I don't think you have to be a Platonist to allow that numbers that do not exactly correspond to humanly measurable quantities can yet be part of a calculation.

I don't think you have to be a Platonist to allow that numbers that do not exactly correspond to humanly measurable quantities can yet be part of a calculation. Another example would be Binet's formula for Fibonacci n[1], which though it involves Phi, sqrt(5), etc., always evaluates to an integer, given integer n. The existence of these irrationals in Platonic heaven doesn't follow from the formula, which afaik depends only on the usual rules of algebra and logic, though I admit I'm not sure what constructivists make of this type of calculation. 1: see https://r-knott.surrey.ac.uk/Fibonacci/fibFormula.html https://r-knott.surrey.ac.uk/Fibonacci/fibFormula.html or https://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html https://mathworld.wolfram.com/BinetsFibonacciNumberFormula.h... for example