The circumference of the Earth has been measured to be $40,075 \,\pu{km}$, which is only $21 \,\pu{km}$ from $40,096 = 2^{12}$. For reference, $40,075 \approx 2^{11.992}$. This is probably a strange coincidence, but originally a meter was set to be $1/10,000,000$-th of the distance from the North Pole to the Equator, so maybe there is a mathematical explanation.
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34$\begingroup$ $2^{12}$ is 4096 not 40,096 $\endgroup$– uhohCommented Apr 24, 2022 at 23:04
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3$\begingroup$ @uhoh Is it a coincidence that your name perfectly fits to the comment $\endgroup$– glinda93Commented Apr 26, 2022 at 6:23
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1$\begingroup$ So what is that in light years? Still a coincidence? $\endgroup$– AtmosphericPrisonEscapeCommented Apr 27, 2022 at 0:44
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2 Answers
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Well, as others have pointed out we're a little off from $2^{12}$ kilometers. However, there is no coincidence that our world's circumference is close to $40000$ kilometers. From Wikipedia:
The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's circumference is approximately 40000 km.
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9$\begingroup$ Additional comment on this: another value that is not a coincidence is 21600=360*60 nautical miles, since the nautical mile originally measured a minute = 1/60 degree of latitude (or longitude at equator) $\endgroup$ Commented Apr 25, 2022 at 18:34
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There's something wrong with your math, $2^{12} \ = \ 4096$:
$2^x \ = \ 40\ 000$
$\therefore x\log2 \ = \ \log\ 40\ 000$
$\therefore x \ = \ \frac{\log\ 40000}{\log\ 2}$
$\therefore x \ = \ 15.28771$
Thus, $2^{15.28771} \ = \ 40\ 000$
