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Geometric Interpretation of LCM and GCD in 3D

Geometric Interpretation of LCM and GCD in 3D
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2017-11-20 02:12
SequenceCoordinate GeometrySolid Geometry
This example demonstrates the geometric interpretation of least common multiple (LCM) and greatest common divisor (GCD) using 3D geometry. It involves fundamental concepts from number theory. Construction highlights include using the Polygon command to build geometric shapes and applying GCD and LCM commands for numerical calculations. Suitable for middle school and above students learning number theory and geometry.

GeoGebra Commands & Parameters

  1. Polygon(G, E, F, H) → q1, g, e, f, h
  2. Polygon(G, B, C, H) → q2, g_1, b_1, c_1, h_1
  3. Polygon(D, F, H, C) → q4, d_1, f_1, h_2, c_3
  4. Polygon(F, E, A, D) → q5, f_2, e_1, a_2, d_2
  5. Polygon(E, G, B, A) → q6, e_2, g_2, b_3, a_3
  6. GCD({a, b, c}) → i
  7. Polygon(J, L, C, B) → q7, j, l, c_4, b_4
  8. Polygon(L, K, D, C) → q8, l_1, k, d_3, c_5
  9. Polygon(K, I, A, D) → q9, k_1, i_1, a_4, d_4
  10. Polygon(I, A, B, J) → q10, i_2, a_5, b_5, j_1
  11. Polygon(B, A, D, C) → q11, b_6, a_6, d_5, c_6
  12. Polygon(J, L, K, I) → q12, j_2, l_2, k_2, i_3
  13. LCM({a, b}) → m
  14. LCM({m, c}) → n
  15. Sequence(n / i, n, 1, i - 1) → L_1