continued fraction of e

eContinuedFraction.py

# %%
# continued fraction of e
# https://mathworld.wolfram.com/eContinuedFraction.html
# e = 1+1+1/(1+1/(2+2/(3+3/(4+4/(5+5/(...))))))
def eContinuedFraction(n: int) -> float:
    ret = 1
    for i in range(n, 0, -1):
        ret = i+i/ret
    return 1+1+1/ret

gistfile1.txt

# %%
# continued fraction of pi
https://mathworld.wolfram.com/PiContinuedFraction.html
def piContinuedFraction(n: int):
    ret = 1
    for i in range(n, 0, -1):
        ret = 1-(1 if i==1 else (2*i-3)*(2*i-2))/(3-(2*i*(2*i+1))/ret)
    return 2*ret

piContinuedFraction

# %%
# continued fraction of pi
https://mathworld.wolfram.com/PiContinuedFraction.html
def piContinuedFraction(n: int):
    ret = 1
    for i in range(n, -1, -1):
        ret = 2+((2*i+1)**2)/ret
    return 4/(ret - 1)

print(eContinuedFraction(20))
2.7182818284590455
piContinuedFraction(100000)
3.1415826536897913