Integer triangle we today use the term Heronian triangle; Somos uses it to refer to triangles whose ratios of sides are rational; Conway and Guy define a rational triangle as one with rational sides and rational angles measured in degrees—in which case the only rational triangle is the rational-sided equilateral triangle. There are various general properties for an integer triangle, given in the first section below. All other sections refer to classes of integer triangles with specific properties. Any triple of positive integers can serve as the side lengths of an integer triangle as long as it satisfies the triangle inequality: the
Euler angles from −1 to 1, and let "β" = arccos("z"). Other properties of Euler angles and rotations in general can be found from the Geometric algebra(GA). GA is a higher level abstraction, in which the quaternions are an even subalgebra. The principal tool in GA is the rotor formula_42 where formula_43angle of rotation, formula_44rotation axis (unitary vector) and formula_45pseudoscalar (trivector in formula_46) It is possible to define parameters analogous to the Euler angles in dimensions higher than three. The number of degrees of freedom of a rotation matrix is always less than the dimension of the matrix squared. That is, the