  The three gap theorem was originally a conjecture by Steinhaus, who asserted
that there are at most three distinct gap lengths in the fractional parts of
the sequence {\alpha},{2}{\alpha},{\cdots},{N}{\alpha} for any integer {N} and
real number {\alpha}. This conjecture has been proved by many different
methods, and extended to higher dimensional cases. For the three gap theorem,
what is the frequence of two gaps or three gaps? On the basis of Ravenstein's
work, this paper studies the frequency of the three gap theorem through cake
model. We show that for almost all {\alpha\in (0,1)\backslash \mathbb {Q}} in
the sence of the Lebesgue measure, the frequency of the two gaps is {0}, in
other words, the frequency of the three gaps is {1}. The proof makes full use
of the continued fraction expansion of {\alpha}, as well as partial results in
the Diophantine approximation. Finally, we illustrate that two gaps occur with
a frequency of {0}.
