Three, (50 points) Find the smallest positive integer $t$, such that for any convex $n$-gon $A_{1} A_{2} \cdots A_{n}$, as long as $n \geqslant t$, there must exist three points $A_{i} 、 A_{j} 、 A_{k}(1 \leqslant i<j<k \leqslant n)$, such that the area of $\triangle A_{i} A_{j} A_{k}$ is no more than $\frac{1}{n}$ of the area of the convex $n$-gon $A_{1} A_{2} \cdots A_{n}$.
Three, first prove a lemma.
Lemma For any convex hexagon $A_{1} A_{2} \cdots A_{6}$, there exists $1 \leqslant i\frac{S}{k+1}$, then
$S_{\text {pentagon } A_{1} A_{2} \cdots A_{k}}<S-\frac{S}{k+1}=\frac{k S}{k+1}$.
By the induction hypothesis, there must be $1 \leqslant i<j<r \leqslant n$, such that $S_{\triangle A_{i} A_{j} A_{1}} \leqslant \frac{1}{k} \cdot \frac{k S}{k+1}=\frac{S}{k+1}$.
The conclusion holds.
In summary, the minimum value of $t$ is 6.
(Feng Yuefeng, Shenzhen Senior High School, 518040)