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Pappus Area-2

Pappus Area-2
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2020-12-16 10:12
CirclePolygonVectorFunctionGeometric Construction
This example demonstrates the area calculation of Pappus theorem. Key concepts include area, centroid, circle, circumcircle, general quadrilateral, geometric distribution, plane figures, polygons, quadrilaterals, symmetry, geometric transformations, logarithm, step functions, vectors, square, and exponential functions. Using GeoGebra commands such as Polygon, Centroid, Segment, Intersect, Point, Line, Midpoint, OrthogonalLine, Perimeter, and PointIn, a geometric figure is constructed, suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 8) → poly1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  2. Centroid(poly1) → I
  3. Segment(B, I) → n
  4. Segment(A, I) → p
  5. Segment(H, I) → q
  6. Segment(G, I) → r
  7. Segment(F, I) → s
  8. Segment(E, I) → t
  9. Segment(D, I) → a
  10. Segment(C, I) → b
  11. Intersect(n, poly1) → L
  12. Point(n) → J
  13. Segment(B, A) → c
  14. Line(J, f) → d
  15. Intersect(d, p) → K
  16. Intersect(d, p) → M
  17. Polygon(M, J, 8) → poly2, e, O, P, Q, R, S, f_1, g_1, h_1, i_1, j_1, k_1, l_1, N
  18. Midpoint(B, J) → T
  19. Line(T, d) → m_1
  20. Intersect(m_1, p) → U
  21. Segment(U, T) → n_1
  22. Polygon(U, T, 8) → poly3, p_1, W, Z, A_1, B_1, C_1, q_1, r_1, s_1, t_1, a_1, b_1, c_1, V
  23. Segment(B, J) → e_1
  24. OrthogonalLine(I, g) → d_1
  25. Intersect(d_1, g) → D_1
  26. Intersect(d_1, f_1) → E_1
  27. Segment(D_1, E_1) → f_2
  28. Perimeter(poly3) → perimeterpoly3
  29. PointIn(poly3) → Pointpoly3_{1}
  30. PointIn(poly3) → Pointpoly3_{2}
  31. Perimeter(poly3) → u
  32. PointIn(poly3) → Pointpoly3_{3}
  33. Perimeter(poly1) → perimeterpoly1
  34. PointIn(poly1) → Pointpoly1_{1}
  35. Perimeter(poly1) → v
  36. PointIn(poly1) → Pointpoly1_{2}
  37. Perimeter(poly2) → perimeterpoly2
  38. PointIn(poly2) → Pointpoly2_{1}
  39. Intersect(q_1, f_2) → F_1
  40. PointIn(poly1) → Pointpoly1
  41. PointIn(poly3) → Pointpoly3
  42. PointIn(poly2) → Pointpoly2

AI Drawing Prompt Reference

Draw a regular octagon with its center marked. Connect the center to each vertex with line segments, creating eight radial lines. Pick a point on one radial line, draw a line through it parallel to one side of the octagon, intersecting an adjacent radial line. Use this intersection and the point to form a second regular octagon. Take the midpoint of the segment between the original point and the intersection, draw a parallel line through it, and construct a third regular octagon. Finally, place a random point inside each of the three octagons and display their perimeters.
The prompt above was compiled from the original drawing commands and is for reference only.