Similarly, this NASA blog post has some fun facts about the precision of pi that JPL uses in its calculations:

https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimal...

* JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793.

* How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom (the simplest atom)? The answer is that you would need 39 or 40 decimal places.

So if he'd only had interplanetary probes, غیاث الدین جمشید کاشانی‎ Ghiyās-ud-dīn Jamshīd Kāshānī could in principle have navigated them to the proper accuracy in 1424.

By 1596 Ludolph van Ceulen had 20 digits, and even more by the time he designed his tombstone: https://upload.wikimedia.org/wikipedia/commons/e/e8/Monument...

39 or 40 decimal places would have to wait until 1699.

https://en.wikipedia.org/wiki/Chronology_of_computation_of_π

Note that 3.141592653589793 is the shortest decimal representation for the closest double precision float to pi.

Is that 2 or 3 dimensions?

As many dimensions as you like, you would use one coordinate for each dimension.

well, 2 dimensions of 64 bits is 128 bits, while 3 dimensions of 64 bit precision is 192 bits... so mm precision to pluto is along 1 dimension I take. I just wasn't sure of the magnitude we were talking.

The precision doesn’t change when you change the number of dimensions.

If you are using a 64-bit float, then you have 53 bits of precision in 1D, 53 bits of precision in 2D, and 53 bits of precision in 3D. The precision doesn’t change as you add or remove dimensions.