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Function Calculus Magic Machine

Function Calculus Magic Machine
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2020-03-13 05:13
FunctionCalculusDerivativeIntegralLimit
This example demonstrates the dynamic process of function calculus, involving concepts such as derivatives, integrals, and limits. Using GeoGebra commands like CurveCartesian, Circle, and Polygon, it provides an intuitive view of function changes. Suitable for high school and above students learning calculus.

GeoGebra Commands & Parameters

  1. CurveCartesian(x(A) + ((r * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * cos(t + v)), y(A) + ((r * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * sin(t + v)), t, 0, 6.28319) → c
  2. CurveCartesian(x(B) + ((R * (a + (1 / b * tanh((b * sin((n * t) - v)))))) * cos(t - v)), y(B) + ((R * (a + (1 / b * tanh((b * sin((n * t) - v)))))) * sin(t - v)), t, 0, 6.28319) → d
  3. Circle(B, R + 0.9) → e
  4. Circle(A, r + 0.9) → g
  5. Circle(A, r + 0.9) → h
  6. CurveCartesian(x(A) + ((r * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * cos(t + v)), y(A) + ((r * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * sin(t + v)), t, 0, 6.28319) → i
  7. CurveCartesian(x(C) + ((R * (a + (1 / b * tanh((b * sin((n * t) - v)))))) * cos(t - v)), y(C) + ((R * (a + (1 / b * tanh((b * sin((n * t) - v)))))) * sin(t - v)), t, 0, 6.28319) → j
  8. CurveCartesian(x(C) + ((r / 2 * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * cos(t + v)), y(C) + ((r / 2 * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * sin(t + v)), t, 0, 6.28319) → o
  9. Polygon(D, E, F, G) → poly1, d_1, e_1, f_1, g_1
  10. Point(g_1) → H
  11. Point(g_1) → I
  12. Polygon(H, I, J, K) → poly2, h_1, i_1, j_1, k
  13. Polygon(L, K, J, M) → poly3, l, k_1, j_2, m
  14. Point(f_1) → N
  15. Polygon(N, O, P, F) → poly4, n_1, o_1, p, f_2
  16. Textfield(s) → ChampTexte1
  17. Vector(Q, S) → u
  18. Textfield(f) → ChampTexte2
  19. Vector(U, V) → w
  20. Vector(W, Z) → z
  21. Polygon(C_1, M, L, D_1) → poly5, c_1, m_1, l_1, d_2
  22. Polygon(E_1, F_1, G_1, H_1) → poly6, e_2, f_3, g_2, h_2
  23. Semicircle(F_1, G_1) → q
  24. Mod(v / °, 2) → t_1
  25. Semicircle(F_1, G_1) → p_1
  26. Segment(A_1, B_1) → a_1
  27. Coefficients(f) → liste1
  28. Polynomial(f) → ff
  29. Coefficients(ff) → mm
  30. Element(liste1, 1) → aa
  31. Element(liste1, 2) → bb
  32. Element(liste1, 3) → cc

AI Drawing Prompt Reference

Create a visual representation of function calculus dynamics. Start with two base points as centers, draw two closed curves defined by parametric equations with hyperbolic tangent modulation, creating wavy edges. Add a large auxiliary circle around one center and two concentric circles around the other. From a third point, draw a similar curve with half radius. Connect several key points with polygons to form quadrilateral regions, and add semicircles on some edges. Include two text input fields and several vector arrows to indicate relationships between functions, derivatives, and integrals. The overall layout shows an intuitive visualization of function transformations.
The prompt above was compiled from the original drawing commands and is for reference only.