Dini Surface (Superficie de Dini) Dynamic Construction

Dini Surface (Superficie de Dini) Dynamic Construction
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2018-01-29 06:28
① This example demonstrates how to construct the classic Dini surface using GeoGebra's Surface command, a spiral-like minimal surface with constant negative Gaussian curvature, resembling a twisted horn or helical cone. ② Core mathematical concepts include parametric surfaces, constant negative curvature in differential geometry, the deformation of helicoids and pseudospheres, and parametric equations in 3D space. ③ Construction highlights: from the summary, it uses Polygon and Surface commands, involving objects such as rotation axes (ejessi, ejesno), buttons (botón3, botón1), parameters a, b, n, g, color controls (red, green, blue, op), and text (texto1), with sliders or buttons to dynamically adjust parameters and alter the surface shape and display. ④ Suitable for university-level differential geometry courses, advanced calculus teaching on parametric surfaces, or as a GeoGebra 3D modeling example for learners to understand parametric surfaces and curvature concepts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → c1, a_1, b_1, c_1, d_1
  2. Surface(((a * cos(u)) * sin(v)), ((a * sin(u)) * sin(v)), (a * (cos(v) + log(tan((0.5 * v))))) + (b * u), u, 0, (n * π / 2), v, 0, π / 2) → Dini