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Balance Game

Balance Game
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2018-02-08 15:18
VectorCoordinate GeometryProbability & StatisticsOptimizationGeometric Construction
This example dynamically demonstrates the principle of leverage and torque equilibrium in a balance scale, visually illustrating core concepts like vector operations, geometric constructions, coordinate geometry, and probability statistics (e.g., expected value). It utilizes GeoGebra commands such as Join, RandomElement, Random, Point, Polygon, Segment, If, and Textfield to calculate and display dynamic balance points. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Join({Sequence[Point[{i, 8}], i, -22, -10], Sequence[Point[{i, 8}], i, 6, 18]}) → startingPoint
  2. RandomElement(startingPoint) → K_1anchor
  3. Random(1, 40) → weight
  4. Point({(-14 * cos((-tipper))), (14 * sin((-tipper))) + 20}) → leftPoint
  5. Polygon(C_1 + (-2, 2), C_1 + (-2, -2), C_1 + (16, -2), C_1 + (16, 2)) → leftZone, t_1, a_1, b_1, c_1
  6. Polygon(A, B, 4) → poly1, f, g, h, i, K, L
  7. Polygon(C, D, 4) → poly2, j, k, l, m, M, N
  8. Polygon(E, F, 4) → poly3, n, p, q, r, O, P
  9. Polygon(G, H, 4) → poly4, s, t, a, b, Q, R
  10. Polygon(I, J, 4) → poly5, c, d, e, f_1, S, T
  11. Point(xAxis) → U
  12. Point(xAxis) → V
  13. Point(yAxis) → W
  14. Polygon(U, V, W) → poly6, w, u, v
  15. Segment(W, Z) → g_1
  16. Point(g_1) → A_1
  17. Point({(14 * cos(tipper)), (14 * sin(tipper)) + 20}) → rightPoint
  18. Segment(leftPoint, rightPoint) → h_1
  19. Segment(C_1, D_1) → i_1
  20. Segment(F_1, E_1) → j_1
  21. Segment(leftPoint, D_1) → k_1
  22. Segment(C_1, leftPoint) → l_1
  23. Segment(E_1, rightPoint) → n_1
  24. Segment(rightPoint, F_1) → m_1
  25. Polygon(F_1 + (-2, 2), F_1 + (-2, -2), F_1 + (16, -2), F_1 + (16, 2)) → rightZone, p_1, q_1, r_1, s_1
  26. If(abs(tipper) ≟ π / 6, true, false) → tipped
  27. Textfield(answerText) → InputBox1
  28. RandomElement({-1, 1}) → starter
  29. If(Max[rightTotal, leftTotal] ≟ Min[rightTotal, leftTotal], 0, (1 / 3 * (Max[rightTotal, leftTotal] - Min[rightTotal, leftTotal])) + 4 / 3) → speed

AI Drawing Prompt Reference

Draw a dynamic balance scale demonstrating the principle of leverage and torque equilibrium. Include two fulcrums with randomly generated weights placed on either side, connected by lines. Visualize vector operations and geometric constructions to calculate and display the balance point, incorporating probability statistics and dynamic text annotations.
The prompt above was compiled from the original drawing commands and is for reference only.