## The small cousines of Buggles

Today, we will meet the small cousines of the buggles: the turtles. In fact, turtles are much olders than the buggles. They were invented in the 70's by a scientific from MIT called Seymour Papert to help teaching programming, and the buggles are a variation on the idea invented by Lyn Turbak from Wellesley College later.

Turtles are thus a bit like buggles, but smaller. Just like buggles, you can order them to move forward, to turn, to move backward, etc. Just like buggles, they leave a line on their path when they move (but the line is much smaller).

The main difference is that where buggles can only move of right angles, turtles can move of any arbitrary angles specified by a real number (a double). This gives them much more liberty in their movings. The buggles can do several other tricks, like reading and writting messages, picking or dropping objects, and there is sometimes walls in their worlds (but all this is completely above the capacities of turtles).

From a practical point of view, most of the methods you knew about buggles still work with turtles, with some minor adaptations. In particular, the `forward()` method takes the amount of steps to do not as an integer, but as a [!python]point number[/!][!java|scala|c]double[/!] (see "About this world" for more details).

[!java|scala|c]

### Doubles? But what is it?

It's simply a point number. Example:

    double x = 3.72;
    x + 1.234 // Value = 4.954
    x + 2. // Value = 5.72 (2. means 2.0)
    x + 2 // [!java|c]Value = 5.72 (2 automatically converted to 2.0)[/!][!scala]Type error (+ operator don't mix Double and Int); manual conversion mandatory[/!]
    x * 2. // Value = 7.44
    x / 2. // Value = 1.86
    [!java|c](int) x[/!][!scala]x.asInstanceOf[Int][/!] // Value = 1 (“casting to int”, converted to integer by truncating)
    Math.round(x) // Value = 2 (1.86 rounded to nearest integer)
    Math.floor(x) // Value = 1 (1.86 rounded toward minus infinity)
    Math.floor(-5.12) // Value = -6 (rounded toward minus infinity)
    Math.ceiling(x) // Value = 2 (1.86 rounded toward plus infinity)
    Math.ceiling(-5.12) // Value = -5 (rounded toward plus infinity)
    [!java|c](double) 17[/!][!scala]17.asInstanceOf[Double][/!] // Value = 17.0 (“casted to double”, converted to double)

[/!]

### Traguardo dell'esercizio

Even if this is the first exercise on the recursivity lesson, the code you have to write is not recursive. The goal is to get familiar with the turtle world before getting on serious matter.

You must reproduce a simple geometrical painting constituted of four 100 steps long squares (see the objective world for more details). It is obviously a good idea to write a method to draw a square, and then use it in your code.