proposed solution to Fermats Last Theorem using Colour

Teaching the Future.
In the late 1990’s I had a dream about teaching ordinary people the solutions to seemingly extraordinary problems using holistic analogies from the natural world.
At the time I called it zero paradox university
http://offtheplanet.blogspot.com/2009/11/interstellar-university-101.html
It became a hobby drawing out multimedia solutions to allegedly impossible to solve paradoxes.
Here is perhaps a model for a solution to Fermats often impossible paradox using simple analogies from the natural world.


A PROPOSED SOLUTION TO FERMATS LAST THEOREM USING A COLOUR ANALOGY

Andrew Hennessey

In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. This theorem was first conjectured by Pierre de Fermat in 1637, famously in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. No successful proof was published until 1995 despite the efforts of many mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th. It is among the most famous theorems in the history of mathematics and prior to its 1995 proof was in the Guinness Book of World Records for "most difficult math problem".

Fermat's equation xn + yn = zn is an example of a Diophantine equation.[6] A Diophantine equation is a polynomial equation in which the solutions are required to be integers.[7]

The integers (from the Latin integer, literally "untouched", hence "whole": the word entire comes from the same origin, but via French[1]) are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (−1, −2, −3, ...). Viewed as a subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {... −2, −1, 0, 1, 2, ...}. For example, 65, 7, and −756 are integers; 1.6 and 1½ are not integers.

However, in this example of a solution to Fermats problem the numbers do not have to be of the set of integers but of the set of CMYK colours as rendered into the Pantone colour system.

Colours chosen from the CMYK process are then converted into real world applications in shops and commerce etc by the Pantone colour system.
The maximum criteria for Fermats n is usually 2 in the set of integers – but in the CMYK colour/maths system – n could be any number whatsoever and most are greater than 2.
In this model though n could be absolutely any real number within the CMYK colour system [and ultimately its Pantone real-world commercial application] and still be valid without any constraints or paradoxes imposed by Fermat.

In CMYK, The CMYK color model (process color, four color) is a subtractive color model, used in color printing, and is also used to describe the printing process itself. CMYK refers to the four inks used in some color printing: cyan, magenta, yellow, and key black.

CMYK Blue number four [ultimately a commercial Pantone number] added to CMYK Orange number 4 will give if mixed in equal proportions, CMYK Grey number 4, where n could be literally hundreds of real numbers that are part of the black weighting of K as it mixes with CMY. Also a and b are self cancelling complementary colours within the colour spectrum such as e.g. red and green, or orange and blue, or purple and yellow, or black and white, [all of these mix together to produce a grey] and c is always a grey of black weighting n identical to the black weighting or K within the selected a and b taken from the CMYK colour spectrum.

Thus an + bn = cn

In the CMYK system when selecting the black weighting of a colour e.g. n = 1 – 100 or 1-1000 for example is always a true and solvable when applied to the Fermat equation. N isn’t restricted to Fermats 2 in the CMYK colour process
Where a and b are Complementary colours a c is always produced of the same black weighting n in the Pantone series in the CMYK colour system.

http://simple.wikipedia.org/wiki/Complementary_color
http://en.wikipedia.org/wiki/CMYK_color_model
http://en.wikipedia.org/wiki/Set_theory

Although all of these colours and processes going into the tins at Walmart are natural substances, neither the blue or the orange used could be called mathematically natural by Mr Fermat .
We get the refutation of Fermats Last Theorem from this context sensitive analogical colour model. Even if n is greater than 2 of the K, black weighting in the CyanMagentaYellow [cmyk] colour system - we still get a knowable and positive solution for any n.

Although Pantone numbers [commercial colour scale derived from the CMYK colour set] are of a set of numbers in a colour system – they do correspond with measurable empirical readings in the natural world and its natural mathematics.
The real numbers that convert to their equivalent decimal places on optometric equipment that calibrate the frequency of the light emissions in the spectra of the blue and orange paint would have been thought an impossible correlation by thousands of mathematicians after the time of Fermat.

Fermats Last Theorem therefore has no paradox or problem within the colour analogy of Complementary colours within the CMYK colour system.
That fact suggests that there is a general systems theory solution in the natural world to Fermats paradoxical theorem using set theory and real numbers - where a and b are complementary colours, c is the resultant grey and n is the number equal to the k or black weighting scale within the CMYK colour process.

Comments

Patrick said…
Dude, it was known long before Fermat that a^n+b^n=c^n has infinitely many trivial solutions for n>2 if a, b and c are allowed to be any real numbers. For example, a=b=1 and c = 2^(1/3) for n=3.
caledonia said…
hi patrick thats great - it was just one of these things that i was looking at - I modelled solutions to the collapsing wave paradox, goedels numbers paradox, the turing problem and stuff like that - and generally created the basis that would make executive AI robotics viable.

fermat was just another footnote on one of my pages.

however - its no big deal to me at all and I'm happy that everyone is happy with infinite recursion in computation ...
these days I have nothing more to do with the charade called science ..

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