import math class Polygon: def __init__(self, n, R): if n < 3: raise ValueError('Polygon must have at least 3 vertices.') self._n = n self._R = R def __repr__(self): return f'Polygon(n={self._n}, R={self._R})' @property def count_vertices(self): return self._n @property def count_edges(self): return self._n @property def circumradius(self): return self._R @property def interior_angle(self): return (self._n - 2) * 180 / self._n @property def side_length(self): return 2 * self._R * math.sin(math.pi / self._n) @property def apothem(self): return self._R * math.cos(math.pi / self._n) @property def area(self): return self._n / 2 * self.side_length * self.apothem @property def perimeter(self): return self._n * self.side_length def __eq__(self, other): if isinstance(other, self.__class__): return (self.count_edges == other.count_edges and self.circumradius == other.circumradius) else: return NotImplemented def __gt__(self, other): if isinstance(other, self.__class__): return self.count_vertices > other.count_vertices else: return NotImplemented

def test_polygon(): abs_tol = 0.001 rel_tol = 0.001 try: p = Polygon(2, 10) assert False, ('Creating a Polygon with 2 sides: ' ' Exception expected, not received') except ValueError: pass n = 3 R = 1 p = Polygon(n, R) assert str(p) == 'Polygon(n=3, R=1)', f'actual: {str(p)}' assert p.count_vertices == n, (f'actual: {p.count_vertices},' f' expected: {n}') assert p.count_edges == n, f'actual: {p.count_edges}, expected: {n}' assert p.circumradius == R, f'actual: {p.circumradius}, expected: {n}' assert p.interior_angle == 60, (f'actual: {p.interior_angle},' ' expected: 60') n = 4 R = 1 p = Polygon(n, R) assert p.interior_angle == 90, (f'actual: {p.interior_angle}, ' ' expected: 90') assert math.isclose(p.area, 2, rel_tol=abs_tol, abs_tol=abs_tol), (f'actual: {p.area},' ' expected: 2.0') assert math.isclose(p.side_length, math.sqrt(2), rel_tol=rel_tol, abs_tol=abs_tol), (f'actual: {p.side_length},' f' expected: {math.sqrt(2)}') assert math.isclose(p.perimeter, 4 * math.sqrt(2), rel_tol=rel_tol, abs_tol=abs_tol), (f'actual: {p.perimeter},' f' expected: {4 * math.sqrt(2)}') assert math.isclose(p.apothem, 0.707, rel_tol=rel_tol, abs_tol=abs_tol), (f'actual: {p.perimeter},' ' expected: 0.707') p = Polygon(6, 2) assert math.isclose(p.side_length, 2, rel_tol=rel_tol, abs_tol=abs_tol) assert math.isclose(p.apothem, 1.73205, rel_tol=rel_tol, abs_tol=abs_tol) assert math.isclose(p.area, 10.3923, rel_tol=rel_tol, abs_tol=abs_tol) assert math.isclose(p.perimeter, 12, rel_tol=rel_tol, abs_tol=abs_tol) assert math.isclose(p.interior_angle, 120, rel_tol=rel_tol, abs_tol=abs_tol) p = Polygon(12, 3) assert math.isclose(p.side_length, 1.55291, rel_tol=rel_tol, abs_tol=abs_tol) assert math.isclose(p.apothem, 2.89778, rel_tol=rel_tol, abs_tol=abs_tol) assert math.isclose(p.area, 27, rel_tol=rel_tol, abs_tol=abs_tol) assert math.isclose(p.perimeter, 18.635, rel_tol=rel_tol, abs_tol=abs_tol) assert math.isclose(p.interior_angle, 150, rel_tol=rel_tol, abs_tol=abs_tol) p1 = Polygon(3, 10) p2 = Polygon(10, 10) p3 = Polygon(15, 10) p4 = Polygon(15, 100) p5 = Polygon(15, 100) assert p2 > p1 assert p2 < p3 assert p3 != p4 assert p1 != p4 assert p4 == p5

class Polygons: def __init__(self, m, R): if m < 3: raise ValueError('m must be greater than 3') self._m = m self._R = R self._polygons = [Polygon(i, R) for i in range(3, m+1)] def __len__(self): return self._m - 2 def __repr__(self): return f'Polygons(m={self._m}, R={self._R})' def __getitem__(self, s): return self._polygons[s] @property def max_efficiency_polygon(self): sorted_polygons = sorted(self._polygons, key=lambda p: p.area/p.perimeter, reverse=True) return sorted_polygons[0]