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Ellipse by Folding by Katey

Ellipse by Folding by Katey
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2017-09-13 05:07
AngleCoordinate GeometryGeometric ConstructionLocus
This example demonstrates the geometric construction of an ellipse through paper folding, illustrating the underlying principles of the shape. It involves core mathematical concepts such as angles, linear regression, differential calculus, binomial distribution, and functions. The construction utilizes GeoGebra commands like Intersect, Circle, PointIn, LineBisector, Fold, Sequence, Segment, Polygon, and Locus. It is suitable for high school and advanced learners to explore the properties of ellipses and their algebraic representations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, r) → c
  3. PointIn(c) → B
  4. Point(c) → C
  5. LineBisector(C, B) → f
  6. Fold(B, C, c) → g
  7. Sequence(((r * cos(((k * 2) * π / n))), (r * sin(((k * 2) * π / n)))), k, 1, n) → list1
  8. Intersect(c, g) → F, G
  9. Sequence(Fold[B, Element[list1, k], c], k, 1, n) → list2
  10. Segment(A, C) → h
  11. Intersect(g, h) → D
  12. Segment(B, C) → i
  13. Intersect(g, i) → E
  14. Polygon(C, E, D) → poly1, d, c_1, e
  15. Polygon(D, B, E) → poly2, e_1, d_1, b
  16. Locus(D, C) → loc1