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.It then follows straightforwardly that 1° ≡ 1/90 × 10^7 m = 111 111.111... m.It also follows straightforwardly that the circumference of Earth is approximately forty million metres, or 40 000 km.[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.Given the formula T ≈ 2π√(L/g), letting T = 2 and L = 1, we have 1 = π√(1/g), and 1 = π²/g.This is also why g is so close to the value of π²—because the former is expressed in units that are defined that way. It's also not a coincidence that 1 cm³ of water is 1 g—for a long time, that was the definition of the gram.