Man and History: Python 量子運算（一六）：和角

Python 量子運算（一六）：和角

2023/01/24

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Fig. 1. Angle sum.

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和角 angle sum

和角公式 angle sum formula

差角 angle difference

差角公式 angle difference formula

「Along with angle difference formulas, we have angle sum formulas as well.」[1]。

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代碼 16.1

# Program 16.1：Angle sum
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt


# defined by angle
class PointT1:
    def __init__(self, t, r):
        self.t = t  # theta

        self.r = r  # radius
        self.x = r * np.cos(t)
        self.y = r * np.sin(t)


# defined by points
class PointT2:
    def __init__(self, x, y):
        self.x = x
        self.y = y


def Subplot_1():
    ax = plt.subplot(111)

    # circle
    c = np.linspace(0, np.pi*2, 100)
    r = 1
    c_x = r * np.cos(c)
    c_y = r * np.sin(c)
    ax.plot(c_x, c_y, 'g', linestyle='--')

    # points
    t_A = (31/24) * np.pi                # theta A setting
    PA = PointT1(t_A, r)                 # A
    PC = PointT1(t_A-np.pi, r)           # C, determined by A
    ax.plot([PA.x, PC.x], [PA.y, PC.y], 'purple', linewidth=5.0)  # AC
    ax.text(PA.x-0.1, PA.y-0.1, 'A')
    ax.text(PC.x+0.05, PC.y+0.05, 'C')

    PB = PointT2(PC.x, PA.y)             # B, determined by A, C
    ax.plot([PA.x, PB.x], [PA.y, PA.y], 'r', linestyle='--')  # AB
    ax.plot([PB.x, PB.x], [PB.y, PC.y], 'purple', linestyle='--')  # BC
    ax.text(PB.x+0.05, PB.y-0.1, 'B')

    PG = PointT2(PA.x, PC.y)             # G, determined by A, C
    ax.plot([PA.x, PG.x], [PA.y, PG.y], 'purple', linestyle='--')  # AG
    ax.plot([PC.x, PG.x], [PC.y, PG.y], 'purple', linestyle='--')  # CG
    ax.text(PG.x-0.1, PG.y+0.05, 'G')

    t_E = (47/24) * np.pi                # theta E setting
    PE = PointT1(t_E, r)                 # E
    ax.plot([PA.x, PE.x], [PA.y, PE.y], 'r', linewidth=5.0)  # AE
    ax.plot([PC.x, PE.x], [PC.y, PE.y], 'b', linewidth=5.0)  # CE
    ax.text(PE.x+0.05, PE.y, 'E')

    PD = PointT2(PE.x, PC.y)             # D, determined by C, E
    ax.plot([PC.x, PD.x], [PC.y, PD.y], 'b', linestyle='--')  # CD
    ax.plot([PD.x, PE.x], [PD.y, PE.y], 'b', linestyle='--')  # DE
    ax.text(PD.x+0.05, PD.y+0.05, 'D')

    PF = PointT2(PE.x, PB.y)             # F, determined by B, E
    ax.plot([PB.x, PF.x], [PB.y, PF.y], 'r', linestyle='--')  # BF
    ax.plot([PE.x, PF.x], [PE.y, PF.y], 'r', linestyle='--')  # EF
    ax.text(PF.x+0.05, PF.y-0.1, 'F')

    # angles
    ax.text(PA.x+0.25, PA.y+0.20, r'$\alpha$')
    ax.text(PA.x+0.35, PA.y+0.05, r'$\beta$')
    ax.text(PE.x-0.08, PE.y+0.25, r'$\beta$')
    ax.text(PC.x-0.35, PC.y-0.10, r'$\alpha+\beta$')

    # edges
    ax.text((PA.x+PE.x)/2-0.2, (PA.y+PE.y)/2,
            r'$\cos\alpha$', color='r')
    ax.text((PA.x+PF.x)/2-0.1, (PA.y+PF.y)/2,
            r'$\cos\alpha\cos\beta$', color='r')
    ax.text((PE.x+PF.x)/2, (PE.y+PF.y)/2,
            r'$\cos\alpha\sin\beta$', color='r')

    ax.text((PC.x+PE.x)/2-0.2, (PC.y+PE.y)/2,
            r'$\sin\alpha$', color='b')
    ax.text((PD.x+PE.x)/2, (PD.y+PE.y)/2,
            r'$\sin\alpha\cos\beta$', color='b')
    ax.text((PC.x+PD.x)/2-0.15, (PC.y+PD.y)/2,
            r'$\sin\alpha\sin\beta$', color='b')

    ax.text((PC.x+PG.x)/2-0.2, (PC.y+PG.y)/2,
            r'$\cos(\alpha+\beta)$', color='purple')
    ax.text((PA.x+PG.x)/2-0.4, (PA.y+PG.y)/2,
            r'$\sin(\alpha+\beta)$', color='purple')

    ax.set_aspect(1)  # height : width
    ax.set_axis_off()

    return


mpl.rcParams['text.usetex'] = True
mpl.rcParams['text.latex.preamble'] = r'\usepackage{{amsmath}}'
mpl.rcParams['font.size'] = 40
fig = plt.figure(figsize=(16, 16))

Subplot_1()

# plt.savefig('/content/drive/My Drive/pqc/0016_001.png')
plt.show()