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Explore the Interior Structure of a Parabola

Explore the Interior Structure of a Parabola
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2018-12-26 18:07
FunctionCoordinate GeometryTransformation
This example uses a window to explore the internal structure of a parabola. It involves the geometric properties of parabolas and function graphs. Using GeoGebra commands such as Surface, CurveCartesian, Sequence, Vector, and Translate, it dynamically demonstrates the tangents, vectors, and translations of the parabola. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Surface(((r / n * ((n * cos(u)) + cos((n * u)))) * sin(v)), ((r / n * ((n * sin(u)) + sin((n * u)))) * sin(v)), (r * cos(v)), u, 0, (2 * π), v, 0, c2) → b
  2. Surface(((r / n * ((n * cos(u)) + cos((n * u)))) * sin(v)), ((r / n * ((n * sin(u)) + sin((n * u)))) * sin(v)), (r * cos(v)), u, 0, (2 * π), v, c2 + k2, π) → c
  3. Surface(((r / n * ((n * cos(u)) + cos((n * u)))) * sin(v)), ((r / n * ((n * sin(u)) + sin((n * u)))) * sin(v)), (r * cos(v)), u, 0, (2 * π), v, 0, π) → e
  4. CurveCartesian(e(t, c2), t, c1, c1 + k1) → f
  5. CurveCartesian(e(t, c2 + k2), t, c1, c1 + k1) → g
  6. CurveCartesian(e(c1, t), t, c2, c2 + k2) → h
  7. CurveCartesian(e(c1 + k1, t), t, c2, c2 + k2) → i
  8. Surface((k * h(t)), t, c2, c2 + k2, k, 0, 1) → j
  9. Surface((k * f(t)), t, c1, c1 + k1, k, 0, 1) → k
  10. Surface((k * i(t)), t, c2, c2 + k2, k, 0, 1) → l
  11. Surface((k * g(t)), t, c1, c1 + k1, k, 0, 1) → m
  12. Surface(e((k * c1) + ((1 - k) * (c1 + k1)), t), t, c2, c2 + k2, k, 0, 1) → p
  13. Sequence(CurveCartesian[e(k, t), t, c2 + k2, π], k, c1, c1 + k1, k2 / 8) → l5
  14. Sequence(CurveCartesian[e(k, t), t, 0, c2], k, c1, c1 + k1, k2 / 8) → l6
  15. Sequence(CurveCartesian[e(t, k), t, 0, (2 * π)], k, 0, c2, k1 / 15) → l2
  16. Sequence(CurveCartesian[e(t, k), t, 0, (2 * π)], k, c2 + k2, π, k1 / 15) → l3
  17. Sequence(CurveCartesian[e(t, k), t, c1, c1 + k1], k, c2, c2 + k2, k2 / 8) → l7
  18. Sequence(CurveCartesian[e(k, t), t, c2, c2 + k2], k, c1, c1 + k1, k2 / 8) → l8
  19. Vector((0, 0), (10 * CG)) → u
  20. Translate(ls, Vector[(tr * u)]) → ls'
  21. Translate(ll, Vector[(tr * u)]) → ll'
  22. Translate(lc, Vector[(tr * u)]) → lc'
  23. Sequence(CurveCartesian[e(t, k), t, c1 + k1 - (2 * π), c1], k, c2, c2 + k2, k2 / 8) → l4
  24. Surface(((r / n * ((n * cos(u)) + cos((n * u)))) * sin(v)), ((r / n * ((n * sin(u)) + sin((n * u)))) * sin(v)), (r * cos(v)), u, c1 + k1 - (2 * π), c1, v, c2, c2 + k2) → a
  25. Sequence(CurveCartesian[e(k, t), t, 0, π], k, c1 + k1 - (2 * π), c1, k2 / 8) → l1

AI Drawing Prompt Reference

Draw the internal structure of a parabola, including its tangents, vectors, and transformations. First, draw the surface of the parabola, then dynamically show the tangents and vectors using transformation and sequence commands, and finally demonstrate the translation of the parabola through translation and rotation.
The prompt above was compiled from the original drawing commands and is for reference only.