# Is it a coincidence that the circumference of the Earth in kilometers is almost $2^{12}$?

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.

• $2^{12}$ is 4096 not 40,096
– uhoh
Apr 24, 2022 at 23:04
• @uhoh Is it a coincidence that your name perfectly fits to the comment Apr 26, 2022 at 6:23
• So what is that in light years? Still a coincidence? Apr 27, 2022 at 0:44

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.

• 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) Apr 25, 2022 at 18:34

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, $$2^{15.28771} \ = \ 40\ 000$$