I didn’t contribute much in class today while we were having an open debate on the definitions of mathematics and art. I don’t think I agreed with most of the points most people came up with though, so I spent some time afterwards thinking about what I think makes more sense to me. Note: I have a tendency to not share anything unless I’ve worded my idea into a neat, concise, and cohesive argument. That should change, because I want to share more of my ideas in the future more openly like some of my other more outspoken classmates. I need to understand that nothing needs to be perfect.
Anyway, I think mathematics is the human understanding of the world. Art on the other hand is the human expression of the world.
There is a distinct difference between understanding and expression. Understanding is cold logic devoid of emotion. Let’s say I have an apple. All will have the understanding that this apple is red, sweet and white on the inside, has around six black seeds at the core, and so on. It doesn’t matter what language you’re using, every culture, every person would have an equivalent in their language that matches your understanding of this apple. Expression on the other hand is applying a meaning or association with this understanding.
Expression deals more with abstract things such as feelings so it is more subjective and differs from person to person. Using the apple again the apple could symbolise temptation and sin linking to the Bible. On the other hand it could mean good health and perfection to some. The red of the apple could mean anger while the white means all that is pure and fragile, thus when combined gives the idea of a defense mechanism of an innocent, but traumatised child. In another perspective the red could represent blood giving its association to life while the white represents the good in life and the black seeds are the obstacles we overcome during our lifetime. You can get different meanings of the apple with different people. Although there is a difference between Math (understanding) and Art (expression) that doesn’t mean that the two can’t be related.
In the case where Math and Art are combined, you get a mathematical interpretation of beauty and an artistic interpretation of truth. A great example of this is fractal art.
The arrangement, colours, and form of a fractal is beautiful. The pattern of this beauty is based the mathematical equation of the fractal while other aspects of the piece such as form and colour express the truth in the equation. Truth and beauty are subjective, however, that truth is the human perception of what appears to be true. They could be completely wrong, or completely correct. The same can be said for beauty. Different people have different ideas of what is beautiful, however, that doesn’t necessarily mean that there is anything that is right or wrong. Thus, it is entirely possible for math and art to exist in the same place, sharing an intertwined relationship depending on the perception of each individual.
Nets
I quite liked drawing out nets for the different shapes today. In highschool geometry was my favourite because I thought it was fun since you get to make 3D shapes out of flat paper nets. I also find that I get a longer sense of fulfillment when I do things like making objects out of something flat, empty and “unimportant”. This is because, usually, nothing gives me happiness and satisfaction for more than a few minutes so I’d rather spend my time working hard than let my thinking time go to dangerous places.
I did some googling on that for the net of the icosahedron. It turns out I was right and the lecturer made a small mistake. The icosahedron is the one with twenty equilateral triangular faces while the dodecahedron is the one with twelve regular pentagonal faces. [1] [2](Farlex, inc., 2011; MathIsFun.com, 2010) So it turns out we accidentally got them mixed up.
The two-piece pyramid puzzle
Made a test net and the one given made no sense. It couldn’t even fold up properly to make a decent shape as some of the edges couldn’t meet to close up the shape.
So I did some googling to see what the final solution looked like so that I could get an idea of how the correct net should look like.
I found a picture of the solution and a brief bit of information about pyramid puzzles from: http://gamesmuseum.uwaterloo.ca/VirtualExhibits/puzzles/pyramid/index.html
From that I sketched a little diagram of the solution in my book with all hidden edges. Then drew up the simplest net for a tetrahedron to map out where the edges of one of the two pieces should be, and from that I got the measurements to create a net for one of the pieces.
Did a test net for that one; it worked, so I then colour-coded which edges were congruent and added in angles to make it easier to draw the side flaps in the final nets. Then the final two nets were cut out from stiffer, sturdier paper, glued and put together to show the solution of the puzzle.
That was quite fun to be honest. I was expecting this paper to be extremely boring, but after reading the planned schedule for what we’ll be doing I’m extremely pleased because geometry is my favourite. I’m especially looking forward to the session about Fibonacci, golden ratios, and spirals. I’ve always had a special interest in golden ratios and golden spirals because I think they’re perfect. It’s much like my love for circular, spherical, and curved objects. I find them to be the most beautiful forms because the number of sides they’re actually made out of are so infinite that it appears that they only have one surface or one side depending on whether you’re going 3D or 2D. I’m also looking forward to working in pairs for this. Since my love for working with other people has grown greatly and because geometry has always been my favourite, I think I will enjoy it very much provided that I don’t end up working with somebody lazy and unreliable.
[1] Farlex, inc. (2011). Icosahedron – definition of icosahedron by the Free Online Dictionary, Thesaurus and Encyclopedia. Retrieved July 19, 2011, from http://www.thefreedictionary.com/icosahedron
[2] MathIsFun.com. (2010). Definition of Dodecahedron. Retrieved July 19, 2011, from http://www.mathsisfun.com/definitions/dodecahedron.html
Lucy there is some great reflection here - im not sure I agree with some of your premises about Art. Expression assumes some sort of knowledge - intuitive a priori or otherwise. I think many artist make art as a way of trying to understand the world / themselves. Maybe its useful to think about the distinction between the art work and the artist?
ReplyDelete