<p>Well, as others have pointed out we're a little off from <span class="math-container">$2^{12}$</span> kilometers. However, there is no coincidence that our world's circumference is close to <span class="math-container">$40000$</span> kilometers. From <a href="https://en.wikipedia.org/wiki/Metre" rel="noreferrer">Wikipedia</a>:</p>
<blockquote>
<p>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.</p>
</blockquote>

CC BY-SA 4.0
2022-04-25T18:34:04.300Z
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)
Max Xiong
CC BY-SA 4.0
2022-04-24T18:08:51.280Z
2022-04-24T18:08:51.280Z
Oscar Lanzi
<p>There's something wrong with your math, <span class="math-container">$2^{12} \ = \ 4096$</span>:</p>
<p><span class="math-container">$2^x \ = \ 40\ 000$</span></p>
<p><span class="math-container">$\therefore x\log2 \ = \ \log\ 40\ 000$</span></p>
<p><span class="math-container">$\therefore x \ = \ \frac{\log\ 40000}{\log\ 2}$</span></p>
<p><span class="math-container">$\therefore x \ = \ 15.28771$</span></p>
<p>Thus, <span class="math-container">$2^{15.28771} \ = \ 40\ 000$</span></p>

CC BY-SA 4.0
2022-04-24T17:38:09.160Z
2022-04-25T09:41:35.140Z
2022-04-25T09:41:35.140Z
Fred
<p>The circumference of the Earth has been measured to be <span class="math-container">$40,075 \,\pu{km}$</span>, which is only <span class="math-container">$21 \,\pu{km}$</span> from <span class="math-container">$40,096 = 2^{12}$</span>. For reference, <span class="math-container">$40,075 \approx 2^{11.992}$</span>. This is probably a strange coincidence, but originally a meter was set to be <span class="math-container">$1/10,000,000$</span>-th of the distance from the North Pole to the Equator, so maybe there is a mathematical explanation.</p>

CC BY-SA 4.0
2022-04-24T23:04:47.053Z
$2^{12}$ is 4096 not 40,096
uhoh
CC BY-SA 4.0
2022-04-26T06:23:47.400Z
@uhoh Is it a coincidence that your name perfectly fits to the comment
glinda93
CC BY-SA 4.0
2022-04-27T00:44:43.723Z
So what is that in light years? Still a coincidence?
AtmosphericPrisonEscape
<geodesy>
Is it a coincidence that the circumference of the Earth in kilometers is almost $2^{12}$?
LMol
# Is it a coincidence that the circumference of the Earth in kilometers is almost $2^{12}$?

(Asked by: username_0 on 2022-04-24)

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.

**Tags:** geodesy

> **Comments:**
> **username_1**: $2^{12}$ is 4096 not 40,096  
> **username_2**: @username_1 Is it a coincidence that your name perfectly fits to the comment  
> **username_3**: So what is that in light years? Still a coincidence?  

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## 2 answers

### Answer by username_4 on 2022-04-24. Score: 37

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](https://en.wikipedia.org/wiki/Metre):

> 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.

> **Comments:**
> **username_5**: 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)  

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### Answer by username_6 on 2022-04-24. Score: 12

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


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