Integer triangle side of the formula are integers it follows that all integer triangles must have an integer value of "16T" and "T" will be rational. By the law of cosines, every angle of an integer triangle has a rational cosine. If the angles of any triangle form an arithmetic progression then one of its angles must be 60°. For integer triangles the remaining angles must also have rational cosines and a method of generating such triangles is given below. However, apart from the trivial case of an equilateral triangle there are no integer triangles whose angles form either a geometric or
Equilateral triangle segments PD and DA with DA having length "z" and PD having length "y", then which also equals formula_41 if "t" ≠ "q"; and which is the optic equation. There are numerous triangle inequalities that hold with equality if and only if the triangle is equilateral. An equilateral triangle is the most symmetrical triangle, having 3 lines of reflection and rotational symmetry of order 3 about its center. Its symmetry group is the dihedral group of order 6 "D". Equilateral triangles are the only triangles whose Steiner inellipse is a circle (specifically, it is the incircle). The integer-sided equilateral triangle