Now, i have a geometric question about what the authors write: in sec 1.1.2 they say that the following logo code:

TO ARCR R DEG REPEAT DEG FORWARD R RIGHT 1

produce a circular arc as output, having "DEG" degrees and "R" radius; and that it's true, actually; if DEG = 180 the arc is a semicircumference and so on...

But, the "R" in the code is the single step forward the turtle does in its path so i can't understand how this R can be seen as the radius of the circular arc. Any hint is very appreciated.

It is true that R specifies the radius of the arc, but it is not a measure of the radius of the arc: If R is small the arc will have a small radius If R is larger the arc will have a larger radius But R is not the length of that radius. Daniel