Learn Icelandic: Ég er búinn að teikna ferninginn.

In Icelandic, the construction vera búinn að plus an infinitive is the most natural way to say you have completed an action. While hef teiknað (have drawn) is grammatically correct, er búinn að teikna is much more common in everyday speech to emphasize that the task is finished.

Why does the word búinn have two Ns here, and does it change depending on who is speaking?

Yes, it changes! In this phrase, búinn functions as an adjective and must match the subject in gender and number. Here, the speaker (Ég) is masculine. A female speaker would use the feminine form and say Ég er búin að teikna with just one N.

Why is the word for 'the square' ferninginn instead of ferningurinn?

The verb teikna (to draw) requires its direct object to be in the accusative case. The basic masculine word for a square is ferningur, which drops the '-ur' ending in the accusative to become ferning. When you attach the masculine accusative definite article ('the'), it becomes ferninginn.

Could I use ferninginn to say I drew a town square?

No, the word ferningur refers specifically to the geometric shape. If you wanted to say you drew a town square or a public plaza, you would use the word torgið instead.