Elastic Rubber Band and Gerono Lemniscate

Elastic Rubber Band and Gerono Lemniscate
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2018-04-22 22:36
This example demonstrates the dynamic formation of Gerono lemniscate curves created by an elastic rubber band at varying positions. It involves core mathematical concepts such as functions, coordinate geometry, geometric transformations, and locus. Construction highlights the use of GeoGebra commands like Spline, Translate, Eina1, and CurveCartesian, along with objects A, B, C, etc. Suitable for high school and above learners to explore the relationship between function graphs and geometric transformations.

GeoGebra Commands & Parameters

  1. Spline(punts, 3) → a
  2. Translate(punts, Vector[(0, 0, 0)]) → punts'
  3. Eina1(C) → N
  4. Eina1(D) → O
  5. Eina1(E) → Q
  6. Eina1(F) → R
  7. Eina1(G) → S
  8. Eina1(H) → T
  9. Eina1(I) → U
  10. Eina1(J) → V
  11. Eina1(K) → W
  12. Eina1(L) → Z
  13. CurveCartesian(f(t), g(t), t, 0, 1) → c