Today we had our first Math lesson in our Mathematics and Art Paper. A new lecturer and we were introduced to some open source software written in Java called C.a.R. C.a.R stands for Compass and Ruler, it simulates whatever you can do with a compass and a straight edge along with more advanced functions. We learnt the 5 axioms of Euclidean geometry which are basically 5 "common sense" rules that no one tries to prove (heavily paraphrased for simplicity):

1. A line exists between 2 points.
2. Any line segment can be extended.
3. A circle consists of one  fix point (the centre) and one point that is constant distance from that fixed point.
4. All right angles are congruent.
5. Any point outside of a line can only have one line going through it that is parallel to the original line.

From there we constructed parallel lines, right angles and intersections using only a ruler and a compass. Except we did it in C.a.R, not with an actual ruler and a compass. I'd have found an actual ruler and a compass much easier actually. This is all basic technical drawing that I learnt in 4th form. Although in my head a stronger connection was made between this geometry and radians, which is something I ignored when I was at school, not being interested in maths in the slightest. I'm interested these days.

We also touched on the Golden Ratio which is the idea that 1.618....(an irrational number) is an easily calculated and plotted geometrical construction that also happens to look visually pleasing. As such lots of ancient buildings are built to this ratio.

What I've been pondering so far is how Art in the Maths and more widely the Science world seems to be regarded as what I'd call design. There seems to be some attempt to connect the two worlds but it assumes and old definition of Art. I'm really not sure how one can give any mathematical meaning to post modern art unless one was to look at chaos theory or... something. Also everything I have read so far talks about beauty. To me art is not necessarily beautiful by any definition. I don't just mean aesthetically although it seems to me some of the simpler connections are only talking about aesthetics but I also mean in terms of unifying anything. Anyway, while art may once have been about aesthetics, it's certainly not always the case now. Aesthetics is more of an applied art like design, and usually for commercial reasons.