It didn't take long for artists, especially those so learned in the multi-discplinary approach that classical and Renaissance art heralded at the time, to notice that this principle, if as pleasingas it is in all other aspects of life, should as feature in their paintings too. In many ways, it seems to defy explanation and has thus taken on the 'rivine' moniker many refer to it as. Highly connected with the Golden Ratio, also known as the Divine Ratio, it can be witnessed in flowers, the human face, the gorgeous geomtery of the flowering artichoke and ratio of male and female honeybees present in their family tree (ie how many female and males are present in the ancestry of one particular bee). Its shell-like shape has wonderously spread in many naturally ocurring phenomena and as such, been adopted into many famous artistic pieces, perhaps most so in the Mona Lisa. DUring the Italian Renaissance, the idea in particular allowed the more visually inclined to envisage the numerical sequence as a pattern somewhat resembling a shell - something that equated to a highly aesthetially pleasing proportion. The exact history of each is paramount in understand their uses.Īn Italian mathematician from the late 11th century, Fibonacci was credited with bringing the Arabic numerical system to Europe and very quickly his eponymous sequence, the combination of numbers that graduated from the sum of its previous two numbers (for example 1, 1, 2, 3, 5, 8, 13, 21, 34 etc). Here, mathematics no longer represents numbers, but like 'logic' that would come largely from Greek study, these mathematical formulations become philosophical representations as well as tried-and-tested ideas that occur both physically and naturally all throughout our world. In further notes of the Italian polymath, his scrupulous and obsessive studies of human anatomy lean further on these ancient mathematical ideas. In this diagram, where Leonardo da Vinci illustratrates the proportion of the male body, we can see the anatomical scale as signified by the exactitudes of the manner a body can fit into a series of shapes. Mathematics has that magic quality of trascending genre - beyond just numbers, they represent shapes and aesthetically pleasing quanities - or even more significantly as ideas - most perfectly represented - or at least memorably so - in Leonardo da Vinci's Vitruvian Man. Mathematicians found that it was abundant in nature, in places as diverse as the proportions of the human face, the flowering of an artichoke or a sunflower, the ancestry of the ideal bee and the family tree of a rabbit.Ratios and proportions have been present in art almost since time immemorial. The Golden Ratio is sometimes called the Divine Ratio. And here is a surprise: when we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio.Īs you can see, the bigger the pair of Fibonacci Numbers, the closer the approximation. There is a special relationship between the Golden Ratio and the Fibonacci Sequence. The Fibonacci Sequence is intimately connected with another mathematical construct, the Golden Ratio (two quantities whose ratio is the same as the sum of the total to the larger ratio). When we make squares with those widths, we get a nice spiral:
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