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Is there maths behind M.C. Escher’s work? If so, what elements are there?

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Introduction

Is there maths behind M.C. Escher’s work? If so, what elements are there?

In this essay, before I start anything, I must first clarify that I deeply consider mathematics as a subject that has had a great influence on the artist and his masterpieces, therefore I already alarm you that throughout my essay I will talk about Escher’s work and try to persuade you that there has been a considerable integration of the subject matter with his very artworks. In order to make you understand my objective, I have gathered some of his work, then selected a few, which I found had more mathematical elements, then with a decreased amount of drawings to work with, I would be able to study all components and show you that there has been a great influence of maths on him. I believe these images without the existence of any mathematical aspect would not be able to be fully accomplished.

Elements like: symmetry (reflection also included), pattern/tessellation (repetition), transformation, crystallography, “impossible shapes”, proportion and the ‘Fibonacci Sequence’ or the ‘Golden Ratio’. Are suggested to be present in M.C. Escher’s artworks, these I believe have been responsible to create the effect they create on the viewer, which is wonder and marvellous of the impressive art that cannot belong to the real world. Later

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Middle

Apart from topology, geometry and proportion are involved. Geometry has been needed in order to create the construction itself as it is based on parallelograms (the floors, walls and balcony) and circles (the roof, balcony – a mixture of both circle and rectangle). The parallelograms are ‘transformed’ into rectangles or rectangular objects, this is due to perspective and the direction to which it points. Though there are much more to it, for instance pattern made by: squares (actually rhombus, but appears as squares due to perspective) to make a squared floor and the balcony, which is composed of rectangles and half circles (these two shapes together make up the actual spacing between each of the supports on the balcony). But what is really amazing is that Escher was able to separate the image into 2 halves. The top half, where it seemed to be viewed from left to right, and the bottom half, which seems to be viewed from right to left, and on the middle the transformation occurring, which gathers both views into one in order to make the illusion.

Moving on to another interesting topic that acquires geometry, Escher’s spheres have been responsible for much criticism and value. A few of the works like: Three Spheres, Hand with Reflecting Sphere and Concentric Rinds use what mathematicians call perfect shapes. I have taken Hand with Reflecting Sphere, a well- known and criticised artwork, into consideration to be analysed.

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Conclusion

n the addition of the last two numbers) actually called ‘Fibonacci Sequence’ derived from the fact that most of the elements in nature grow this way i.e. 0 represents nothing, then 1 represents an individual and together with another individual there might be a newborn and so on. With this sequence the ‘Golden Ratio’ was created: 1/1, 2/1. 3/2, 5/3, 8/5 and so on, being that the ratio is based upon one of the numbers from the sequence as the denominator and the next number as the nominator, being that the greater the nominator and denominator, the nearest it gets to the ‘Golden Ratio’ (1,61804- approximated to 5 decimal places).

The ‘Golden Ratio’ that might be present on this artwork is in its very outline or the structure of the image. I presume that with the used proportion (x and 2x, as seen on the notes beside the artwork) where the number 1 and 2 are used and together they add up to 3 is possible to be associated with the golden proportion. What I mean is that as these numbers follow the same numbers of the elements which follow the ‘Golden Mean’

e.g. image04.pngimage05.pngimage03.png

This spiral is an example of a shell that follows the ‘Golden Proportion’: as you may see each number from the sequence represents a square in a certain size, as the number increases of size, so does the square.

Escher’s work: Reflecting Hand on Sphere seems to have a similar idea:

                                          X (as shown on artwork)image02.pngimage02.pngimage01.pngimage00.png

                                2x (as shown on artwork)         3x

  • This

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