_{nat}, representing the Inside Region, the increase in angle follows an inverse pattern. That is to say, instead of the series 1, 2, 3, 4,... , it would be:

1, (1 + 1/2), (1 + 1/2 + 1/3), (1 + 1/2 + 1/3 + 1/4), ...

The physical effect of this diminishing nature of the angular increment in the Inside Region is to pack infinite angle in the finite Cartesian circle of 2π radians. Once again, an implication not foreseen by common sense!

2. There is also a dimensional implication. In the Outside Region multiplying two orthogonal lines (m * m) produces an area (m

^{2}). Further multiplying the area by an orthogonal line produces volume (m

^{3}). In the Inside Region, an angle (θ) sweeps an area (A = 0.5 * θ * r

^{2}), and a two-dimensional angle (θ

^{2}) sweeps a four-dimensional hypervolume (H = 0.25 * θ

^{2}* r

^{4}).

Bruce, Nehru