MathPlotAI Logo MathPlotAI

Mapping Triangles with Equal Areas

Mapping Triangles with Equal Areas
Loading the math board and drawing, please wait…
2017-04-10 01:21
TrianglePolygonSolid GeometryCalculusGeometric Construction
This example demonstrates how to map triangles to triangles of equal area through a transformation. Key math concepts include area, triangles, functions, cones, definite integrals, pyramids, and circles. Construction highlights the use of GeoGebra commands and objects like Vector, Line, Point, Translate, Polygon, Rotate, Intersect, and If. Suitable for high school mathematics students and teachers exploring geometric transformations and integral applications.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Line(A, B) → g
  3. Point(g) → E_1
  4. Translate(E_1, u) → E'
  5. Polygon(A, B, C) → poly1, c, a, b
  6. Line(C, c) → f
  7. Point(f) → D_1
  8. Vector(D_1, E_1) → v
  9. Translate(E', Vector[(0.35 * v)]) → E''
  10. Polygon(D_1, E_1, E'') → poly2, e'', d, e
  11. Translate(D_1, (1, -1)) → D'
  12. Translate(E_1, (1, -1)) → E
  13. Translate(E'', (1, -1)) → E'''
  14. Polygon(D', E, E''') → poly2', e''', d', e'_1
  15. Rotate(D', -135°, E) → D
  16. Rotate(E, -135°, E) → F
  17. Rotate(E''', -135°, E) → G
  18. Polygon(D, F, G) → poly2'', g_1, d'', f_1
  19. Line(C, c) → i
  20. Line(D, d'') → j
  21. Intersect(i, j) → H
  22. If(1 ≤ h < 2, Dilate[D, 2 - h, H], H) → J
  23. If(1 ≤ h < 2, Polygon[G, E, Dilate[D, 2 - h, H]], Polygon[G, E, H]) → poly4
  24. Line(A, B) → k
  25. Line(G, E) → l
  26. Intersect(i, l) → K
  27. Intersect(j, k) → L
  28. Intersect(k, l) → I
  29. If(3 ≤ h < 4, Dilate[E, 4 - h, I], I) → M
  30. Translate(M, Vector[E, G]) → M'
  31. If(3 ≤ h < 4, Polygon[M', M, H], Polygon[M', I, H]) → poly3
  32. Line(I, H) → m
  33. Line(M', m) → n
  34. Intersect(k, n) → N
  35. If(6 ≤ h < 7, Polygon[M, Dilate[M', 7 - h, N], H], Polygon[M, N, H]) → poly5
  36. If(8 ≤ h < 9, Polygon[M, N, Dilate[H, 9 - h, C]], Polygon[M, N, C]) → poly6
  37. If(10 ≤ h < 11, Polygon[C, Dilate[M, 11 - h, A], Translate[Dilate[M, 11 - h, A], Vector[A, B]]], Polygon[C, A, B]) → poly7