正笛卡尔整数V1.1

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2019-08-19 21:09

解析几何最值优化

该范例展示了正笛卡尔整数的构造过程。涉及的核心数学概念包括整数、方程、算术和最值优化。通过使用GeoGebra命令如Segment、Join、Flatten等，可以直观地理解这些概念。适合初中及以上学生或教师使用。

GeoGebra 命令及参数

Segment(A, B) → seg_{real025}
Segment(C, D) → seg_{real075}
Join(Sequence[Sequence[Sequence[If[true, Text["(" + (k) + " + " + (j) + " + " + (i) + ") = " + (k + j + i) + " ", (k + xp, j + yp, i + zp), true, true]], i, sv, ev, inc], j, sv, ev, inc], k, sv, ev, inc]) → L_3b
Join(Sequence[Sequence[Sequence[If[k + j + i ∈ List_{Odd-Ints}, Vector[Origin, (k + xp, j + yp, i + zp)]], i, sv, ev, inc], j, sv, ev, inc], k, sv, ev, inc]) → L_1c
Join(Sequence[Sequence[Sequence[If[k + j + i ∈ List_{Odd-Ints}, Sphere[(k + xp, j + yp, i + zp), abs(ps_{01})]], i, sv, ev, inc], j, sv, ev, inc], k, sv, ev, inc]) → L_1a
Flatten(Join[Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ∈ List_{Odd-Ints}, k + j + i], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]]) → L_1w
Join(Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ∈ List_{Odd-Ints} ≠ 0, Text["(" + (k) + " + " + (j) + " + " + (i) + ") = " + (k + j + i) + " ", (ps_{01} + k + xp, ps_{01} + j + yp, ps_{01} + i + zp), true, true]], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]) → L_1b
Join(Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ∈ List_{Odd-Ints} ≠ 1, Text["(" + (k) + " + " + (j) + " + " + (i) + ") = " + (k + j + i) + " ", (ps_{01} + k + xp, ps_{01} + j + yp, ps_{01} + i + zp), true, true]], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]) → L_2b
Point(zAxis) → E
Join(Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ≟ 0, Sphere[(k, j, i), abs(ps_{02} - 0.009)]], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]) → L_{zeros}
Join(Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ∈ List_{Even-Ints} ≠ 0, Sphere[(k, j, i), abs(ps_{02} - 0.01)]], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]) → L_2a