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Triangle Paradox (Missing Square Puzzle)

Triangle Paradox (Missing Square Puzzle)
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2012-01-18 04:56
TrianglePolygonGeometric Construction
In collections Jessica's Fraction Book
This example demonstrates a famous geometric paradox where two shapes with the same area appear to suddenly lose a black square. Core math concepts include area, polygons, triangles, rotation, congruence, and construction. GeoGebra commands and objects used are Intersect, Point, If, Polygon, Rotate. Suitable for middle school and above students learning geometric construction, area calculation, and logical reasoning.

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