from math import sin, sqrt

def dichotomie_pi(alpha):
    a=3
    b=4
    while ........ :
        m=(a+b)/2
        if (sin(m)*sin(a)>0):
            a=.....
        else:
            b=.....
    return a,b

# def leibnitz_pi(alpha):
#     a,i,b=1,1,1
#     while (i<(1-alpha/4)/(alpha/4)):
#         b=-b
#         a += ......
#         i +=1
#     return 4*a


# def briggs(x,alpha):
#     n=0
#     while x>1+alpha:
#         x = sqrt(x)
#         n=n+1
#     return ............


# def exp(alpha):
#     a,b,c=1,1,1
#     while(abs(b)>alpha):
#         b=..................
#         a=..................
#         n +=1
#     return a