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The US Survey foot is defined as 1200/3937 and the international survey foot is exactly 0.3048 meters. When taking data into applications such as Autodesk Civil 3D, you need to transpose Lat/Long GIS data into a flat Cartesian coordinate system. For example, X,Y values in California start in X=6,000,000 Y=2,000,000 which starts eating up floating point precision. Because 1200/3937 doesn't divide cleanly, you'll end up with varying values depending on where you cut off your precision. That's why Highly Composite Numbers are critical.

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> For example, X,Y values in California start in X=6,000,000 Y=2,000,000 which starts eating up floating point precision.

Why isn't the origin at (0, 0)? It's like saying your ground is at 1,532 volts: You're defining the coordinate system, why make work for yourself?

One reason for the large numbers is that so when data is imported into a drawing it is immediately obvious whether it shares the same coordinate system. If multiple sets of points from different disciplines are imported into the program then the draftsman knows whether the coordinate systems are the same by visual inspection (to a rough degree).

Also because nobody wants to use negative numbers or have the possibility of a negative number showing up.

> “... nobody wants to use negative numbers”

It’s hard to understand these priorities. An unholy mix of base-12 and base-16 is fine, but negative numbers are too difficult to work with?

When you’re working with a couple guys who probably went on a bender last night out in the middle of nowhere with no cell service and a piece of shit walkie talkie that has spotty transmission you sometimes end up having to throw up hand signs to signal northing and easting values. There’s no hand signal for negative. So yeah, negative numbers are hard to work with in that case.

You lost me there with the 6 million X coordinates in California. 6 million whats starting from where? It can't be feet from the prime meridian, that's not far enough.

I've been scraping my county assessor's GIS database for property outlines and I noticed that the coordinates are huge, as you mentioned. I assumed it was just some fanciful origin but I'd love to know the story.

Yeah, it's feet measured east and north of an arbitrary point southwest of everything in the state. There is an actual point inside the state used as a base but they set up a false easting and false northing by subtracting a large round number such that the origin of the coordinate system is southwest of everything in the state. A lot of things in surveying are designed such that the math is easier for people working in the field to reliably get correct.

Probably a https://en.wikipedia.org/wiki/State_Plane_Coordinate_System zone.

Typically designed to have similar error across the whole area and things like that.

No number has all factors in. Better to work in a way that handles uneven fraction properly than sweep the problem under the rug.

Well, you could just use the first few primes multiplied together as a base. 2 * 3 gives you base6, 2 * 3 * 5 gives you base30. Neither commonly used system does that, base12 uses 2 twice, base10 skips 3. So from a divisibility PoV both are lacking. But arithmetics is base10 anyways, since thats close to the average number of fingers for humans, so...

Use fixed point?

You'll need rational numbers, not just fixed point, since it's a recurring decimal. (Unless it's a non-recurring decimal in base 2, I guess, but even then, the moment you do something with it you'll probably need a rational representation.)

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