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In this paper, we consider the intrinsic Diophantine approximation on thetriadic Cantor set $\mathcal{K}$, i.e. approximating the points in$\mathcal{K}$ by rational numbers inside $\mathcal{K}$, a question posed by K.Mahler. By using another height function of a rational number in $\mathcal{K}$,i.e. the denominator obtained from its periodic 3-adic expansion, a completemetric theory for this variant intrinsic Diophantine approximation is presentedwhich yields the divergence theory of Mahler's original question.

Mahler's question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory