复二次函数与方程的映射图

几何画板及绘图内容加载中，请稍等……

2018-01-20 03:16

所属专题 Mapping Diagrams to Visualize Complex Analysis

①本范例演示复二次函数与方程的映射图，直观展示函数图像与映射关系；②涉及核心数学概念包括复数、函数映射、坐标几何、解析几何；③作图要点提炼自构造摘要，使用 GeoGebra 命令 Sequence, Zip, Line, Circle, Point, If, Vector, Textfield, Locus 等构建图形；④适合高中及以上数学学习者，用于理解复变函数的几何意义与性质。

GeoGebra 命令及参数

Sequence(0, n) → M_1
Zip(((2 * pi) * k / n), k, M_1) → t_*
Zip((δ * ℯ^((t * ί))) + z_#, t, t_*) → z_c
Zip(z_# + ((t - pi) * (P_l - z_#)), t, t_*) → z_l
Line(z_#, P_l) → l
Circle(z_#, δ) → c
Point(c) → Pc
If(m ≟ 1, z_c, z_l) → z_*
Zip(s1(z), z, z_*) → fz_*
Line(O, ZY1) → Im_{axis}
Line(O, ZX1) → Real_{axis}
Vector(z_#, fz1_#) → vecf_#
Textfield(F) → InputBox1
Zip((x(z), y(z), ht), z, fz_*) → fpt_*
Zip(Vector[z, w], z, z_*, w, fpt_*) → fvec_*
Locus(Pts1Pc, Pc) → loc_c
Point(l) → Pl
Locus(Pts1Pl, Pl) → loc_l
Line((x(O2), y(O2), z(O2)), Vector[(1, 0, 0)]) → Real_{axis2}
Line((x(O2), y(O2), z(O2)), Vector[(0, 1, 0)]) → Im_{axis2}
Zip(g(s1(z)), z, z_*) → gfz_*
Zip((x(z), y(z), (2 * ht)), z, gfz_*) → gfpt_*
Zip(Vector[z, w], z, fpt_*, w, gfpt_*) → gfvec_*
Locus(Ptgs1Pc, Pc) → loc2_c
Textfield(G) → InputBox2
Sequence(n_p) → Np
Zip(z = (ht * k), k, Np) → Planes
Zip(mf(g(s1(z))), z, z_*) → Agfz_*
Zip((x(z), y(z), (3 * ht)), z, Agfz_*) → Agfpt_*
Zip(Vector[z, w], z, gfpt_*, w, Agfpt_*) → Agfvec_*
Zip(s2(mf(SQ(s1(z)))), z, z_*) → kAgfz_*
Zip((x(z), y(z), (4 * ht)), z, kAgfz_*) → kAgfpt_*
Zip(Vector[z, w], z, Agfpt_*, w, kAgfpt_*) → kAgfvec_*
Locus(PtAgs1Pc, Pc) → Loc3_c
Locus(Pts2Ags1Pc, Pc) → Loc4_c
Locus(Ptgs1Pl, Pl) → loc2_l
Locus(PtAgs1Pl, Pl) → Loc3_l
Locus(Pts2Ags1Pl, Pl) → Loc4_l
Vector(B3, Is2B3) → u
Vector(Is2B3, IAIs2B3) → v
Vector(IAIs2B3, SQRPIAIs2B3) → w
Vector(IAIs2B3, SQRNIAIs2B3) → b
Vector(SQRPIAIs2B3, Is1SQRPIAIs2B) → e
Vector(SQRNIAIs2B3, Is1SQRNIAIs2B) → d