In Memoirs of a Geisha, how does Mameha work as a foil to Sayuri? In other words, how does the relationship between them illuminate the meaning of...

In Memoirs of a Geisha, Mameha may be
considered a foil to Sayuri early in their relationship because Mameha is all that
Sayuri hopes (and needs) to be.  Mameha agrees to take on Sayuri as her apprentice
mostly because Mameha knows that her rival Hatsumomo is desperately trying to ruin
Sayuri's career as a geisha.  Mameha is not as beautiful as Hatsumomo; however, she is
much more elegant and revered, particularly because she is high-earning on account of
her danna.  At this point, Sayuri, although she has potential, is still awkward and
immature.  Mameha teaches Sayuri the nuances of being a geisha and the social reality
that comes with the position.  Mameha's experience and intelligence stand in contrast to
Sayuri's naivete, and in this way, Mameha serves as Sayuri's foil.  Eventually, Sayuri
embodies the qualities that make Mameha successful, and Sayuri then becomes popular. 
The bond between the two women has driven this success, and this is one of themes of the
novel.