Spoiler below! The relationship between radius and circumference is linear (C = 2pi * r). When the circumference is increased by 1, the radius increases by 1/2

Spoiler below! The relationship between radius and circumference is linear (C = 2pi * r). When the circumference is increased by 1, the radius increases by 1/2pi. Therefore, the gap has the same size. Let g be the gap. Then C + 1 = 2pi * (r + g) 2pi * r + 1 = 2pi * (r + g) r + 1 / 2pi = r + g 1 / 2pi = g