Four versions of finding the nth element on the Fibonacci series

Fibonacci.rb

# Four versions of the Fibonacci solution for the nth element

# Iterative
def fib(n)
 if n < 2
   num  = n
 else
   n1 = 1
   n2 = 0
   n-1.times do |i|
     num = n1+n2
     n1 = num
     n2 = n1
   end
 end
 num
end

# Recursive Big O(2^n) - bi-nomial 
def fib_recursive_factorial(n)
  if n < 2
    n
  else
    fib_recursive_factorial(n-1) + fib_recursive_factorial(n-2)
  end
end

#Recursive Big O(n) - linear
def fib_recursive_linear(n, i=2,n1=1,n2=0)
  if n < 2
    n
  else
   if i < n
     fib_recursive_linear(n,i+1,n1+n2, n1)
   else
     n1+n2
   end
  end
end

# Using phi(Golden ratio) to solve in O(1), but with side effect of rounding
def fib_phi(n)
   phi =(1+Math.sqrt(5))/2
   phi1 = (1-Math.sqrt(5))/2
   (phi**n / Math.sqrt(5)  -  (1-phi)**n / Math.sqrt(5)).round
end