import matplotlib.pyplot as plt

import numpy as np

# Set up the figure and axis

fig, ax = plt.subplots(figsize=(8, 6))

ax.set_xlim(-1.2, 1.2)

ax.set_ylim(0, 1.2)

ax.set_aspect('equal')

ax.axhline(y=0, color='k', linewidth=0.5)  # Base line

ax.axvline(x=0, color='k', linewidth=0.5)  # Axis

# Parameters

r = 1.0  # Radius/height for simplicity

# 1. Cylinder cross-section: Rectangle from y=0 to y=r, x=-r to x=r

ax.add_patch(plt.Rectangle((-r, 0), 2*r, r, fill=False, edgecolor='blue', linewidth=2, label='Cylinder'))

# 2. Cone cross-section: Triangle from base at y=0 (x=-r to r) to apex at y=r (x=0)

ax.plot([-r, 0, r], [0, r, 0], color='red', linewidth=2, label='Cone')

# 3. Hemisphere cross-section: Semicircle with diameter at y=r (x=-r to r), curving down to point at y=0 (x=0)

theta = np.linspace(np.pi, 2*np.pi, 100)  # From pi to 2pi for lower semicircle

x_semi = r * np.cos(theta)

y_semi = r + r * np.sin(theta)  # Shift up by r so it starts at y=r and goes down to y=0

ax.plot(x_semi, y_semi, color='green', linewidth=2, label='Hemisphere (pole-down)')

# Labels and ticks for heights

ax.set_xticks([-r, 0, r])

ax.set_xticklabels(['-r', 'Axis', 'r'])

ax.set_yticks([0, 0.5*r, r])

ax.set_yticklabels(['h=0 (Base)', 'h=r/2', 'h=r (Top)'])

ax.set_xlabel('Width (2r total)')

ax.set_ylabel('Height h')

ax.set_title("Vertical Cross-Sections: Cone + Hemisphere = Cylinder\n(Archimedes' Cavalieri Setup)")

# Legend

ax.legend(loc='upper right')

# Fill to show overlap (optional: fills the cone and hemisphere lightly)

ax.fill([-r, 0, r], [0, r, 0], alpha=0.3, color='red')  # Cone fill

ax.fill_between(x_semi, y_semi, 0, alpha=0.3, color='green')  # Hemisphere fill (from curve to base, but since base is at 0, approximate)

plt.grid(True, alpha=0.3)

plt.show()