From Lecture 14 ...

h(x) = 1 if point is inside the triangle or on an edge
h(x) = -1 if point is outside the triangle

For a finite conistent Hypothesis Class

$$ m >= \frac{1}{ \epsilon } ( ln | H | + ln ( \frac{1}{\delta}) ) $$

We want 95 percent probablility of being correct so $$ \delta = 0.05$$

The error allowed is 0.15.

We need |H|

There points are from 0 to 99 on the x and the y axis.
There are 100x100 = 10000 Points To pick a triangle you need thre points so there are 10,000 x 9,999 x 9998 = possible triangles ln (10,000 x 9,999 x 9998 ) = 66.2

$$ m >= \frac{1}{ 0.15 } ( 66.2 + ln ( 1/ 0.05)) = 204.1 $$

So m is at least 205.