python - 用python计算圆周围的多边形面积、周长和边长

Question

我有计算圆上内切多边形的面积、周长和边长的函数，但我想找到类似的通用方法来计算围绕圆绘制的多边形的相同属性。

# Area of an equal sided polygon with given radius and number of sides
def polygon_area(r, n):
    return ((n*pow(r, 2))/2)*sin(2*pi/n)

# Perimeter of an equal sided polygon with given radius and number of sides
def polygon_perimeter(r, n):
    return 2*n*r*sin(pi/n)

# Side length of an equal sided polygon with given radius and number of sides
def polygon_side(r, n):
    return polygon_perimeter(r, n)/n

答案可能与 apothem 有关，就像这张照片上的那样。问题是，我只知道圆的半径:

Answer 1

您只需在现有公式中使用边心因数 (apothem = radius * cos(pi/n))(我没有检查):

# Area of an equal sided polygon with given radius and number of sides
def polygon_area_outer(r, n):
    return n * r**2 / 2 * sin(2*pi/n) / cos(pi/n)**2

# Side length of an equal sided polygon with given radius and number of sides
def polygon_side_outer(r, n):
    return 2 * r * sin(pi/n) / cos(pi/n)

# Perimeter of an equal sided polygon with given radius and number of sides
def polygon_perimeter_outer(r, n):
    return polygon_side_outer(r, n) * n

我更改了函数的顺序，将周长基于一侧(反之亦然)，以避免乘以然后潜水n 计算多边形边长时。