111,111.1 meters is reliably 1 degree of latitude
The metre was re-defined[0] in 1791 as one ten-millionth of the quarter-meridian, or ninety degrees of arc, through Paris.<p>It then follows straightforwardly that 1° ≡ 1/90 × 10^7 m = 111 111.111... m.<p>It also follows straightforwardly that the circumference of Earth is approximately forty million metres, or 40 000 km.<p>[0]: Edit: the initial definition of the metre was the length of a seconds pendulum, i.e. the length of a pendulum with a period of two seconds.<p>Given the formula <i>T</i> ≈ 2<i>π</i>√(<i>L</i>/<i>g</i>), letting <i>T</i> = 2 and <i>L</i> = 1, we have 1 = <i>π</i>√(1/<i>g</i>), and 1 = <i>π</i>²/<i>g</i>.<p>This is also why <i>g</i> is so close to the value of π²—because the former is expressed in units that are <i>defined</i> that way. It's also not a coincidence that 1 cm³ of water is 1 g—for a long time, that was the <i>definition</i> of the gram.