$\begingroup$

The circumference of the Earth has been measured to be $twoscore,075 \,\pu{km}$, which is only $21 \,\pu{km}$ from $40,096 = 2^{12}$. For reference, $40,075 \approx 2^{11.992}$. This is probably a foreign coincidence, but originally a meter was ready to be $1/x,000,000$-th of the altitude from the North Pole to the Equator, then maybe in that location is a mathematical explanation.

  • geodesy

Fred's user avatar

Fred

21.9k 5 gold badges 45 argent badges 87 bronze badges

asked Apr 24 at 13:53

LMol's user avatar

$\endgroup$

3

  • $\begingroup$ $2^{12}$ is 4096 not 40,096 $\endgroup$

    Apr 24 at 23:04

  • $\begingroup$ @uhoh Is information technology a coincidence that your proper name perfectly fits to the comment $\endgroup$

    Apr 26 at half dozen:23

  • $\begingroup$ So what is that in low-cal years? Still a coincidence? $\endgroup$

    Apr 27 at 0:44

2 Answers 2

$\begingroup$

Well, as others have pointed out nosotros're a little off from $2^{12}$ kilometers. However, there is no coincidence that our world'southward circumference is close to $40000$ kilometers. From Wikipedia:

The metre was originally defined in 1793 as one 10-millionth of the distance from the equator to the North Pole forth a great circle, then the Earth'southward circumference is approximately 40000 km.

answered April 24 at xviii:08

Oscar Lanzi's user avatar

$\endgroup$

ane

  • $\begingroup$ Additional annotate on this: another value that is not a coincidence is 21600=360*lx nautical miles, since the nautical mile originally measured a infinitesimal = 1/60 degree of breadth (or longitude at equator) $\endgroup$

    Apr 25 at 18:34

$\begingroup$

There'southward something wrong with your math, $2^{12} \ = \ 4096$:

$two^x \ = \ forty\ 000$

$\therefore x\log2 \ = \ \log\ forty\ 000$

$\therefore ten \ = \ \frac{\log\ 40000}{\log\ 2}$

$\therefore x \ = \ 15.28771$

Thus, $2^{xv.28771} \ = \ 40\ 000$

Federico's user avatar

answered April 24 at 17:38

Fred's user avatar

$\endgroup$

0