On Growth and Form

by D'Arcy Wentworth Thompson

R′ = a e^{(θ + 2π)cot α} ,

r = λa e^{θ cot α} = a e^{(θ − β)cot α} ,

and

r′ = λa e^{(θ + 2π)cot α} = a e^{(θ + 2π − β)cot α} .

Now in the three cases (a, b, c) represented in Fig. [278], it is plain that r′

R, respectively. That is to say,

λa e^{(θ + 2π)cot α}

a e^{θ cot α} ,