An equilateral triangle may have integer sides with three rational angles as measured in degrees, known for the only acute triangle that is similar to its orthic triangle (with vertices at the feet of the altitudes), and the only triangle whose Steiner inellipse is a circle (specifically, the incircle). The triangle of the largest area of all those inscribed in a given circle is equilateral, and the triangle of the smallest area of all those circumscribed around a given circle is also equilateral. It is the only regular polygon aside from the square that can be inscribed inside any other regular polygon.
An equilateral triangle may have integer sides with three rational angles as measured in degrees known for the only acute triangle that is similar to its orthic triangle (with vertices at the feet of the altitudes) and the only triangle whose Steiner inellipse is a circle (specifically the incircle) The triangle of the largest area of all those inscribed in a given circle is equilateral and the triangle of the smallest area of all those circumscribed around a given circle is also equilateral It is the only regular polygon aside from the square that can be inscribed inside any other regular polygon