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Balance (The Farmer's Stone)

Balance (The Farmer's Stone)
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2017-03-14 00:11
Coordinate GeometryProbability & StatisticsGeometric Construction
This example demonstrates a dynamic balance geometric model, showing the lever principle by adjusting weights and positions; core math concepts include equations, probability & statistics, area calculation, stochastic processes; constructed using GeoGebra commands like Join, RandomElement, Point, Polygon, Segment, If, Textfield, involving objects such as tipper, startingPoint, K_1anchor, weight; suitable for high school and above students to understand the integration of mechanics, probability, and geometric construction.

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 geometric model demonstrating the lever principle, showing equilibrium by adjusting weights and positions. Include a tiltable lever with different weights at each end, calculated and probabilistic elements determining balance. Show the lever's starting point, pivot, weight positions, and areas formed by the lever and weights, with colors indicating weight differences, and label key points and areas.
The prompt above was compiled from the original drawing commands and is for reference only.