%matplotlib inline
import numpy as np
import sympy as sp
import matplotlib.pyplot as plt
π = np.pi
θ = np.linspace(-2*π, 2*π, 1000)
r = 3
x = r * np.cos(θ)
y = r * np.sin(θ)
plt.axis('equal')
plt.plot(x, y)
[<matplotlib.lines.Line2D at 0x7f132dd03490>]
r = 1 - np.sin(θ)
x = r * np.cos(θ)
y = r * np.sin(θ)
plt.axis('equal')
plt.plot(x, y)
[<matplotlib.lines.Line2D at 0x7f132d75fc90>]
plt.axis('equal')
plt.fill(x, y, c='#F1C0EB')
[<matplotlib.patches.Polygon at 0x7f132d520910>]
課本的 Example 8
$$r = \cos 2\theta$$r = np.cos(3*θ)
x = r * np.cos(θ)
y = r * np.sin(θ)
plt.axis('equal')
plt.plot(x, y, c='r')
[<matplotlib.lines.Line2D at 0x7f132d4ebd90>]
θ = np.linspace(-6*π, 6*π, 1000)
r = np.sin(8*θ/5)
x = r * np.cos(θ)
y = r * np.sin(θ)
plt.axis('equal')
plt.plot(x, y)
[<matplotlib.lines.Line2D at 0x7f132d013a50>]
from ipywidgets import interact
θ = np.linspace(-2*π, 2*π, 1000)
def polar1(c):
r = 1 + c * np.sin(θ)
x = r * np.cos(θ)
y = r * np.sin(θ)
plt.axis('equal')
plt.plot(x, y, c='r')
polar1(1.7)
interact(polar1, c=(-2., 2.));
interactive(children=(FloatSlider(value=0.0, description='c', max=2.0, min=-2.0), Output()), _dom_classes=('wi…
def polar2(n):
r = np.cos(n*θ)
x = r * np.cos(θ)
y = r * np.sin(θ)
plt.axis('equal')
plt.plot(x, y, c='r')
polar2(3)
interact(polar2, n=(1, 10));
interactive(children=(IntSlider(value=5, description='n', max=10, min=1), Output()), _dom_classes=('widget-int…