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Division Algorithm Demonstration

Division Algorithm Demonstration
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2018-11-03 21:44
Coordinate GeometryGeometric Construction
This example dynamically visualizes the division algorithm, showing how to split a line segment into two parts such that one part's length equals the other part's length plus the given segment's length. It involves core mathematical concepts like the division algorithm principle, segment length calculation, proportional relationships, and remainder concepts. Constructed using GeoGebra commands/objects including Point, Segment, Polygon, Text, Sequence, and Midpoint. Suitable for high school mathematics teaching to help students intuitively understand the geometric meaning of the division algorithm.

GeoGebra Commands & Parameters

  1. Point(Circle[A, abs((a * q))]) → B
  2. Segment(A, B) → c
  3. Polygon(A + (abs(c), 0), A + (abs(c), 6), A + (0, 6), A) → poly1, d, e, f, n
  4. Polygon(C + (abs(r), 0), C + (abs(r), 6), C + (0, 6), C) → poly2, g, h, i, p
  5. Polygon(D + (abs(b), 0), D + (abs(b), 6), D + (0, 6), D) → poly3, j, k, l, m
  6. Text(("a=" * a)) → text3
  7. Text(("b=" * b)) → text4
  8. Text(("q=" * q)) → text5
  9. Text(("r=" * r)) → text6
  10. Text("b", D + (abs(b) / 2, 2.4)) → text1
  11. Sequence(Text["a", A + (abs(a) / 2 + (abs(a) * p), 2.4)], p, 0, q - 1) → list2
  12. Sequence(Segment[A + ((i * abs(a)), 0), A + ((i * abs(a)), 6)], i, 1, q) → list1
  13. Text("r", A + ((q * abs(a)) + abs(r) / 2, 2.4)) → text2
  14. Midpoint(Midpoint[Corner[4], Midpoint[Corner[4], Midpoint[Corner[4], Corner[1]]]], Midpoint[Corner[4], Midpoint[Corner[4], Corner[1]]]) → O
  15. Midpoint(Midpoint[Corner[3], Midpoint[Corner[3], Midpoint[Corner[3], Corner[2]]]], Midpoint[Corner[3], Midpoint[Corner[3], Corner[2]]]) → P

AI Drawing Prompt Reference

Draw a line segment AB and divide it into two parts such that one part's length equals the other part's length plus a given segment's length, illustrating the division algorithm. First, draw line segment AB, then draw segment c, and finally draw three rectangles to represent different length relationships. Lastly, label the values of a, b, q, and r at appropriate positions.
The prompt above was compiled from the original drawing commands and is for reference only.