Modeling the Five Elements Using Angles

In a sense, the Five Elements relationship between two elements can be understood as an angular distance on a circle. Therefore, if two elements are known, the angle between them can in fact be computed. If the clockwise angle from A to B is between 0 and 72 degrees, then B and A are in a mutual (companion) relationship in the Five Elements; if it is between 72 and 144 degrees, A generates B. This way, the generating and overcoming cycles are simulated.

The difficulty here is how to codify this — computing the angle between two vectors. The Python code is as follows:

import numpy as np

def get_clockwise_rotation_angle(vector1, vector2):
    # Compute the dot product of the two vectors
    dot_product = np.dot(vector1, vector2)
    
    # Compute the norms (magnitudes) of the two vectors
    norm_vector1 = np.linalg.norm(vector1)
    norm_vector2 = np.linalg.norm(vector2)
    
    # Compute the cosine value
    cos_theta = dot_product / (norm_vector1 * norm_vector2)
    
    # Use the arccos function to compute the value in radians
    radians = np.arccos(cos_theta)
    
    # Convert radians to degrees
    degrees = np.degrees(radians)
    
    # Use the cross product to determine the direction of rotation
    cross_product = np.cross(vector1, vector2)
    
    # If the cross product is positive, adjust the angle to 360 - angle
    if cross_product > 0:
        degrees = 360 - degrees
    
    return degrees