M·Casquilho, IST: invert-add

"Invert and add"

Successively, computes x := x + a ⁄ x.

2025.Feb.19 21:28:16

x

(x > 0)

Initial value, x₁. •

a

(a > 0)

Constant a. •

n

(n ≤ 5e+8)

Number of terms. (If sci., 'IeJ', ¬ 'I+J'.) •

Show values

Shows the coordinates of the graph. •

Computes, successively, x := x + a ⁄ x, and plots x. Conjecture: x tends to √(2 n . a) — independent of the initial value of x.

If the number of terms is n > m, with m = 1000, then it will be rounded (up) to a multiple of m, and the graphic will show m points.

References:

Plate: InvertAdd

• 1916-12-24: Mosteller, Charles Frederick (2006-07-23).