BORING BECOMES BEAUTIFUL

During a recent visit to the Science Museum in London (now amongst my favourite places on earth), I came across a display of 'Klein Bottles', made by British glassblower Alan Bennett. Not being a mathematician, the thing that first stuck me was the beauty and detail of the work, but as I read on, the mathematical basis of these 'bottles' was what really intrigued me. A Klein Bottle is what is called a 'non-orientable surface'. It has no inside or outside, and no boundary (a sphere, on the other hand, also has no boundary, but is an orientable surface). No inside or outside? Sound impossible? Have a look:
 Inside becomes outside, outside becomes inside. It's confusing and mysterious and beautiful. A 'true' Klein bottle can only exist in 4 dimensions, so the bottles made by glassblowers are 3-dimensional representations of  'true' Klein bottles. If dissected into two halves, the Klein Bottle produces two Mobius Strips - a well known phenomenon produced most commonly by taking a (two-sided) strip of paper, twisting it, and gluing the ends together to create a (one-sided) figure. Bennett experimented further with his Klein Bottles, creating more and more complex bottles which, when dissected, produced ever-expanding numbers of Mobius Strips.
History is littered with mathematicians who, inspired by the splendor of the mathematical world, have transformed their 'work' into works of art. After all, the ancient and ultimate challenge of many artists was to successfully represent a 3-dimensional scene or object, in a 2-dimensional format. Architecture is the ultimate crossroad of art and mathematics; check out this 'Klein Bottle House' by McBride Charles Ryan in Hawthorn:
Historically, artists/mathematicians such as Leonardo da Vinci, Giovanni Battista Piranesi and Piero della Francesca explored and utilised this relationship - uncovering and unlocking the secrets of perspective and accurately representing the human anatomical form, but the correlation continues today, inspiring artist such as Nikki Graziano - a photography and mathematics student. 
Recently I've begun realizing that mathematics isn't the boring, static subject that I studied in school, but rather, fascinating and relevant - not only in art, but also in nature (which is another observation for another day..)


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