Mathematics Posted on July 26, 2020July 26, 2020 by Julia Johnson AllMathematicsLeonardo da Vinci "Vitruvian Man", circa 1490. More a technical drawing than an ‘artwork’, created to prove a mathematical point. It's based on the writings of Vitruvius, a Roman architect who related human & architectural proportion. The text is an explanation of the proportions of man in the kind of list where maths loses me. Despite this relatively mundane purpose, I had to include it here because it’s become THE symbol in Western culture for the ‘rationality’ of man.Katsushika Hokusai “The Great Wave off Kanagawa”, circa 1830. If you Google “Hokusai Fibonacci” you’ll find a whole series of images imposing spirals onto the shape of the wave. A Fibonacci Spiral is one which follows the Fibonacci sequence – which even a maths dunce like me can follow. At its centre are two “1x1” tiles, then as the line moves up and around it moves into a “2x2”, a “3x3”, a “5x5”, “8x8” and so on. Yet the final image doesn’t feel forced into a style, but like a real wave. The Fibonacci sequence apparently has a lot of influence in nature – who’s to say that doesn’t last for the split second of a wave’s lifetime, like this, in real life?Sandro Botticelli “The Birth of Venus”, circa 1482. Another work that’s believed to specifically use maths to make itself pleasing to the eye. The “golden ratio” is 1 to 1.618 and analysis of this work has show that it uses it everywhere. Venus’ body follow this ratio above & below her navel; the left & right sides of the composition - even the dimensions of the canvas itself have been found to follow these proportions.A traditional Javanese batik print, of the Solo type. I’m not going to pretend that I understood very any of the equations in the academic paper I read investigating the occurrence of fractals in batik motifs, but I understood that it found they’re there. The idea of fractals kind of makes my brain melt at the best of times: structures which are infinitely reoccurring, symmetrical at the deepest points, formed out of what maths calls ‘chaos’ – and in nature potentially between dimensions. OK. Well, turns out that it’s possible to find at least the potential for these qualities in a range of traditional Javanese batik patterns. I don’t really know what that means – is it because the art borrows from nature or has been formalised in its own way? But the results are pretty nice, aren’t they?‘Zellige’ tiles from the Place El-Hedine, Meknes, Morocco. Zellige is just one form of Islamic architecture, particularly associated with Morocco. The geometric pattern is immediately obvious and geometry has an important role in Islamic art in general, as figurative images aren’t common in sacred contexts. What you see here in this pattern is intricate craftmanship – each coloured piece is an individually shaped tile, the total of which create a complex and beautiful mosaic of shapes and overall patterns.Albrecht Dürer, “Melencolia I”, 1514. What we’re looking at is the personification of melancholy – and isn’t her face a spectacular depiction of dark brooding? Notice that she’s holding a compass, and there’s other mathematical tools around which imply that what’s plaguing her soul is the quest for knowledge. It was during the Renaissance that the idea of gloominess- perhaps what we’d not recognise as depression, but certainly all the way up to insanity – became seen as a possible driver of artistic creativity. So what we have here is possibly the first, certainly the first significant – visual representation of the ‘tortured genius’ trope.M.C. Escher, “Day & Night”, 1938. I hate Escher. I associate his drawings with the covers of those dreaded maths textbooks, and the opening slides of imcomprehensible powerpoints. But this means that he’s the first artist who came to mind when I chose the ‘Maths’ theme, so here he is. And “Day & Night” certainly has its mathematical basis, with its tesselating birds and almost-not-quite symmetry. It feels closely related to Surrealism – but I’m afraid as with that movement, I can’t see it as anything other than twee.