Estimation quiz!

[Albert Chan]

(08-07-2020 09:03 AM)Thomas Okken Wrote:  My reasoning is that while traveling at a certain compass heading, the ratio between the total distance traveled and the distance traveled north is constant (although it now looks to me like the value of that constant that I figured, sqrt(6-sqrt(2))/2, is wrong, and the actual value is slightly greater). And since NNW is only 22.5° from N, that ratio is not much greater than one.

Is the ratio sec(22.5°) ?

cos(22.5°)^2 = (1 + cos(45°))/2 = (2+√2)/4

→ L = pi*R / cos(22.5°) = pi*R * 2/√(2+√2) ≈ 20000 km * 1.0824 = 21648 km