Euler's rotation theorem
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In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the body remains fixed, is equivalent to a single rotation about so
Figure 1: Blue great circle on sphere transforms into red great circle when rotated about diameter through O.
Figure 2: Arcs connecting preimage α and image a of A with bisector AO of the angle at A.
Figure 3: O goes to O′, but O′ must coincide with O.
Quaternion
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In mathematics, the quaternions form a number system similar to the complex numbers, with the usual arithmetical operations of addition, subtraction, multiplication, and division, but with four real-n
Quaternion plaque on Brougham (Broom) Bridge, Dublin, which reads: Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication i2 = j2 = k2 = i j k = −1 & cut it on a stone of this bridge
The Julia sets and Mandelbrot sets can be extended to the Quaternions, but they must use cross sections to be rendered visually in 3 dimensions. This Julia set is cross sectioned at the x y plane.