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Division Algorithm Demonstration by 昌SIR

Division Algorithm Demonstration by 昌SIR
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2015-01-12 15:14
Coordinate GeometryGeometric Construction
This example visually demonstrates the geometric meaning of the division algorithm by dynamically partitioning a line segment into an integer and fractional part. Key mathematical concepts include the division algorithm principle, line segment division, and integer/fractional representation. GeoGebra commands and objects used in construction are Segment, Polygon, Text, Midpoint, and Sequence. Suitable for high school mathematics education to help students understand the geometric application and computational process of the division algorithm.

GeoGebra Commands & Parameters

  1. Segment(A, B) → c
  2. Polygon(A, A + (0, 6), B + (0, 6), B) → poly1, d, e, f, n
  3. Polygon(F + (r, 12), F + (r, 18), F + (0, 18), F + (0, 12)) → poly2, g, h, i, p
  4. Polygon(D + (b, 0), D + (b, 6), D + (0, 6), D) → poly3, j, k, l, m
  5. Text(("a=" * a)) → text3
  6. Text(("b=" * b)) → text4
  7. Text(("q=" * q)) → text5
  8. Text(("r=" * r)) → text6
  9. Midpoint(Midpoint[Corner[4], Midpoint[Corner[4], Midpoint[Corner[4], Corner[1]]]], Midpoint[Corner[4], Midpoint[Corner[4], Corner[1]]]) → O
  10. Midpoint(Midpoint[Corner[3], Midpoint[Corner[3], Midpoint[Corner[3], Corner[2]]]], Midpoint[Corner[3], Midpoint[Corner[3], Corner[2]]]) → P
  11. Text("b", D + (b / 2, 2.4)) → text1
  12. Polygon(A + (0, 12), A + (0, 18), A + ((a * q) + r, 18), A + ((a * q) + r, 12)) → poly4, s, t, a_1, b_1
  13. Polygon(A + (0, 12), A + (0, 18), F + (0, 18), F + (0, 12)) → poly5, f_1, g_1, h_1, i_1
  14. Text(("q_1=" * q_1)) → text9
  15. Sequence(Segment[A + ((i * a), 12), A + ((i * a), 18)], i, 1, q - 1) → list4
  16. Sequence(Segment[A + ((i * a), 0), A + ((i * a), 6)], i, 1, q_1) → list1
  17. Sequence(Segment[A + ((i * a), 0), A + ((i * a), 6)], i, q_1, 0) → list3
  18. Sequence(Segment[A + ((i * a), 12), A + ((i * a), 18)], i, q, 0) → 列表4
  19. Sequence(Text["a", A + (a / 2.2 + (a * p), 14.4)], p, 0, q - 1) → 列表2
  20. Sequence(Text["a", A + (a / 2.2 + (a * p), 2.4)], p, 0, q_1 - 1) → list2
  21. Sequence(Text["a", A + (a / 2.2 + (a * p), 14.4)], p, q, -1) → 列表3
  22. Sequence(Text["a", A + (a / 2.2 + (a * p), 2.4)], p, q_1, -1) → 列表1
  23. Segment(A + ((a * q) + r, 12.15), A + ((a * q) + r, 17.85)) → e_1
  24. Text("r", A + ((q * a) + r / 2, 14.4)) → text2
  25. Text("aq", A + (((a * q)) / 2, 19.4)) → text8
  26. Text("aq_1", A + (((a * q_1)) / 2, (-2.5))) → text10
  27. Polygon(A, A + (0, 18), F + (0, 18), F) → poly6, a_2, d_1, j_1, f_2

AI Drawing Prompt Reference

Draw a geometric diagram showing the dynamic partitioning of a line segment into integer and fractional parts, including a large rectangle and several smaller rectangles, with text labels indicating values like a, b, q, r, starting from the whole rectangle and progressively dividing it into integer and fractional parts, annotated with key numerical values.
The prompt above was compiled from the original drawing commands and is for reference only.