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Sicherman Dice Proof Using Factoring

Sicherman Dice Proof Using Factoring
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2019-07-04 17:37
FunctionCoordinate GeometryProbability & Statistics
This example demonstrates the uniqueness of Sicherman Dice through a proof involving factoring. Key math concepts include polynomial factoring, coefficients, and probability statistics. GeoGebra commands used are Factor, Polynomial, Coefficients, Flatten, Sequence, TableText, and Sum. Suitable for high school and above students interested in probability theory and algebraic applications.

GeoGebra Commands & Parameters

  1. Factor(r) → t
  2. Polynomial(t) → tt
  3. Coefficients(tt) → l2
  4. Flatten(Sequence[Sequence[j, i, 1, Element[l2, j]], j, 1, Length[l2]]) → l4
  5. Factor(q) → s
  6. Polynomial(s) → ss
  7. Coefficients(ss) → l1
  8. Flatten(Sequence[Sequence[j, i, 1, Element[l1, j]], j, 1, Length[l1]]) → l3
  9. Sequence(Sequence[Element[l5, i] + Element[l6, j], i, 1, Length[l3]], j, 1, Length[l4]) → m1
  10. Sequence(Sequence[If[i ≟ 0 ∧ j ≟ 0, "+", If[i ≟ 0, "" + (Element[l6, j]), If[j ≟ 0, "" + (Element[l5, i]), "" + (Element[m1, j, i])]]], i, 0, Length[l3]], j, 0, Length[l4]) → m2
  11. TableText(m2, "_01000000000000000000000000000000000000|01000000000000000000000000000000000000") → text8
  12. Sum(Coefficients[ss]) → sumSS
  13. Sum(Coefficients[tt]) → sumTT