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Multiplication of Directed Numbers by 現代數學 Modern Mathematics

Multiplication of Directed Numbers by 現代數學 Modern Mathematics
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2020-02-28 18:51
VectorTrigonometryCoordinate Geometry
This example demonstrates the multiplication of directed numbers. Key mathematical concepts include the properties and rules of directed number multiplication. Using GeoGebra commands such as Segment, Vector, and Point, the geometric meaning of directed number multiplication is dynamically illustrated. Suitable for students at the junior high school level and above.

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, (k * dis) + y(A)), (x(A) + 0.5, ((k - 1) * dis) + y(A))], k, 1, Div[y(B) - y(A), dis]) → l1
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. If(SelectedIndex[l9] ≟ 2, "rise", If[SelectedIndex[l9] ≟ 3, "drop", ""]) → text0
  21. If(n > 0, "later", "ago") → text1
  22. If(n' ≟ 1, "minute", "minutes") → textp
  23. Vector(D, E) → w

AI Drawing Prompt Reference

Draw a geometric representation of directed number multiplication, including a line segment AB, a vector u starting from point A, and a vector v starting from point B. Use line segment AB to illustrate the multiplication process, where vector u represents the multiplier and vector v represents the multiplicand, adjusting the direction and length of the vectors to show the multiplication result.
The prompt above was compiled from the original drawing commands and is for reference only.