Quaternions and spatial rotation of a circle representing a particular rotation angle will be half of the angle represented by that rotation, since as the point is moved from the north to south pole, the latitude ranges from zero to 180 degrees, while the angle of rotation ranges from 0 to 360 degrees. (the "longitude" of a point then represents a particular axis of rotation.) Note however that this set of rotations is not closed under composition. Two successive rotations with axes in the "xy" plane will not necessarily give a rotation whose axis lies in the "xy" plane, and thus cannot be represented
Allied Masonic Degrees with the presiding officer being denominated 'Sovereign Master." The Councils are given wide discretion as to choose how frequently they meet and what programs to pursue. Generally speaking, Councils study or discuss Freemasonry in some way at each meeting. The Grand Council has created some internal honors, the most notable being "Knight Grand Cross". The degrees conferred in the United States are: In Canada, the degrees conferred are: Optional degrees are: Royal Order of the Red Branch of Eri: "Fun" degrees: (given at the Annual Assembly) Allied Masonic Degrees The Allied Masonic Degrees (AMD) are a series of Masonic degrees