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永续日历：用模运算与数列表达日期周期

永续日历：用模运算与数列表达日期周期
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2025-01-13 21:16
函数数列几何作图滑块动画函数图像
所属专题 Earth and Sun
该范例演示如何用几何与交互组件构建一个“永续日历”，在不固定年份的情况下，通过周期规则自动对应日期的星期与月份结构。核心数学概念包括：模运算（Mod）刻画年份与月份的周期性，数列（Sequence）生成规则化的索引/中间量，以及表格文本（TableText）把计算结果映射到日历格子中；同时利用条件分支（If）实现不同月份/日期情形的选择显示。作图要点可从构造摘要提炼为：使用 Textfield 提供可输入的日期或参数；用 If 与 Mod 计算落入的周期位置；用 Sequence 生成需要的序列索引；最后用 TableText 将对象（如日历格子 cuuadro/或 ac、calendario 等）按表格形式渲染为可读的日历界面。适合中学及高校初阶学习者用于函数/离散数学、算法思想与可视化建模的课堂演示，也适合数学社团或计算思维课程作为交互式项目展示。

GeoGebra 命令及参数

  1. Textfield(a) → CasillaDeEntrada1
  2. If(IsInteger[a / 400] ∨ IsInteger[a / 4] ∧ (¬IsInteger[a / 100]) ∧ a ≠ 4, 1, 0) → b
  3. Mod((a < 4) + 1 - b + If[a < 1583, Mod[11 - If[a < 1583, Mod[c, 7], Mod[c, 4]], 7], 6 - (2 * If[a < 1583, Mod[c, 7], Mod[c, 4]])] + Mod[a - (100 * c), 28] + floor(Mod[a - (100 * c), 28] / 4), 7) → e1
  4. Sequence({{1, 2, 3, 4, 5, 6, 7} - Mod[k + e, 7], {1, 2, 3, 4, 5, 6, 7} - Mod[k + e, 7] + 7, {1, 2, 3, 4, 5, 6, 7} - Mod[k + e, 7] + 14, {1, 2, 3, 4, 5, 6, 7} - Mod[k + e, 7] + 21, {1, 2, 3, 4, 5, 6, 7} - Mod[k + e, 7] + 28, {1, 2, 3, 4, 5, 6, 7} - Mod[k + e, 7] + 35}, k, 0, 6) → m
  5. Sequence(TableText[Join[{{D}, Sequence[Sequence[If[j ≟ 7, r, ""] + (If[m(o(k), i, j) < 1 ∨ m(o(k), i, j) > 31 - f(k), w, ""]) + (If[m(o(k), i, j) < 1, 0, m(o(k), i, j)]), j, 1, 7], i, 1, 6]}], "rc"], k, 1, 12) → t
  6. TableText({"             JANUARY              ", "              FEBRUARY            ", "               MARCH               "}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {"APRIL", "MAY", "JUNE"}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {"JULY", "AUGUST", "SEPTEMBER"}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {"OCTOBER", "NOVEMBER", "DECEMBER"}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, "c | _1100000000000000000001100000000000000000001100000000000000000001100000000000000000001", {}) → cuadro
  7. TableText(Join[{{D}, {{"1", "2", "3", "\textbf{4}", "\textbf{15}", "16", (r * "17")}, {"18", "19", "20", "21", "22", "23", (r * "24")}, {"25", "26", "27", "28", "29", "30", (r * "31")}}}], "rc") → M10'
  8. TableText(Join[{{D}, {{"1", "2", "3", "4", "5", "6", (r * "7")}, {"8", "9", "10", "11", "12", "13", (r * "14")}, {"15", "16", "17", "18", "19", "20", (r * "21")}, {"22", "23", "24", "25", "26", "27", (r * "28")}, {"29", "30", (w * 0), (w * 0), (w * 0), (w * 0), (w * 0)}}}], "rc") → M11'

AI 绘图提示语参考

绘制一个交互式万年历表格，包含十二个月份的日历网格，每个网格有六行七列，显示日期数字。顶部有输入年份的文本框，根据年份计算每个月的第一天是星期几，并自动排列日期。某些日期用粗体或特殊标记突出显示，如4、15、31等。表格周围有月份标题，如一月、二月等，整体布局整齐，适合教学演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。