Reuleaux triangle any curve of given constant width. This area is where "s" is the constant width. One method for deriving this area formula is to partition the Reuleaux triangle into an inner equilateral triangle and three curvilinear regions between this inner triangle and the arcs forming the Reuleaux triangle, and then add the areas of these four sets. At the other extreme, the curve of constant width that has the maximum possible area is a circular disk, which has area formula_2. The angles made by each pair of arcs at the corners of a Reuleaux triangle are all equal to 120°.
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