# October 31st, class 4
## Fibonacci
```elixir
defmodule Fibonacci do
# def calc(0), do: 0
# def calc(1), do: 1
# def calc(n) when n > 1 do
# calc(n - 1) + calc(n - 2)
# end
def find(nth) do
list = [1, 1]
fib(list, nth)
end
defp fib(list, 2) do
Enum.reverse(list)
end
defp fib(list, n) do
[first_element, second_element | _rest] = list
fib([first_element + second_element | list], n - 1)
end
def nth_v2(n) do
find(n)
|> Enum.reverse()
|> hd()
end
end
```
```elixir
Fibonacci.find(2000)
```
```elixir
Fibonacci.nth_v2(2000)
```
```elixir
defmodule HeronMethod do
def sqrt(n, error \\ 1.0e-10) do
sqrt(n, error, 1.0, 0.5 * (1 + n))
end
defp sqrt(n, error, prev, new) when abs(new - prev) > error do
sqrt(n, error, new, 0.5 * (new + n / new))
end
defp sqrt(_, _, _, new), do: new
def pow(base, exponent) do
base ** exponent
end
def cbcrt(x) do
x ** (1 / 3)
end
end
```
```elixir
ExUnit.start(auto_run: false)
defmodule HeronMethodTest do
use ExUnit.Case, async: false
describe "Testing the square root function" do
test "the square root of 9 is 3.0" do
assert HeronMethod.sqrt(9) == 3.0
end
end
describe "Testing the power function" do
test "3 raised to the power of 2 is 9" do
assert HeronMethod.pow(3, 2) == 9
end
end
describe "Testing the cubic root function" do
test "the cubic root of 27 is 3.0" do
assert HeronMethod.cbcrt(27) == 3.0
end
test "the cubic root of 64 is 4.0" do
assert_in_delta HeronMethod.cbcrt(64), 4.0, 0.1
end
end
end
ExUnit.run()
```
```elixir
HeronMethod.sqrt(16)
```
