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Missing Area Puzzle

Missing Area Puzzle
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2014-11-27 03:20
TrigonometryGeometric Construction
This example demonstrates a visual phenomenon of missing area in a geometric figure. Core math concepts include area, congruence, trigonometric functions, ratios, and differential calculus. Construction highlights GeoGebra commands and objects like Intersect, Point, If, Polygon, and Rotate. Suitable for high school and above to explore geometric transformations, area calculations, and calculus applications.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. If(aa < 0, 0, If[aa > 1, 1, aa]) → a
  4. Polygon(A, B, C) → poly1, c, a_1, b
  5. Polygon(D, E, F) → poly2, f, d, e
  6. Polygon(G, J, I, H) → poly3, g, j, i, h
  7. Polygon(M, N, K, L) → poly4, m, n, k, l
  8. Polygon(O, P, Q) → poly5, q, o, p
  9. Point(a_1) → R
  10. Point(a_1) → U
  11. Polygon(R, S, T, U) → poly6, r, s, t, u
  12. Rotate(R, (90° * a), R) → R'
  13. Rotate(S, (90° * a), R) → S'
  14. Rotate(T, (90° * a), R) → T'
  15. Rotate(U, (90° * a), R) → U'
  16. Polygon(R', S', T', U') → poly6', r', s', t', u'
  17. Polygon(W, Z, A_1, V) → poly7, w, z, a_2, v