The identification of this point was posed as a challenge by Pierre de Fermat to Evangelista Torricelli. For this reason, the point is usually known as the Fermat point or the Fermat-Torricelli point.

The usual construction of this point is, given the triangle ABC, to construct a point D, on the opposite side of BC to A, such that BCD is equilateral. The Fermat/Fermat-Torricelli/Steiner point is the intersection of AD with the circumcircle of BCD.