Python math常量详解 - math.pi、math.e、math.inf、math.nan使用指南

import math

math.pi    # 圆周率 π
math.e     # 自然常数 e
math.tau   # 2倍圆周率 τ = 2π
math.inf   # 正无穷
math.nan   # 非数字（Not a Number）

import math

# 圆周率
print(f"pi  = {math.pi}")
print(f"tau = {math.tau}")
print(f"2 * pi == tau: {2 * math.pi == math.tau}")

# 自然常数
print(f"\ne = {math.e}")
print(f"ln(e) = {math.log(math.e)}")
print(f"e^1 = {math.exp(1)}")

# 圆的面积与周长
radius = 5
area = math.pi * radius ** 2
circumference = 2 * math.pi * radius
print(f"\n半径{radius}的圆:")
print(f"  面积 = pi * r^2 = {area:.4f}")
print(f"  周长 = 2 * pi * r = {circumference:.4f}")

# 使用 tau 简化公式
circumference_tau = math.tau * radius
print(f"  周长 = tau * r = {circumference_tau:.4f}")

# 输出：
# pi  = 3.141592653589793
# tau = 6.283185307179586
# 2 * pi == tau: True
#
# e = 2.718281828459045
# ln(e) = 1.0
# e^1 = 2.718281828459045
#
# 半径5的圆:
#   面积 = pi * r^2 = 78.5398
#   周长 = 2 * pi * r = 31.4159
#   周长 = tau * r = 31.4159

import math

# 正无穷
print(f"inf = {math.inf}")
print(f"inf + 1 = {math.inf + 1}")
print(f"inf * 2 = {math.inf * 2}")
print(f"inf > 1e308 = {math.inf > 1e308}")
print(f"-inf = {-math.inf}")

# 无穷大的运算
print(f"\n1 / inf = {1 / math.inf}")         # 0.0
print(f"inf - inf = {math.inf - math.inf}")  # nan
print(f"inf / inf = {math.inf / math.inf}")  # nan

# NaN 的特殊性质
print(f"\nnan = {math.nan}")
print(f"nan == nan: {math.nan == math.nan}")          # False! NaN不等于自身
print(f"nan != nan: {math.nan != math.nan}")          # True
print(f"nan > 0: {math.nan > 0}")                     # False
print(f"nan < 0: {math.nan < 0}")                     # False
print(f"math.isnan(nan): {math.isnan(math.nan)}")     # 正确的判断方式
print(f"math.isinf(inf): {math.isinf(math.inf)}")     # 判断无穷大
print(f"math.isfinite(1.0): {math.isfinite(1.0)}")    # 判断有限数

# 输出：
# inf = inf
# inf + 1 = inf
# inf * 2 = inf
# inf > 1e308 = True
# -inf = -inf
#
# 1 / inf = 0.0
# inf - inf = nan
# inf / inf = nan
#
# nan = nan
# nan == nan: False
# nan != nan: True
# nan > 0: False
# nan < 0: False
# math.isnan(nan): True
# math.isinf(inf): True
# math.isfinite(1.0): True

import math

# 使用 pi 计算球体体积
def sphere_volume(radius):
    return (4/3) * math.pi * radius ** 3

# 使用 e 计算连续复利
def continuous_compound(principal, rate, time):
    """A = P * e^(rt)"""
    return principal * math.exp(rate * time)

# 使用 tau 简化角度计算
def rad_to_deg(rad):
    """弧度转角度：1弧度 = 360/tau 度"""
    return rad * 360 / math.tau

def deg_to_rad(deg):
    """角度转弧度：1度 = tau/360 弧度"""
    return deg * math.tau / 360

# 使用 inf 作为初始值
def find_min(numbers):
    """找最小值，用 inf 作为初始值"""
    min_val = math.inf
    for n in numbers:
        if n < min_val:
            min_val = n
    return min_val

# 使用 nan 标记无效数据
def safe_divide(a, b):
    """安全除法，除零返回 nan"""
    if b == 0:
        return math.nan
    return a / b

# 测试
print(f"地球体积: {sphere_volume(6371):.3e} km³")
print(f"1万元5%利率10年: {continuous_compound(10000, 0.05, 10):.2f}元")
print(f"pi弧度 = {rad_to_deg(math.pi):.1f}度")
print(f"180度 = {deg_to_rad(180):.4f}弧度")
print(f"最小值: {find_min([3, 1, 4, 1, 5, 9, 2, 6])}")
print(f"1/0 = {safe_divide(1, 0)}")
print(f"是否无效: {math.isnan(safe_divide(1, 0))}")

# 输出：
# 地球体积: 1.083e+12 km³
# 1万元5%利率10年: 16487.21元
# pi弧度 = 180.0度
# 180度 = 3.1416弧度
# 最小值: 1
# 1/0 = nan
# 是否无效: True