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The metre was re-defined[0] in 1791 as one ten-millionth of the quarter-meridian, or ninety degrees of arc, through Paris.

It then follows straightforwardly that 1° ≡ 1/90 × 10^7 m = 111 111.111... m.

It also follows straightforwardly that the circumference of Earth is approximately forty million metres, or 40 000 km.

[0]: Edit: the initial definition of the metre was the length of a seconds pendulum, i.e. the length of a pendulum with a period of two seconds.

Given the formula T ≈ 2π√(L/g), letting T = 2 and L = 1, we have 1 = π√(1/g), and 1 = π²/g.

This is also why g is so close to the value of π²—because the former is expressed in units that are defined that way. It's also not a coincidence that 1 cm³ of water is 1 g—for a long time, that was the definition of the gram.

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Given that the second is an older unit [0] than the redefinition of the metre, and defined based on "nice" subdivisions of the day, it would seem that there's still a bit of a coincidence there.

Since the metre was previously defined by the seconds pendulum, it was entirely defined by the definition of a second and the value of g. From the equations, 1 m = 1 s² × g / π².

While this makes g ≈ π² straightforward, it seems coincidental that the Earth's circumference was close enough to 40 000 km that the redefinition of the metre was a nice power or 10 without too much change to the metre.

[0]: Late 16th century, based on https://en.wikipedia.org/wiki/Second#Fraction_of_solar_day

Well, it's not much of a coincidence. There are all kinds of constants around us, and one of them is prone to be close to a round number.

If the Earth's circumference wasn't a nice number, people would have chosen another one.

Was the meter based on the length of the pendulum similar to the length of the meter today? This doesn't necessarily say they were similar:

> In 1675, Tito Livio Burattini suggested the term metre for a unit of length based on a pendulum length, but then it was discovered that the length of a seconds pendulum varies from place to place.

https://en.wikipedia.org/wiki/Metre#Pendulum_or_meridian

The period is also not independent of the amplitude. That is only the case of you approximate sin x ≈ x in the differential equation

My understanding (which could be wrong) is that actual clocks use a fancier pendulum than just a weight on the end of a string.

The difference in gravity around the Earth is small enough that the pendulums would be within a couple percent. (Wikipedia claims a measured difference of 0.3% from the time.)

Assuming the second was also quite accurate, the seconds pendulum wouldn't be too far from its current definition given that g ≈ π² to within ~1 % in modern units.

And a 32-bit integer can represent latitude or longitude to an accuracy of around 1 centimeter :D.

Call that a long long.

long lon

At my last job we used lon long

That’s up there with buffalo buffalo buffalo

If you are serious, 32 bit is a more specific term, therefore better.

Can't be serious, because long long is 64 bits on most platforms.

Right, a 64 bit longitude would be a long long long.

‘long long long’ is to long for GCC, but not for the Beatles who may be made to sing it a long long i; // = todo time

Note that the meter is also basically 3 Paris feet, which comes out to about 0.97m (compared to 3 English feet, which is only around 0.91m). They weren't working in a vacuum to derive the most principled or cosmically beautiful unit length, just trying to find a way to define the unit they already used that wasn't "the length of this stick we have over here".

But in practice the meter ended up being "the length of this special metal stick we keep in Paris".

Yeah, because measuring the mean equatorial and longitudinal circumference of the Earth on a line passing through Paris is a pain in the ass.

The meter was also standardized at a weird golden period for units -- we had global trade and travel (and so it was getting inconvenient to have different standard unit length sticks in different countries, let alone cities), we had enough science to have the notion of basing it on physical constants instead of random sticks, but we also weren't yet in a world where precision mattered all that much. You could change the length of your units by 3% and it wouldn't really matter as much it would today, where every bolt and manufactured part would instantly become a nightmare.

It's kind of a shame, because now we could pick so much cooler definitions for our units, because our science is so much better. Take restandardizing the foot as 1 ns * c -- so much more elegant than the mean circumference of the Earth, or an ugly number of wavelengths of a caesium atom. But changing the foot by 1.5% -- half as much as the difference between the meter and 3 Paris feet -- would be devastating today in a way that it wasn't in 1800. Hell, it'd probably be easier to change the definition of a second than the definition of a foot.

