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I think this is the appropriate SE to ask about the following, but feel free to tell me otherwise.

As I remember it, the meter is a "human" or "natural" length, because it was choosen to be exactly 1/40000th of Earth's circumference.

A few minutes ago, I was thinking about the centimeter and how unnatural it is. It is quite small and even though I am French, I think the centimeter does not come naturally as a unit of measurement.

Anyway, I had this idea. What if the meter had been defined based on the diameter of the planet instead of its circumference?

I had a strange intuition about this.

Anyway, if the circumference is taken to be exactly 40000 meters (real circumference is slightly longer), diameter is 40000 divided by pi, i.e. 12732.39 meters.

And now, let say I use this diameter to define my new meter. For example, I could say the diameter is exactly 10000 new meters.

That would make the new centimeter slightly longer, i.e. 1.2732 centimeter.

And I find this VERY intriguing because, if I simply multiply this by 2, I get 2.54 centimeters which is... an inch!

Is this a mere coincidence or was the circumference choosen over the diameter on purpose to avoid getting back to the imperial system?

Edit: Jean Picard determined Earth radius in 1669. So for the ones arguing it was obvious to use the circumference, as obvious as anything looked in retrospect, I need better arguments.

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  • $\begingroup$ I remember as I was a child. I found a tape line by my grandmother. But... there was some very uncommon with it: the scales were too long. I asked my grandma, wtf is it. She laughed and explained, that it is in inch. And.. honestly, my this "wtf" attitude did not change since then. The whole world uses metric units, except our most wonderful USA & UK... I believe, we should wait until - possibly with the help of the TOE theory - we will have an exact measure of the Planck units, and then use them; until then the metric is the best what we have. $\endgroup$
    – peterh
    Oct 9, 2020 at 14:23
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    $\begingroup$ I give you a "leave open" vote, but please try to reformulate your question to be about the History of the Science (& Math). It has actually nothing to do about HSM, but the answers in the future might have, this is my reason. $\endgroup$
    – peterh
    Oct 9, 2020 at 14:27
  • $\begingroup$ I rewrote the question. $\endgroup$
    – Winston
    Oct 9, 2020 at 16:56

1 Answer 1

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If one decides to choose some measurement of the Earth as a standard of length, circumference has one serious advantage: it is easier to measure directly.

The Earth is not an exact sphere. And the meter was originally defined as 1/40,000 of Paris meridian (not of the equator, not of some other meridian). And this meridian was carefully measured. How would you propose to measure a "diameter"? Which diameter? The distance, say from Paris to the antipodal point by a straight line through the Earth? How would you measure this?

Speaking of what units are "human" or convenient is a matter of opinion. Americans think that old British are "human" and convenient, other people, including the British think otherwise.

And that 4/$\pi$ is approximately 1/2 inches in centimeters is a pure coincidence, of course. The ratio of inch to centimeter has no relation to $\pi$.

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    $\begingroup$ Your last paragraph, unless you add references to it is merely your opinion. Now regarding measurements, are you saying the entire meridian was measured from South pole to North pole, by land and by sea? $\endgroup$
    – Winston
    Oct 9, 2020 at 16:52
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    $\begingroup$ Entire meridian was not actually measured. Only some parts of it, and this was combined with a model of the theoretical shape of this meridian. They measure distances on land only. There is no way to measure a distance in the sea with required accuracy. How exactly the measurement was done is nicely described in the novel Jules Verne, The Adventures of Three Englishmen and Three Russians in South Africa. $\endgroup$
    – Alexandre Eremenko
    Oct 9, 2020 at 17:56
  • $\begingroup$ My last paragraph is based on common sense:-) $\endgroup$
    – Alexandre Eremenko
    Oct 9, 2020 at 18:00
  • $\begingroup$ Common sense, or alleged one, has nothing to do with political choices that have surrounded time and space measurements in history. Now if you allow me to limit this discussion to facts, Earth radius was determined by Jean Picard in 1669. On the other hand, Paris meridian measurement was still in progress in 1792 when the French academy commissioned Delambre and Méchain exploration. So your answer is rather based on flawed intuition. $\endgroup$
    – Winston
    Oct 9, 2020 at 19:06
  • $\begingroup$ And basically your description of the "measurement" of the meridian, that you claimed in your answer to be more real than measuring a diameter (see Picard), is not a measurement but a deduction. $\endgroup$
    – Winston
    Oct 9, 2020 at 19:11

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