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Kite & Lemniscate

Kite & Lemniscate
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2016-05-20 04:46
FunctionCoordinate GeometryCalculusGeometric ConstructionGraphing
This example demonstrates the geometric relationship and properties between a kite and a lemniscate, involving logarithmic functions, differential calculus, geometric mean, hypothesis testing, and statistical characteristics. It uses GeoGebra commands like Circle, Point, Segment, Line, Intersect, OrthogonalLine, Midpoint, Polygon, with objects such as R, A, B, c, C, f, g, d, h, D, E, i, j, k, F, G, l, m, H, I, IP, HP, button1, J, K, poly1, c_1, j_1, a, k_1. Suitable for high school students and math enthusiasts studying function graphs, geometric constructions, and advanced mathematics.

GeoGebra Commands & Parameters

  1. Circle(B, R) → c
  2. Point(c) → C
  3. Segment(A, C) → f
  4. Segment(B, C) → g
  5. Circle(A, R) → d
  6. Line(A, g) → h
  7. Intersect(d, h) → D, E
  8. Segment(A, E) → i
  9. Segment(C, E) → j
  10. OrthogonalLine(E, f) → k
  11. Intersect(d, k) → F, G
  12. Segment(G, A) → l
  13. Segment(C, G) → m
  14. Midpoint(m) → H
  15. Midpoint(j) → I
  16. Intersect(l, m) → J
  17. Intersect(i, j) → K
  18. Polygon(C, J, A, K) → poly1, c_1, j_1, a, k_1