I’m surprised that there isn’t GPS coordinate system which is just kilometers. Instead of 360 degrees uses 40,000 km. The real calculation would use the real distances but the approximation is close enough. This means don’t have to do any conversion to distances, at least for metric folks.

One problem with degrees is that hard to convert to useful distances. This tricks help a lot, but it would be better to have no conversion.

The perfect sphere approximation of Earth is not at all close enough for GIS applications. Geoid data (the actual ellipsoid-ish shape with height variance) is an important factor in accurate GIS software.

> ...don’t have to do any conversion to distances...

Are you advocating for the use of Manhattan distances for everything?

https://en.wikipedia.org/wiki/Earth-centered,_Earth-fixed_co...

In a previous life I had to implement conversions between ECEF and WGS84. If you do it, make sure to use at least 64-bit floats, the Earth is so big that 32-bit arithmetic will introduce errors on the order of meters.

You’ve brought memories of dealing with NAD83 (for local maps) and WGS84 (for everything else) crashing back. The error between those is tiny at the distances I was dealing with, but it was enough that it bothered me.

“I’ll just automate this mapping task in Python, how bad could it be?”

- A very-new-to-everything me, years ago.

Do you have an example in mind? A problem that you may encounter, how do you calculate now, and how could you calculate with a GPS system that is just kilometers?

There is a 'metric' coordinate system, it's called EPSG:3857 and uses meters as its units. Although it is not valid close to the poles and can give error of up to 0.6% so it's not useful for when you need high accuracy or to cover the entire globe.

Most places in world also have local coordinate systems that reproject smaller geographic areas to cartesian coordinates with meter units for making easier to work in those areas.

The main difficulty is that for ease of calculation you'd like a cartesian grid, which maps poorly to the spheroid shape of the earth. One solution is UTM https://en.wikipedia.org/wiki/Universal_Transverse_Mercator_... which divides the earth into 60 zones, and then inside each zone you have a cartesian grid with meters as the unit. So a UTM coordinate consists of the zone designator, and then distances in meters from the equator and the zone's central meridian.

There also MGRS https://en.wikipedia.org/wiki/Military_Grid_Reference_System , the NATO military variant of UTM.

Isn't that what gradians do?

360° = 400 gon, so 1 gon = 100 km of arc length

https://en.wikipedia.org/wiki/Gradian#Relation_to_the_metre

The French also applied decimalization to angle measurements, so it's really 1 gon = 100 km, and 1 km is just 1 centigon.

The work to measure the meridian with the highest possible precision was in itself a fascinating multi-year ordeal: https://en.wikipedia.org/wiki/Arc_measurement_of_Delambre_an....

A nice novel about it is Denis Guedj's "La Méridienne". https://en.wikipedia.org/wiki/Denis_Guedj

Why did they change the definition from the length of the pendulum to the circumference of the Earth?

Couple reasons 1) why use seconds when you can just measure a segment of a known distance? 2) pendulums swing faster or slower depending on altitude, 3) Problems with accurate measurement of seconds, swing time etc.

I guess for (1) I would imagine it was easier for an independent group of scientists to accurately measure a pendulum, than to travel all the way to the north pole in a straight line through Paris.

But I guess they were using the stars or something so maybe it's not as hard as I'd imagine. Also (2) and (3) are great points.

> The metre was re-defined[0] in 1791 as one ten-millionth of the quarter-meridian

Doesn't sound like a good idea. Circumference of earth around Paris is not unchangeable.

Exact geographic measurements where the high technology of 18th century. Each society uses the highest precision measurements available to them. Also, plate tectonics were scifi fantasy until 1950's.

The definition has been updated after that. https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_ba...

> Doesn't sound like a good idea

Which is why the CGPM changed the definition of the metre to:

- the length of the International Metre (a 9:1 platinum-iridium bar) in 1889;

- and then to 1650763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum in 1960;

- and finally to the modern definition, the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second in 1983.

This means the realisation of the metre depends on the definition of the second.

This stuff why the SI units system really is a system. Rather than the collection of unrelated units that was used before.

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