Gaukshofdi is a headland along which River Thjorsa runs where it can be forded when the water level is not too high. The headland was named after Gaukur, who lived at Stong in the Thjorsa Valley in the 10th century.According to one of the Sagas, he was killed on the headland by is foster brother, Asgrimur Ellidagrimsson, because he seduced Asgrimur’s sister. In the 19th century, bones and weapons were unearthened at the foothills of the headland and assumed to have belonged to Gaukur.
It is easy to walk to the top of the headland and the view from there towards Mt. Hekla and the surrounding area is very good on a fine day. The main road crossed the headland before it was moved down to the river.