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'A Representation of Zeckendorf’s Theorem of Fibonacci Numbers' Sculpture

Frank Murri

Australia

Sculpture, Carving on Timber

Size: 29.5 W x 47.3 H x 2 D in

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$1,610

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ABOUT THE ARTWORK

Explanatory notes for: “A Representation of Zeckendorf’s Theorem of Fibonacci Numbers (in a bell curve sequence)” Zeckendorf's theorem, named after Belgian mathematician Edouard Zeckendorf, is a theorem about the representation of integers as sums of Fibonacci numbers. Zeckendorf's theorem states that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers. Fibonacci numbers are a sequence of numbers where the sum of the previous two numbers equals the subsequent number, ie: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, . . . Therefore, a Zeckendorf representation of 100 is: 100 = 3 + 8 + 89 We discover that the sum of these Zeckendorf representations, in turn gain the characteristic of the Fibonacci sequence, ie, 1 + 3 + 8 = 12 2 + 5 + 13 = 20 3 + 8 + 21 = 32 5 + 13 + 34 = 52 8 + 21 + 55 = 84 In this piece, (starting in the top left-hand corner, and proceeding top to bottom left to right), it is the distance between each clear carving, in centimetres, which represents distinct Fibonacci numbers, with the following coloured carving being the sum of the previous carvings. At a particular point in these calculations, due to the exponential nature of the results, I commenced to recede to the initial numbers in the sequences, in a bell curve formation, for aesthetic purposes. Frank Murri Newcastle, Australia

DETAILS AND DIMENSIONS
Sculpture:

Carving on Timber

Original:

One-of-a-kind Artwork

Size:

29.5 W x 47.3 H x 2 D in

SHIPPING AND RETURNS
Delivery Time:

Typically 5-7 business days for domestic shipments, 10-14 business days for international shipments.

Frank Murri (Australia) The nature of my art practice consists of wall-hung, abstract timber relief sculptural works. These pieces are formed by incorporating Mathematical formulas, theorems & sequences; Musical scores & Literary extracts. It is an art form which I have developed, and which I hope one sees as a unique creation. All of my works advocate pure abstraction in an attempt to synthesize a design aesthetic. By looking into the realm of pure mathematics, there lies within a beauty which transcends its usual form. As Bertrand Russell stated, “Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture.” The Mathematical pieces I create are formulated to capture this beauty. ~*~ In addition to my Mathematical art pieces, I have also created abstract representations of Musical scores as wall-hung timber relief sculptural pieces. They represent the first page of sheet music of particular classical works, in particular: Puccini's 'Vissi dárte' (I lived for art) from Tosca; Verdi's 'Grand March from Aida'; Schubert's 'Ave Maria, Op.52, No. 6'; Korsakov's 'The Flight of the Bumble-Bee' and Albinoni's 'Adagio'. Each sculptural piece has the notation of sheet music represented through carvings into the timber staves (also known as staffs), or notes on outer ledger lines. Please note that my pieces are pure abstractions of musical scores, as I have not used the usual and specific music symbols and elements. They have not been created as direct representations to be performed. I have created these sculptural pieces as an artistic expression of the beauty I see held in the musical score (itself a wonderful abstraction and code of notes and symbols) which represent such beautiful pieces of music. ~*~ In addition to the Mathematical & Musical art pieces, I have also created abstract representations of Literary extracts as wall-hung timber relief sculptural pieces. Each segment is carved in a particular sequence representing a specific literary work. The spacing between each carving represents a letter of those words in the piece. ie, the letter “A” = 1mm, whilst “Z” = 26mm spacing.

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