there's nothing special at all in those calculations, and the thesis contains many unjustified statements.
1) what does "optimal" mean, other than "supports me theory"
2) why do you say irrational numbers are impossible to construct with any accuracy in the real world, with the implicit assumption that somehow rationals are constructible to some degree of accuracy, and if so that negates your statement as then phi is realizable as a diagonal of a pentagon?
3) The mathematical presentation of the paper is shockingly bad, such as anyone who looks at the first diagram is given the impression that the betas are all the same when they certainly aren't.
4) why on Earth is 2 so special to the point where you say no other integer will do it better?
5) the idea that you're going to produce a polynomial with phi as a root and 'wth the minimal number of terms' must be considered an ill advised boast since I'm sure i can think of one of degree 1 with phi as a root, and two if you must make me have integer coeffs, which must have fewer terms than the one you derive (a mathematically provable fact), though i didn't see it highlighted later in the text, but then that's because there's so much unnecessary waffle that it's not an easy task to extract information from the article.
6)the ideas of eqn 5.4 indicate a lack of understanding about raising complex numbers to exponents; again nothing special is going on there.
7) it would be beneficial to learn about polar representations of complex numbers to see why these coincedences occur.
