Mental arithmetic in the hills part 1: Grasmoor

We climbed Grasmoor by the improbably steep Red Gill.It was a lot further than it looked from the bottom. I resorted to the little finger method to try to work out how far we'd gone. No calculator with me so this is how I did it in my head: My little finger is worth a 1 degree angle. There are 360 degrees in a circle which is 2 pi radians. So 360 degrees is the same as 6.28 radians. I degree is worth 6.28/360 radians. I said 628/360 is approximately 2 so the 1 degree is approximately 0.02 radians. If you enlarge the lower picture you can see our car park to the right of my finger. The car takes up about 1/10th of my finger so a car is worth about 0.002 radians. A car is about 2 metres long. Arc length = radius x angle in radians. Thus distance to the car (the radius) = arc length/angle. The car acts as the arc length in this sector so distance from car = 2/0.002. Dividing by 0.2 is the same as x5. So dividing by 0.002 is the same as x500. Distance to car = 1000m. By comparing with neighbouring hills I knew that our altitude was about 600m so distance is about right!