Instinctively, you might think that adding one person to a circle composed of thousands will cause each of them to step back less than an inch so that the new comer fits in the circle.

Counterintuitively, it's not the case, because the perimeter and the radius of a circle are proportional :

P = 2 * π * R

Thus, if you increase the perimeter by 5 ft 10 in (which roughly is the stature of a man), you have to increase the radius by (5 ft 10 in)/(2 * π) to keep the circle consistent.