[ojnabieoot]

I don’t think there’s anything here for mathematicians. The only nontrivial fact in the paper is that the approximation works well in medical practice (which is not something that Leibniz or Newton would have been able to tell you since there could be complicated biological factors confounding it - what if the ‘real curve’ has a bunch of spikes that don’t show up in measurements?).

However, the original paper really is incomplete because of its seeming ignorance of the real “trapezoidal rule.” It really needs a discussion along the lines of “the trapezoid rule from ordinary calculus can be used by diabetes practitioners with surprising accuracy” and explained that sources of error, discontinuity, etc., aren’t likely to affects the approximation.

But don’t worry about M.M. Tai’s feelings too much :) The paper is almost 30 years old and it’s world-famous for the silly error, Tai has already been throughly roasted.