Mathematical

This is part of the complete Exercises in Song cycle being released on this site.

"Mathematical" is a bonus exercise, not to be found in Raymond Queneau's original Exercices de Style nor in the translations.

To be sung to the tune of "Show Me The Way To Go Home". More information here.

Consider an oikioid
At the origin; denote it "O".
A random walk can place you, given enough time,
Anywhere you'd want to go.

Of these points, pick just three;
Call them "A", and "B", and "C".
One can prove the plane containing all these
Can extend infinitely.