Today is a birthday of a very good friend of mine, M.D., a founder and a passionate developer of the Natural Math website. As a birthday gift she asked to tell a story related to ‘mathematics in your life’. Such requests usually throw me in a panic state of mind, since “What on Earth I can tell on mathematics?” At that very moment, though, I was sorting out the pictures I made during our summer trip to Switzerland, and suddenly I bumped into one of them, from my epic summit to Mt. Ferret [it is described here in Russian, I have to translate it to English one day] – see it also above.
The ‘mathematical’ question here is – what do you think is a degree of this wall? Perhaps, position from which I made this picture does not give a chance for accurate, so let’s have a look at the side view (the above slope is the right one).
40 degrees? 45 degrees maximum, you say. Not that much even.
When I was crawling down from the top (following the route roughly drawn above), I felt it is next to a vertical! This reminds me an old joke well-known among climbers:
45 degrees – Vertical
50 degrees – Absolutely vertical, sir!
55 degrees – Overhanging!!
How comes that when we evaluate the steepness of the slopes from a distance (i.e., similar to the figures drawn in the notebook), they look much flatter compared to a full-flesh measurement, when entire body is involved, like when we climb, laddering, even simply walk over a slope? There seem to be a very different mathematics when our entire body involved, not only eyes.