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Center of Gravity

Center of Gravity
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2023-03-20 02:46
TrianglePolygonCalculusGeometric Construction
In collections geometriadinamica.es
This GeoGebra example demonstrates the concept of center of gravity. The center of gravity is the point where the weight of an object is concentrated, and it is often used to describe the balance point of an object. This example uses triangles and polygons to illustrate the concept of center of gravity, involving core mathematical concepts such as geometry and balance points. The construction points include using Polygon, Midpoint, Segment, Intersect, and Line GeoGebra commands. Suitable for middle school and high school mathematics education, particularly for explaining geometry and balance point concepts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Polygon(A, C, B) → poly2, b_1, a_1, c_1
  3. Polygon(A, D, C) → poly3, c_2, a_2, d_1
  4. Midpoint(a) → E
  5. Midpoint(b) → F
  6. Segment(A, F) → e
  7. Segment(C, E) → f
  8. Intersect(e, f) → G_1
  9. Midpoint(d) → G
  10. Midpoint(c) → H
  11. Segment(A, H) → g
  12. Segment(C, G) → h
  13. Intersect(g, h) → G_2
  14. Segment(G_1, G_2) → i
  15. Polygon(E, G, H, F) → poly4, e_1, g_1, h_1, f_1
  16. Segment(E, H) → j
  17. Segment(G, F) → k
  18. Intersect(j, k) → I
  19. Segment(B, D) → l
  20. Segment(B, G) → m
  21. Segment(D, E) → n
  22. Segment(D, F) → p
  23. Segment(B, H) → q
  24. Intersect(n, m) → K
  25. Intersect(p, q) → L
  26. Segment(K, L) → r
  27. Intersect(i, r) → J
  28. Segment(A, C) → s
  29. Midpoint(N, D) → Q
  30. Midpoint(D, P) → R
  31. Midpoint(O, B) → S
  32. Midpoint(B, M) → T
  33. Line(M, N) → t
  34. Line(Q, R) → i_1
  35. Line(P, O) → j_1
  36. Line(S, T) → k_1
  37. Intersect(t, k_1) → U
  38. Intersect(t, i_1) → V
  39. Intersect(i_1, j_1) → W
  40. Intersect(j_1, k_1) → Z
  41. Polygon(U, V, W, Z) → poly5, u, v, w, z
  42. Segment(U, W) → l_1
  43. Segment(V, Z) → m_1

AI Drawing Prompt Reference

Draw a figure composed of multiple triangles and quadrilaterals to demonstrate the concept of center of gravity. Start by constructing several triangles, then find the midpoints of their sides and connect them to locate the center of gravity. Next, connect the diagonals to find another center of gravity. Finally, connect these two centers to the midpoints of the sides to form new quadrilaterals, illustrating the balance properties through geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.