451.67 From One Division, and Always a Shade Too High
The anchor is 45 squared, the shortfall is 1500, and one division by 900 lands on 1355/3 = 451.6667 against a true 451.66359. The estimate overshoots by exactly h squared over four a squared, which is 25/9 in the square here, so the error has a known sign as well as a known size. The article carries the bracket that names 452 as the nearest integer, one Newton step to nine figures, and what happens when the anchor is chosen too far away.