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Eratosthenes' Method of Measuring the Earth

Eratosthenes' Method of Measuring the Earth
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2015-07-13 15:46
AngleCoordinate GeometryGeometric Construction
In collections Geometric Constructions Geometric Constructions Geometric Constructions-MINE Geometric Constructions
This example demonstrates Eratosthenes' method of measuring the Earth's circumference, an ancient technique. Key mathematical concepts include angle measurement and geometric construction. Using GeoGebra commands such as Intersect, Point, Ray, etc., precise geometric figures are constructed. Suitable for middle school mathematics education and geography measurement studies.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → E
  2. Point(xAxis) → B_1
  3. Ray(E, B_1) → a_1
  4. Point(yAxis) → A
  5. Line(A, a_1) → b_1
  6. Point(b_1) → D_1
  7. Ray(A, D_1) → c
  8. Segment(A, E) → a
  9. Point(c) → Q
  10. OrthogonalLine(Q, c) → d
  11. Intersect(d, a_1) → H
  12. Segment(H, Q) → e
  13. Point(e) → D
  14. Segment(A, D) → f
  15. Point(c) → N
  16. OrthogonalLine(N, c) → g
  17. Intersect(g, a_1) → G
  18. Segment(N, G) → h
  19. Point(a_1) → F
  20. Segment(A, F) → i
  21. OrthogonalLine(F, a_1) → j
  22. Intersect(j, c) → M
  23. Segment(M, F) → k
  24. Polygon(A, M, F) → poly1, f_1, a_2, m
  25. Line(G, i) → l
  26. Intersect(l, c) → M'
  27. Segment(M', G) → n
  28. Polygon(M', G, N) → poly2, n_1, m', i_1
  29. Line(H, i) → p
  30. Intersect(p, c) → N'
  31. Segment(N', H) → q
  32. Polygon(N', H, Q) → poly3, c_1, n', h_1
  33. Intersect(n, k) → B
  34. Intersect(q, h) → C
  35. Segment(D, H) → b
  36. Distance(B, F) → xx
  37. Distance(C, G) → yy