  Clifford's geometric algebra has enjoyed phenomenal development over the last
60 years by mathematicians, theoretical physicists, engineers and computer
scientists in robotics, artificial intelligence and data analysis, introducing
a myriad of different and often confusing notations. The geometric algebra of
Euclidean 3-space, the natural generalization of both the well-known
Gibbs-Heaviside vector algebra, and Hamilton's quaternions, is used here to
study spheroidal domains, spheroidal-graphic projections, the Laplace equation
and its Lie algebra of symmetries. The Cauchy-Kovalevska extension and the
Cauchy kernel function are treated in a unified way. The concept of a
quasi-monogenic family of functions is introduced and studied.
