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Multiplication of Directed Numbers

Multiplication of Directed Numbers
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2020-05-07 17:21
VectorFunctionCoordinate Geometry
This example uses the Thermometer Tool to demonstrate the multiplication of directed numbers. Key mathematical concepts include directed numbers and multiplication. Using GeoGebra commands such as Segment, Vector, and Point, a thermometer model is constructed to illustrate 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