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Circular Surfaces

Circular Surfaces
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2015-01-08 01:41
CircleSolid GeometryParametric Equation
This example demonstrates the construction of circular surfaces, including cylinders and spheres. It involves the use of parametric equations for these surfaces. The Surface command in GeoGebra is used to create these surfaces. This example is suitable for high school mathematics education, particularly in coordinate geometry and solid geometry.

GeoGebra Commands & Parameters

  1. Surface(((a * v / Vmax) * cos(u)), ((b * v / Vmax) * sin(u)), ((c * (1 + sin(Vmax - π / 2))) * (1 - v / Vmax)) + (2 * c), u, Umin, Umax, v, 0, Vmax) → cone
  2. Surface((a * cos(u)), (b * sin(u)), (c * (1 + sin(v - π / 2))), u, Umin, Umax, v, 0, Vmax) → cylinder
  3. Surface(((a * cos(v - π / 2)) * cos(u)), ((b * cos(v - π / 2)) * sin(u)), (c * sin(v - π / 2)) + (5 * c), u, Umin, Umax, v, 0, Vmax) → ellipsoid
  4. Surface(((a + e + (e * cos((2 * v)))) * cos((d * u))), ((b + e + (e * cos((2 * v)))) * sin((d * u))), (sin((2 * v)) * e) + ((5 * c / ((2 * π))) * u), u, Umin, Umax, v, 0, Vmax) → helix
  5. Surface(((a + e + (e * cos((2 * v)))) * cos(u)), ((b + e + (e * cos((2 * v)))) * sin(u)), (e * sin((2 * v))), u, Umin, Umax, v, 0, Vmax) → ring