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Descartes' Multiplication Model

Descartes' Multiplication Model
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2017-07-08 19:10
VectorCoordinate GeometryCalculusIntegralGeometric Construction
This example demonstrates Descartes' Multiplication Model in geometric space, involving vector operations, coordinate geometry, geometric constructions, and integral calculus. It utilizes commands like Intersect, Line, Point, Ray, Segment, Vector, and Circle in GeoGebra for constructing geometric figures and trajectories. Suitable for high school students and math enthusiasts to understand vector products, spatial geometry, and calculus applications.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → B
  2. Line(U, B) → s
  3. Point(xAxis) → A
  4. Point(xAxis) → D
  5. Ray(B, K) → l
  6. Point(s) → L
  7. Segment(B, A) → Unit
  8. Segment(B, D) → a
  9. Segment(B, C) → b
  10. Line(B, C) → c
  11. Segment(A, C) → e
  12. Line(A, e) → f
  13. Line(D, f) → g
  14. Intersect(g, c) → E
  15. Segment(B, E) → ab
  16. Segment(A, C) → i
  17. Segment(D, E) → j
  18. Segment(B, A) → h
  19. Line(B, D) → d
  20. Vector(B, D) → u
  21. Point(c) → F
  22. Point(c) → G
  23. Point(c) → H
  24. Point(d) → I
  25. Ray(B, D) → k
  26. Circle(A, L, D) → r
  27. Point(s) → T
  28. Line(T, A) → t
  29. Point(s) → J
  30. Vector(T, J) → u_1
  31. Point(t) → P
  32. Segment(P, J) → AC
  33. Line(D, AC) → n
  34. Intersect(s, n) → V
  35. Vector(T, V) → w
  36. Segment(V, D) → DE

AI Drawing Prompt Reference

On a coordinate plane, start at the origin and draw a ray along the positive x-axis. Mark two points on the x-axis: one for unit length and another for a variable length. From the origin, draw a ray along the y-axis and pick a point on it. Connect this point to the first x-axis point to form a slanted line. Through the second x-axis point, draw a line parallel to the slanted line, intersecting the y-axis ray at a new point. Connect the origin to this intersection to represent the product. On the slanted line, select several points, and through one of them draw a line parallel to the x-axis, intersecting another constructed line to create a dynamic point. Use the first x-axis point as center, draw a circle passing through a point on the slanted line and the second x-axis point. On the slanted line, take a point, connect it to the first x-axis point, and on this segment choose another point to define a vector. Finally, through this last point draw a line parallel to the y-axis, intersecting the slanted line to complete the geometric model of multiplication.
The prompt above was compiled from the original drawing commands and is for reference only.