探索保角映射

GeoGebra 命令及参数

1. Point(yAxis) → C
2. Point(xAxis) → A
3. Sequence(Segment[A + (0, y(C) + (k * dy)), ((-x(A)), y(C) + (k * dy))], k, 0, k0) → l1, {7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807, 7.42658575340807}
4. Point(g1) → z_1
5. Point(l1) → E
6. Locus(fz_{1}, z_1) → loc1
7. Sequence(CurveCartesian[real(f(u, v)), imaginary(f(u, v)), u, -10, 10], v, -10, 10) → l_{uv}, {(real(1 / (z + (0 * ί))(u, -10)), imaginary(1 / (z + (0 * ί))(u, -10))), (real(1 / (z + (0 * ί))(u, -9)), imaginary(1 / (z + (0 * ί))(u, -9))), (real(1 / (z + (0 * ί))(u, -8)), imaginary(1 / (z + (0 * ί))(u, -8))), (real(1 / (z + (0 * ί))(u, -7)), imaginary(1 / (z + (0 * ί))(u, -7))), (real(1 / (z + (0 * ί))(u, -6)), imaginary(1 / (z + (0 * ί))(u, -6))), (real(1 / (z + (0 * ί))(u, -5)), imaginary(1 / (z + (0 * ί))(u, -5))), (real(1 / (z + (0 * ί))(u, -4)), imaginary(1 / (z + (0 * ί))(u, -4))), (real(1 / (z + (0 * ί))(u, -3)), imaginary(1 / (z + (0 * ί))(u, -3))), (real(1 / (z + (0 * ί))(u, -2)), imaginary(1 / (z + (0 * ί))(u, -2))), (real(1 / (z + (0 * ί))(u, -1)), imaginary(1 / (z + (0 * ί))(u, -1))), (real(1 / (z + (0 * ί))(u, 0)), imaginary(1 / (z + (0 * ί))(u, 0))), (real(1 / (z + (0 * ί))(u, 1)), imaginary(1 / (z + (0 * ί))(u, 1))), (real(1 / (z + (0 * ί))(u, 2)), imaginary(1 / (z + (0 * ί))(u, 2))), (real(1 / (z + (0 * ί))(u, 3)), imaginary(1 / (z + (0 * ί))(u, 3))), (real(1 / (z + (0 * ί))(u, 4)), imaginary(1 / (z + (0 * ί))(u, 4))), (real(1 / (z + (0 * ί))(u, 5)), imaginary(1 / (z + (0 * ί))(u, 5))), (real(1 / (z + (0 * ί))(u, 6)), imaginary(1 / (z + (0 * ί))(u, 6))), (real(1 / (z + (0 * ί))(u, 7)), imaginary(1 / (z + (0 * ί))(u, 7))), (real(1 / (z + (0 * ί))(u, 8)), imaginary(1 / (z + (0 * ί))(u, 8))), (real(1 / (z + (0 * ί))(u, 9)), imaginary(1 / (z + (0 * ί))(u, 9))), (real(1 / (z + (0 * ί))(u, 10)), imaginary(1 / (z + (0 * ί))(u, 10)))}
8. Sequence(CurveCartesian[real(f(u, v)), imaginary(f(u, v)), v, -10, 10], u, -10, 10) → l_{vu}, {(real(1 / (z + (0 * ί))(-10, v)), imaginary(1 / (z + (0 * ί))(-10, v))), (real(1 / (z + (0 * ί))(-9, v)), imaginary(1 / (z + (0 * ί))(-9, v))), (real(1 / (z + (0 * ί))(-8, v)), imaginary(1 / (z + (0 * ί))(-8, v))), (real(1 / (z + (0 * ί))(-7, v)), imaginary(1 / (z + (0 * ί))(-7, v))), (real(1 / (z + (0 * ί))(-6, v)), imaginary(1 / (z + (0 * ί))(-6, v))), (real(1 / (z + (0 * ί))(-5, v)), imaginary(1 / (z + (0 * ί))(-5, v))), (real(1 / (z + (0 * ί))(-4, v)), imaginary(1 / (z + (0 * ί))(-4, v))), (real(1 / (z + (0 * ί))(-3, v)), imaginary(1 / (z + (0 * ί))(-3, v))), (real(1 / (z + (0 * ί))(-2, v)), imaginary(1 / (z + (0 * ί))(-2, v))), (real(1 / (z + (0 * ί))(-1, v)), imaginary(1 / (z + (0 * ί))(-1, v))), (real(1 / (z + (0 * ί))(0, v)), imaginary(1 / (z + (0 * ί))(0, v))), (real(1 / (z + (0 * ί))(1, v)), imaginary(1 / (z + (0 * ί))(1, v))), (real(1 / (z + (0 * ί))(2, v)), imaginary(1 / (z + (0 * ί))(2, v))), (real(1 / (z + (0 * ί))(3, v)), imaginary(1 / (z + (0 * ί))(3, v))), (real(1 / (z + (0 * ί))(4, v)), imaginary(1 / (z + (0 * ί))(4, v))), (real(1 / (z + (0 * ί))(5, v)), imaginary(1 / (z + (0 * ί))(5, v))), (real(1 / (z + (0 * ί))(6, v)), imaginary(1 / (z + (0 * ί))(6, v))), (real(1 / (z + (0 * ί))(7, v)), imaginary(1 / (z + (0 * ί))(7, v))), (real(1 / (z + (0 * ί))(8, v)), imaginary(1 / (z + (0 * ί))(8, v))), (real(1 / (z + (0 * ί))(9, v)), imaginary(1 / (z + (0 * ί))(9, v))), (real(1 / (z + (0 * ί))(10, v)), imaginary(1 / (z + (0 * ί))(10, v)))}
9. Sequence(Segment[C + (x(A) + (k * dx), 0), (0, (-y(C))) + (x(A) + (k * dx), 0)], k, 0, k0) → l2, {5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664, 5.623720789100664}
10. Point(g2) → z_{2}
11. Locus(fz_{2}, z_{2}) → loc2
12. Textfield(k0) → InputBox1
13. Textfield(m1) → InputBox2
14. Textfield(m2) → InputBox3
15. Polygon(D, F, n) → poli1, s, l, J, N, R, V, H, I, K, L, t, f_1, j_1, n_1, s_1, i, j, k
16. Point(poli1) → z_3
17. Locus(fz_{3}, z_3) → loc3
18. Surface(f(u + (v * ί)), u, -2, 2, v, -2, 2) → p