Square¶
288 words
Being the maths geeks that we are, Jan-Philipp and me ended up discussing certain basic topological things relating to footballs after dinner. [Basically that was about the simple combinatorical fact that when assembling a football out of pentagons and hexagons as it is usually done, you'll need any number of hexagons but a number of pentagons which is a multiple of 12. I could write about it some other day, it's quite accessible.]
Then we ended up talking about triangulations and simplices and how, from a topologist's point of view, triangles seem much more natural than squares (which in a way is a bit strange, as they're not all that different for a topologist to begin with). Even in the 'real' world this is apparent, as graphics cards like to assemble every surface of triangles. Yet, most things built seem to be rectangular. Jan-Phillipp's theory for that was that right angles seem quite natural because of gravity – build a house with walls that are not in a 90° angle with the ground and you'll be in for some trouble to make it stand.
Can that be a good explanation why humanity seems to be obsessed with right angles? What do you think is more natural: a square or a triangle. Which kind of triangle do you consider most 'natural': (a) one with a right angle, (b) an equilateral triangle or (c) a general one? [Just try drawing them and notice that any triangle that you may be inclined to draw will look like it's one of the first two kinds. That's really a problem when trying to make drawings for 'general' triangles.]
This juxtaposition of incoherent thoughts and silly questions was typed while I should've been sleeping.
