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Eratosthenes' Measurement of Earth's Circumference

Eratosthenes' Measurement of Earth's Circumference
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2019-02-19 23:16
AngleTrigonometryGeometric Construction
This example demonstrates how the ancient Greek scholar Eratosthenes estimated the Earth's circumference by measuring the angle of the sun's rays at two different locations. Key mathematical concepts include trigonometric functions and angle measurement. Using GeoGebra commands such as Circle, Point, Ray, Angle, etc., the geometric model of Eratosthenes' experiment can be constructed. Suitable for high school mathematics education and applications in geography, such as scale ratios.

GeoGebra Commands & Parameters

  1. Circle((0, 0), r) → c
  2. Point(c) → B
  3. Ray(O, B) → f
  4. Point(f) → C
  5. Ray(B, C) → g
  6. Point(g) → T
  7. OrthogonalLine(B, f) → h
  8. OrthogonalLine(T, xAxis) → i
  9. Intersect(h, i) → D
  10. Angle(D, B, T) → α
  11. CircleArc(O, B, A) → d
  12. Polygon(B, D, T) → t1, t, b, d_1
  13. Sequence(Ray[(i, 10), (i, 0)], i, -6, 6, 0.5) → L_1
  14. Sequence(Intersect[c, Element[L_1, i]], i, 1, Length[L_1]) → L_2
  15. Sequence(Vector[(i, 10), Element[L_2, (2 * i) + 13]], i, -6, 6, 0.5) → L_3
  16. Segment(O, B) → j
  17. Segment(O, A) → k
  18. Midpoint(B, O) → E
  19. Midpoint(A, O) → F
  20. Segment(B, T) → l
  21. Segment(B, D) → m