



from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
a_    :  Optional[int]						  =		numpy.array([0, 0])
a_    :  int						  =		numpy.array([0.5, 0.8660254])
a_    :  Dict						  =		numpy.array([1, 0])
a_    :  Optional[Any]						  =		[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]

def      __lowercase(						UpperCAmelCase__ , UpperCAmelCase__			):


      """simple docstring"""



      lowerCamelCase             =		initial_vectors
      for _ in range(UpperCAmelCase__			):
            lowerCamelCase             =		iteration_step(UpperCAmelCase__			)
      return vectors

def      __lowercase(						UpperCAmelCase__			):


      """simple docstring"""



      lowerCamelCase             =		[]
      for i, start_vector in enumerate(vectors[:-1]			):
            lowerCamelCase             =		vectors[i + 1]
            new_vectors.append(UpperCAmelCase__			)
            lowerCamelCase             =		end_vector - start_vector
            new_vectors.append(start_vector + difference_vector / 3			)
            new_vectors.append(
                start_vector + difference_vector / 3 + rotate(difference_vector / 3 , 60			)			)
            new_vectors.append(start_vector + difference_vector * 2 / 3			)
      new_vectors.append(vectors[-1]			)
      return new_vectors

def      __lowercase(						UpperCAmelCase__ , UpperCAmelCase__			):


      """simple docstring"""



      lowerCamelCase             =		numpy.radians(UpperCAmelCase__			)
      lowerCamelCase      ,				lowerCamelCase             =		numpy.cos(UpperCAmelCase__			), numpy.sin(UpperCAmelCase__			)
      lowerCamelCase             =		numpy.array(((c, -s), (s, c))			)
      return numpy.dot(UpperCAmelCase__ , UpperCAmelCase__			)

def      __lowercase(						UpperCAmelCase__			):


      """simple docstring"""



      lowerCamelCase             =		plt.gca()
      axes.set_aspect("equal"			)

      # matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
      # y-coordinates as inputs, which are constructed from the vector-list using
      # zip()
      lowerCamelCase      ,				lowerCamelCase             =		zip(*UpperCAmelCase__			)
      plt.plot(UpperCAmelCase__ , UpperCAmelCase__			)
      plt.show()


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     a_    :  Optional[Any]						  =		iterate(INITIAL_VECTORS, 5)
     plot(processed_vectors)




from __future__ import annotations

from math import pow, sqrt

def      __lowercase(						UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__			):


      """simple docstring"""



      if (resistance, reactance, impedance).count(0			) != 1:
            raise ValueError("One and only one argument must be 0"			)
      if resistance == 0:
            return {"resistance": sqrt(pow(UpperCAmelCase__ , 2			) - pow(UpperCAmelCase__ , 2			)			)}
      elif reactance == 0:
            return {"reactance": sqrt(pow(UpperCAmelCase__ , 2			) - pow(UpperCAmelCase__ , 2			)			)}
      elif impedance == 0:
            return {"impedance": sqrt(pow(UpperCAmelCase__ , 2			) + pow(UpperCAmelCase__ , 2			)			)}
      else:
            raise ValueError("Exactly one argument must be 0"			)


if __name__ == "__main__":
     import doctest

     doctest.testmod()