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Multiplication of Directed Numbers by Patrick Chung

Multiplication of Directed Numbers by Patrick Chung
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2020-02-14 03:35
VectorFunctionProbability & Statistics
This example demonstrates the multiplication of directed numbers, involving key mathematical concepts such as directed numbers and multiplication. Using GeoGebra commands like Segment, Vector, Point, etc., it visually illustrates the geometric meaning of directed number multiplication. Suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. Segment((x(L), y(L) + 2), (x(U), y(U) - 2)) → f
  2. Vector(L, (x(L), y(L) + 20)) → u
  3. Point(f) → B
  4. If(x(B) - x(A) > 0, "+", "") → sign2
  5. If(x(B) - x(A) < 0, "+", "") → sign3
  6. If(x(A) > 0, "+", "") → signa
  7. If(x(B) - x(A) > 0, "+", "") → signba
  8. If(x(B) > x(A), "+", "-") → op2
  9. If(x(B) > 0, "+", "") → signb
  10. Corner(1) → C
  11. Vector((x(L), y(L) + 20), L) → v
  12. Sequence(Segment[(x(L) - 0.3, y(L) + (2 * k)), (x(L) + 0.3, y(L) + (2 * k))], k, 1, 9) → l7
  13. Sequence((x(L) - 0.3, y(L) + (2 * k)), k, 1, 9) → l8
  14. Sequence(Semicircle[(x(A) + 0.5, ((1 - k) * dis) + y(A)), (x(A) + 0.5, ((-k) * dis) + y(A))], k, 1, Div[y(A) - y(B), dis]) → l3
  15. Sequence(Vector[(x(A) + 1, (k * dis) + y(A) + 0.1), (x(A) + 0.4, (k * dis) + y(A))], k, 0, Div[y(B) - y(A), dis] - 1) → l5
  16. Sequence(Vector[(x(A) + 1, (k * dis) + y(A) - 0.1), (x(A) + 0.4, (k * dis) + y(A))], k, 1, Div[y(B) - y(A), dis]) → l2
  17. Sequence(Vector[(x(A) + 1, ((-k) * dis) + y(A) - 0.1), (x(A) + 0.4, ((-k) * dis) + y(A))], k, 0, Div[y(A) - y(B), dis] - 1) → l4
  18. Sequence(Vector[(x(A) + 1, ((-k) * dis) + y(A) + 0.1), (x(A) + 0.4, ((-k) * dis) + y(A))], k, 1, Div[y(A) - y(B), dis]) → l6
  19. If(SelectedIndex[l9] ≟ 2, "rise", If[SelectedIndex[l9] ≟ 3, "drop", ""]) → text0
  20. If(n > 0, "later", "ago") → text1
  21. If(n' ≟ 1, "minute", "minutes") → textp
  22. Vector(D, E) → w
  23. If(SelectedIndex[l9] ≟ 2, "上升", If[SelectedIndex[l9] ≟ 3, "下降", ""]) → text0_1
  24. If(n > 0, "後", "前") → text1_1
  25. If(chi ≟ false, "Select...", "請選擇...") → text28
  26. Sequence(Semicircle[(x(A) + 0.5, (k * dis) + y(A)), (x(A) + 0.5, ((k - 1) * dis) + y(A))], k, 1, Div[y(B) - y(A), dis]) → l1

AI Drawing Prompt Reference

Draw a number line scene illustrating the geometric meaning of multiplying directed numbers. Above the number line, place a slanted segment with a movable point on it. From a fixed point on the number line, draw an upward vertical vector and also a downward vertical vector. Based on the horizontal positions of the movable point relative to the fixed point, display plus or minus signs as text near the points. Between the fixed point and the movable point, show a series of semicircles and arrows indicating multiplication steps, with arrow directions changing for rise or drop. Add explanatory text in a corner, such as "rise" or "drop", "later" or "ago", and include a selection prompt. Keep the layout clear for teaching.
The prompt above was compiled from the original drawing commands and is for reference only.