极坐标曲线的构造与对称反射几何展示

GeoGebra 命令及参数

1. CurveCartesian(A + (1 + cos(θ); θ), θ, 0, a) → a_{1}
2. CurveCartesian(B + (1.5 * (sin((n * θ)); θ)), θ, 0, a) → b
3. CurveCartesian(D + (1.5 * (cos(θ)^(2); θ)), θ, 0, a) → d
4. CurveCartesian(F + (3 * ((cos(θ) * cos((2 * θ))); θ)), θ, 0, a) → f
5. CurveCartesian(G + (2 * (sin(θ) / θ; θ)), θ, (-a), a) → g
6. CurveCartesian(J + (2 * (sqrt(cos((2 * θ))); θ)), θ, 0, a) → j
7. CurveCartesian(M + (3 * (cos(θ)^(3); θ)), θ, 0, a) → k
8. CurveCartesian(N + (5 * ((sin(θ) * cos(θ)^(2)); θ)), θ, 0, a) → l
9. CurveCartesian(O + ((1.5 * sin(θ / 2)); θ), θ, (-a), a) → m
10. CurveCartesian(C + (0.125 * (θ + cos(θ); θ)), θ, 0, (2 * a)) → c
11. CurveCartesian(L + (2 / θ; θ), θ, (-2 * a), -1) → p
12. CurveCartesian(L + (2 / θ; θ), θ, 1, (2 * a)) → q
13. CurveCartesian(K + ((0.05 * θ); θ), θ, 0, (4 * a)) → o
14. CurveCartesian(E + (2 * (tan(θ / 2); θ)), θ, ((-a)) / 3.35, a / 3.35) → e
15. Line(S, T) → r
16. CurveCartesian(H + ((1.2 * cos((2 * θ))); θ), θ, 0, a) → h
17. CurveCartesian(Q + ((0.3 * sqrt(θ)); θ), θ, 0, (3.5 * a)) → u
18. CurveCartesian(Q + ((-0.3 * sqrt(θ)); θ), θ, 0, (3.5 * a)) → t
19. CurveCartesian(R + (tan(θ); θ), θ, ((-a)) / 6, a / 6) → v
20. Mirror(v, R) → v'
21. CurveCartesian(I + (0.65 * (1 + cos((n * θ)) + sin((n * θ))^(2); θ)), θ, 0, a) → i
22. CurveCartesian(T + ((1.42 * sin(θ / 3)); θ), θ, 0, (2 * a)) → w