midsummer night

６月２１日は夏至 summer solstice です。

夏至といえば毎年メンデルスゾーンの真夏の夜の夢だったのですが、midsummer night は夏至の日の前の晩を指すようです。

AI と学ぶ真夏の夜の夢

$\displaystyle{ \frac{(x+y)^2}{810} + \frac{(x-y)^2}{1000} = \pi }$

import numpy as np
import matplotlib.pyplot as plt

# Given values for a^2 and b^2
a2 = 810
b2 = 1000
pi_value = np.pi

# Compute the semi-major and semi-minor axes
a = np.sqrt(a2)
b = np.sqrt(b2)

# Parameters for the ellipse
theta = np.linspace(0, 2 * np.pi, 1000)
x = a * np.cos(theta)
y = b * np.sin(theta)

# Rotate the ellipse by -45 degrees
angle = np.radians(-45)
cos_angle = np.cos(angle)
sin_angle = np.sin(angle)

x_rotated = x * cos_angle - y * sin_angle
y_rotated = x * sin_angle + y * cos_angle

# Scale the ellipse to satisfy the equation = pi
scaling_factor = np.sqrt(pi_value)
x_scaled = x_rotated * scaling_factor
y_scaled = y_rotated * scaling_factor

# Plot the ellipse
plt.figure(figsize=(10, 6))
plt.fill(x_scaled, y_scaled, '#BC8F8F', label=r'$\frac{(x+y)^2}{810} + \frac{(x-y)^2}{1000} = \pi$')
plt.title('A Midsummer Night’s Dream')
plt.xlabel('x-axis')
plt.ylabel('y-axis')
plt.axhline(0, color='gray', lw=0.5)
plt.axvline(0, color='gray', lw=0.5)
plt.legend()
plt.grid(True)
plt.axis('equal')
plt.show()

AI と学ぶ四色問題

John Backus も取り組んだ四色問題ですが、ここでは男色問題・・・

import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np

# 描画領域の設定
fig, ax = plt.subplots(figsize=(8, 6))

# 色の設定
color_circle = '#BC8F8F' # 円の色
color_top_left = '#A8C3C4'  # 左上の色
color_top_right = '#D3C9B3'  # 右上の色
color_bottom = '#3F3548'  # 下の色

# 頂点の座標を定義
triangle1 = [[-0.1, 1], [0.5, 1.0], [0.5, 0.5], [-0.1, 0.2]]
triangle2 = [[ 1.1, 1], [0.5, 1.0], [0.5, 0.5], [ 1.1, 0.2]]
triangle3 = [[-0.1, 0], [1.1, 0], [1.2, 0.2], [0.5, 0.5], [-0.1,0.2]]

# 三角形の描画
ax.add_patch(patches.Polygon(triangle1, color=color_top_left, zorder=0))
ax.add_patch(patches.Polygon(triangle2, color=color_top_right, zorder=0))
ax.add_patch(patches.Polygon(triangle3, color=color_bottom, zorder=0))

# 円の描画
circle = patches.Circle((0.5, 0.5), 0.3, color=color_circle, zorder=1)
ax.add_patch(circle)

# 軸の設定
ax.set_xlim(-0.1, 1.1)
ax.set_ylim(0, 1)
ax.set_aspect('equal')
ax.axis('off')

plt.show()