Python Maths Quiz

def f(x, n=0) :
    head, tail = x
    if n<100 :
        return head + 1.0/(f(tail, n+1))
    return head
x = [1]
x.append(x)
print f(x)

def f2(n) :
    a,b = 1,1
    for i in range(n):
        b,a = a,a+b
    return a/float(b)
print f2(100)

def f3(x) :
    y = 1.0
    for i in range(100) :
        y = 0.5*(1+y + x/y)
    return y

print f3(1.0)

class RabbitPair(object) :
    def __init__(self) :
        self.age = 0
    def mate(self) :
        offspring = []
        if self.age > 0 :
            offspring.append(RabbitPair())
        self.age += 1
        return offspring

populations = []
rabbit_pairs = [RabbitPair()]
for i in range(20) :
    new_rabbits = []
    for rabbit_pair  in rabbit_pairs :
        new_rabbits += rabbit_pair.mate()
    rabbit_pairs += new_rabbits
    populations.append(len(rabbit_pairs))
print populations[-1]/float(populations[-2])

x = [False]
a,b = 1,1
for i in range(30) :
    new = [False for y in x if y]
    x = [True]*len(x) + new
    a,b = b,len(x)
print b/float(a)