# this file available at: https://arachnoid.com/files/python01/
import math

# pythagorean triple:
# https://mathworld.wolfram.com/PythagoreanTriple.html
# https://en.wikipedia.org/wiki/Pythagorean_triple

# define the Triangle class
class Triangle:
    # create an instance of the class
    def __init__(self, a:int, b:int, c:int):
        self.a,self.b,self.c = a,b,c

    def perimeter(self) -> int:
        return self.a + self.b + self.c
    
    def area(self) -> float:
        return (self.a * self.b) / 2.0
    
    def sum_of_squares(self) -> float:
        return self.a**2+self.b**2
    
    def hypotenuse(self) -> float:
        return self.sum_of_squares()**0.5
    
    def coprime(self) -> bool:
        return math.gcd(self.a,math.gcd(self.b,self.c)) == 1
    
    # test: is this instance a primitive Pythagorean triple?
    def triple_test(self) -> bool:
        # are a, b and c coprime?
        if not self.coprime(): return False
        # is the calculated hypotenuse equal to c?
        if self.hypotenuse() != self.c: return False
        else: return True

def triangle_tests():
  label_length = 32
  for values in ((3,4,5),(6,8,10),(5,12,13),(7,24,25),(13,14,19)):
      # create an instance of the Triangle class    
      triangle_instance = Triangle(*values)
      print(f'for Triangle class instance values a,b,c = {values}:')
      print(f'\t{"Perimeter length":{label_length}} = {triangle_instance.perimeter():5.1f}')
      print(f'\t{"Area":{label_length}} = {triangle_instance.area():5.1f}')
      print(f'\t{"Sum of squares : a**2 + b**2":{label_length}} = {triangle_instance.sum_of_squares():5.1f}')
      print(f'\t{"Hypotenuse : sqrt(a**2+b**2)":{label_length}} = {triangle_instance.hypotenuse():5.1f}')
      print(f'\t{"Primitive Pythagorean triple:":{label_length}} = {triangle_instance.triple_test()}')
      print()

if __name__ == "__main__":
    triangle_tests()