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有理数与无理数的十进制表示

有理数与无理数的十进制表示
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2019-02-09 18:49
函数解析几何概率统计
该范例通过展示有理数和无理数的十进制表示，帮助学生理解有理数和无理数的区别。涉及的核心数学概念包括有理数和无理数的定义及其十进制表示。使用了GeoGebra中的Denominator, Factors, Length, Sequence, If, GCD, Element, SelectedIndex, Textfield等命令。适合初中及以上学生学习。

GeoGebra 命令及参数

  1. Denominator(h) → denom_h
  2. Factors(denom_h) → m2
  3. Length(m2) → length_{m2}
  4. Sequence(Element[m2, i, 1], i, 1, length_{m2}) → denomfactorslist
  5. If(Defined[IndexOf[5, denomfactorslist]], IndexOf[5, denomfactorslist], 0) → fiveindexnum
  6. If(Defined[IndexOf[2, denomfactorslist]], IndexOf[2, denomfactorslist], 0) → twoindexnum
  7. GCD(p, q) → commonfactor
  8. Factors(q / commonfactor) → m1
  9. Element(m1, 2, 1) → pf2
  10. Element(m1, 1, 1) → pf1
  11. Length(m1) → e_{length}
  12. SelectedIndex(listChoiceNumber) → f
  13. If(f ≟ 1, If[terminatingDec, textRationalNumTerminating, textRationalNum], textIrrationalNum) → textNumShow
  14. Textfield(p) → InputBox1
  15. Textfield(q) → InputBox2
  16. TextToUnicode(textNumShow) → l01
  17. Length(l01) → b
  18. Textfield(textInputIrrational) → InputBox3
  19. Take(textNumShow, IndexOf[".", textNumShow] + 1) → text2
  20. Sequence("\textcolor{" + ((Element[colors, FromBase[UnicodeToLetter[Element[l01, k]], 10]] * "}{")) + (UnicodeToLetter[Element[l01, k]]) + "}", k, 3, dp + 3) → l4
  21. Sequence(Take[text2, 1 + (n * k), Min[n + (n * k), Length[text2]]], k, 0, Div[Length[text2], n]) → l1
  22. Sequence(Take[l1, 1 + (c * k), Min[c + (c * k), Length[l1] - 1]], k, 0, Div[Length[l1] - 1, c]) → l2
  23. Sequence(Take[l4, 1 + (n * k), Min[n + (n * k), Length[l4]]], k, 0, Div[Length[l4], n]) → l5
  24. Sequence(Take[l5, 1 + k, Min[1 + k, Length[l5] - 1]], k, 0, Div[Length[l5] - 1, 1]) → l6
  25. Length(l6) → lengthI6
  26. If(length_{m2} ≟ 1 ∧ twoindexnum + fiveindexnum ≟ 1 ∨ length_{m2} ≟ 2 ∧ twoindexnum + fiveindexnum ≟ 3 ∨ denom_h ≟ 1, true, false) → terminateDec2