Sicherman Dice 因式分解证明

几何画板及绘图内容加载中，请稍等……

2019-07-04 17:37

函数解析几何概率统计

①本范例演示了如何通过因式分解证明 Sicherman Dice 的唯一性；②涉及的核心数学概念包括因式分解、多项式系数、概率统计；③作图要点——从下方『构造摘要』提炼用到了 Factor, Polynomial, Coefficients, Flatten, Sequence, TableText, Sum 等GeoGebra命令/对象；④适合高中及以上数学爱好者学习概率论与代数应用。

GeoGebra 命令及参数

Factor(r) → t
Polynomial(t) → tt
Coefficients(tt) → l2
Flatten(Sequence[Sequence[j, i, 1, Element[l2, j]], j, 1, Length[l2]]) → l4
Factor(q) → s
Polynomial(s) → ss
Coefficients(ss) → l1
Flatten(Sequence[Sequence[j, i, 1, Element[l1, j]], j, 1, Length[l1]]) → l3
Sequence(Sequence[Element[l5, i] + Element[l6, j], i, 1, Length[l3]], j, 1, Length[l4]) → m1
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
TableText(m2, "_01000000000000000000000000000000000000|01000000000000000000000000000000000000") → text8
Sum(Coefficients[ss]) → sumSS
Sum(Coefficients[tt]) → sumTT