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Proclus' Ellipse Drawer

Proclus' Ellipse Drawer
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2017-09-13 05:13
TrigonometryCoordinate GeometryTransformationGeometric Construction
This example demonstrates the construction of an ellipse using Proclus' method. It involves core mathematical concepts such as the definition of an ellipse, means, derivatives, integers, rotation, and symmetry. The construction utilizes GeoGebra commands and objects like Intersect, Circle, Rotate, Segment, and CurveCartesian. It is suitable for high school and above students to understand the geometric construction and properties of ellipses.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, b) → c_1
  3. Circle(B, a) → d
  4. Intersect(c_1, d, 1) → C
  5. Rotate(C, (-s), B) → D
  6. Segment(B, D) → i
  7. Rotate(D, (2 * π / 3), B) → D'
  8. Rotate(D', (2 * π / 3), B) → D''
  9. Segment(B, D') → j
  10. Segment(B, D'') → h_1
  11. CurveCartesian(f(s), g(s), s, 0, t) → e
  12. Segment(J, F_1) → f_1
  13. Segment(J, F_2) → g_1