"I show that in all kinematic situations, π is 4. For all those going ballistic over my title, I repeat and stress that this paper applies to kinematic situations, not to static or geometric situations. I am analyzing the equivalent of an orbit, which is caused by motion and includes the time variable. In that situation, π becomes 4" -- Miles Mathis (inserted attribution)
I pointed out the only redeeming quality in the article you gave. It was an interesting read, but completely wrong, both mathematically and physically. I can prove that he's pretty incompetent at math, but I'll address the more obvious fact: his pseudo-mathematics doesn't have any bearing in the real world. He can show whatever he wants, but he's contradicted by empirical reality. Drive in a circle. Your fuel consumption will be the circumference (pi approx 3.14) divided by your gas mileage, not what you get when pi = 4. Take a string that's 3.2 times the length of another string. You can lay it in an approximate circle such that the other string passes through the center. You clearly don't need a string of length 4.
He actually has no idea what an orbit is; an orbit is not "caused by motion"; it is the motion of whatever particle. He has no clue what he's talking about. None whatsoever.
As an easier thing to understand, and you can verify this empirically, take a car and drive it in a large circle. Measure its speed. Measure how long it takes to get back to the original point. The circumference is not 4 times the diameter. Clearly, pi = 3.14 is valid in kinematics as well.