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Dynamic Division Measurement Model

Dynamic Division Measurement Model
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2014-10-03 01:59
FunctionGeometric Construction
This example demonstrates the dynamic measurement process of division in the set of natural numbers when the quotient is a whole number. It involves core math concepts like division, functions, line segments, and intersection points. The construction uses GeoGebra commands and objects such as Function, Intersect, and Segment, along with elements like f, g, h, t, A, O, etc. It is suitable for middle school mathematics teaching, providing an intuitive visualization of the geometric meaning and dynamic changes in division operations.

GeoGebra Commands & Parameters

  1. Function((4 - (x)^(2))^(1 / 2), 0, 2) → f
  2. Function((4 - (x - 2)^(2))^(1 / 2), 0, 4) → g
  3. Function((4 - (x - 4)^(2))^(1 / 2), 2, 6) → h
  4. Intersect(g, xAxis, (0, 0)) → O
  5. Segment(O, A) → a
  6. Intersect(f, g, (1, 1.7320508075688772)) → C
  7. Segment(E, B) → b
  8. Function((4 - (x - 6)^(2))^(1 / 2), 4, 8) → p
  9. Function((4 - (x - 8)^(2))^(1 / 2), 6, 10) → q
  10. Function((4 - (x - 10)^(2))^(1 / 2), 8, 12) → r
  11. Function((4 - (x - 12)^(2))^(1 / 2), 10, 14) → s
  12. Segment(D, F) → c
  13. Segment(G, K) → d
  14. Function((4 - (x - 14)^(2))^(1 / 2), 12, 16) → f_1
  15. Function((4 - (x - 16)^(2))^(1 / 2), 14, 18) → g_1
  16. Segment(H, L) → e
  17. Function((4 - (x - 18)^(2))^(1 / 2), 16, 20) → h_1
  18. Function((4 - (x - 20)^(2))^(1 / 2), 18, 22) → p_1
  19. Function((4 - (x - 22)^(2))^(1 / 2), 20, 24) → q_1
  20. Segment(I, M) → i
  21. Function((4 - (x - 24)^(2))^(1 / 2), 22, 26) → r_1
  22. Segment(J, N) → j
  23. Segment(O, P) → k

AI Drawing Prompt Reference

Draw three parabolas with vertices on a circle and centers on the x-axis, then connect the origin to their intersection points with line segments, showing the dynamic geometric meaning of division in natural numbers.
The prompt above was compiled from the original drawing commands and is for reference only.