 3 * ((cos(u) * sin((2 * v))) - ((sqrt(2) * sin(u)) * sin(v)))) * cos(u) / (sqrt(2) - (sin((2 * u)) * sin((3 * v))))), ((sqrt(2) * cos(u)) * cos(u) / (sqrt(2) - (sin((2 * u)) * sin((3 * v))))), u, 0, π - du, v, 0, 3.141592653589793) → bSurface(((2 / 3 * ((cos(u) * cos((2 * v))) + ((sqrt(2) * sin(u)) * cos(v)))) * cos(u) / (sqrt(2) - (sin((2 * u)) * sin((3 * v))))), ((2 / 3 * ((cos(u) * sin((2 * v))) - ((sqrt(2) * sin(u)) * sin(v)))) * cos(u) / (sqrt(2) - (sin((2 * u)) * sin((3 * v))))), ((sqrt(2) * cos(u)) * cos(u) / (sqrt(2) - (sin((2 * u)) * sin((3 * v))))), u, 0, 3.141592653589793, v, 0, π - dv) → c