  It will not be an exaggeration to say that R A Fisher is the Albert Einstein
of Statistics. He pioneered almost all the main branches of statistics, but it
is not as well known that he opened the area of Directional Statistics with his
1953 paper introducing a distribution on the sphere which is now known as the
Fisher distribution. He stressed that for spherical data one should take into
account that the data is on a manifold. We will describe this Fisher
distribution and reanalyse his geological data. We also comment on the two
goals he set himself in that paper, and how he reinvented the von Mises
distribution on the circle. Since then, many extensions of this distribution
have appeared bearing Fisher's name such as the von Mises Fisher distribution
and the matrix Fisher distribution. In fact, the subject of Directional
Statistics has grown tremendously in the last two decades with new applications
emerging in Life Sciences, Image Analysis, Machine Learning and so on. We give
a recent new method of constructing the Fisher type distribution which has been
motivated by some problems in Machine Learning. The subject related to his
distribution has evolved since then more broadly as Statistics on Manifolds
which also includes the new field of Shape Analysis. We end with a historical
note pointing out some correspondence between D'Arcy Thompson and R A Fisher
related to Shape Analysis.
