Linear Flow on Torus (Modified Parameters)

Linear Flow on Torus (Modified Parameters)
Loading the math board and drawing, please wait…
2016-02-15 23:22
This example demonstrates the linear flow on a torus with modified parameters. It involves key mathematical concepts such as coordinate geometry, parametric equations, vector fields, and geometric transformations. The construction utilizes commands like Surface and CurveCartesian, along with objects a, c, b, α, L, γ, δ, d, texto2 for parameter control and visualization. Suitable for high school and above, it helps learners understand the relationship between spatial geometry and dynamic function graphs, as well as the impact of parameters on the shape of the figure.

GeoGebra Commands & Parameters

  1. Surface(((c + (a * cos(v))) * cos(u)), ((c + (a * cos(v))) * sin(u)), (a * sin(v)), v, 0, 6.283185307179586, u, 0, 6.283185307179586) → b
  2. CurveCartesian(((c + (a * cos((α * t)))) * cos(t)), ((c + (a * cos((α * t)))) * sin(t)), (a * sin((α * t))), t, 0, ((2 * L) * π)) → γ
  3. CurveCartesian(c + (a * cos(t)), 0, (a * sin(t)), t, 0, ((2 * L) * π)) → δ