References

These are the working references for the article, “Constructing the Universe from Scratch.”  A running commentary is being developed within my LinkedIn blogging area.  Besides editing the overall document, the end notes will be using some of these reference materials below.
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Reference materials:
https://en.wikipedia.org/wiki/Bifurcation_diagram
https://en.wikipedia.org/wiki/Law_of_Continuity
http://www.academia.edu/748956/The_pythagorean_relationship_between_Pi_Phi_and_e
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/propsOfPhi.html

http://sprott.physics.wisc.edu/pickover/trans.html
https://en.wikipedia.org/wiki/Clifford_A._Pickover
https://en.wikipedia.org/wiki/List_of_mathematical_symbols
Hales: http://arxiv.org/abs/math/9811071v2
https://en.wikipedia.org/wiki/Hopf_algebra#Cohomology_of_Lie_groups
https://en.wikipedia.org/wiki/Cellular_automaton
https://en.wikipedia.org/wiki/E_%28mathematical_constant%29
https://en.wikipedia.org/wiki/Euler’s_formula
https://en.wikipedia.org/wiki/Special:Search/Hierarchy_of_transfinite_cardinals
https://en.wikipedia.org/wiki/Euler’s_identity
https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem
https://www.google.com/search?q=Buckingham+Pi+theorem&ie=utf-8&oe=utf-8
https://www.quora.com/What-is-the-Penrose-number
https://en.wikipedia.org/wiki/Ultrafinitism
https://en.wikipedia.org/wiki/Names_of_large_numbers
https://en.wikipedia.org/wiki/Aleph_number
https://en.wikipedia.org/wiki/Finitism
https://en.wikipedia.org/wiki/Wreath_product
https://en.wikipedia.org/wiki/Spherical_coordinate_system
https://en.wikipedia.org/wiki/Taylor_series
https://en.wikipedia.org/wiki/Hyperreal_number
https://en.wikipedia.org/wiki/Wallpaper_group

Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere by Edward S. Popko

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https://www.linkedin.com/in/costas-bekas-130b635/

http://keithbriggs.info/documents/Keith_Briggs_PhD.pdf

 

Isoperimetric Quotient for Fullerenes and Other Polyhedral Cages  Tomaž Pisanski , Matjaž Kaufman ,* Drago Bokal , Edward C. Kirby , Ante Graovac § Inštitut za matematiko, fiziko in mehaniko, Univerza v Ljubljani, Jadranska 19, 1000 Ljubljana, Slovenia, Resource Use Institute, 14 Lower Oakfield, Pitlochry, Perthshire PH16 5DS, Scotland, UK    The Rugjer Bošković Institute, Bijenička c. 54, HR-10001 Zagreb, POB. 1016, Croatia   J. Chem. Inf. Comput. Sci., 1997, 37 (6), pp 1028–1032   DOI: 10.1021/ci970228e  Publication Date (Web): November 24, 1997 b Copyright © 1997 American Chemical Society   Abstract:  The notion of Isoperimetric Quotient (IQ) of a polyhedron has been already introduced by Polya. It is a measure that tells us how spherical is a given polyhedron. If we are given a polyhedral graph it can be drawn in a variety of ways in 3D space. As the coordinates of vertices belonging to the same face may not be coplanar the usual definition of IQ fails. Therefore, a method based on a proper triangulation (obtained from omni-capping) is developed that enables one to extend the definition of IQ and compute it for any 3D drawing. The IQs of fullerenes and other polyhedral cages are computed and compared for their NiceGraph and standard Laplacian 3D drawings. It is shown that the drawings with the maximal IQ values reproduce well the molecular mechanics geometries in the case of fullerenes and exact geometries for Platonic and Archimedean polyhedra.

https://en.wikipedia.org/wiki/Planck_constant

In the equations of general relativity, G is often multiplied by 8π. Hence writings in particle physics and physical cosmology often normalize G to 1. This normalization results in the reduced Planck energy, defined as:\sqrt{\frac{\hbar{}c^5}{8\pi G}} \approx 0.390 \times 10^9\ \mathrm{J} \approx 2.43 \times 10^{18} \ \mathrm{GeV}.

https://en.wikipedia.org/wiki/Planck_energy

https://en.m.wikipedia.org/wiki/Planck_units#Derived_units

EPP

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THEORY OF DYNAMICAL SYSTEMS AND GENERAL TRANSFORMATION. GROUPS WITH INVARIANT MEASURE. A. B. Katok, Ya. G. Sinai, and A. M. Stepin.

Printing:

page 1= Printable PDF of this page only

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March 20 George Polya can rightly be called the father of problem solving in mathematics education. https://en.wikipedia.org/wiki/George_P%C3%B3lya

rightarrowsmallgreenNotes: March 5, 2017

1. Virtual particles:  https://en.wikipedia.org/wiki/Virtual_particle
2. Pertubation theory: https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)
3. Hamiltonian: https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)

4.  Also Carlo Rovelli, https://plus.google.com/101505201345791903693
http://www.cpt.univ-mrs.fr/~rovelli/
TIME IS NOT WHAT YOU THINK IT IS

5. Richard Muller https://www.amazon.com/Now-Physics-Time-Richard-Muller/dp/0393285235#reader_0393285235

6.  https://en.wikipedia.org/wiki/Cantor_function

7. http://physics.uoregon.edu/profile/jschombe/

http://abyss.uoregon.edu/~js/cosmo/lectures/lec20.html

Notes (2016):

https://en.wikipedia.org/wiki/Planck_units
https://en.wikipedia.org/wiki/Planck_constant

http://abyss.uoregon.edu/~js/cosmo/lectures/lec20.html
http://www.pnas.org/content/103/28/10612.full.pdf Packing, tiling, and covering with tetrahedra J. H. Conway* and S. Torquato
http://doye.chem.ox.ac.uk/research/cluster_structure.html Jonathan Doyle, Cambridge

https://arxiv.org/abs/1608.00119
On inflation, cosmological constant, and SUSY breaking Andrei Linde
July 2016

http://www.aljazeera.com/programmes/talktojazeera/2014/08/andrei-linde-beginning-time-201481195158924940.html

finitum

http://abyss.uoregon.edu/~js/cosmo/lectures/lec20.html
Hartle-Hawking proposal

http://link.springer.com/article/10.1007/s40844-015-0001-6
On the problem of scale: a general theory of morphogenesis and normative policy signals for economic evolution

1.54 steradians = or ≠ a gap of 7.36∗

http://plato.stanford.edu/entries/spacetime-iframes/#LinProAbsSpa   Robert DiSalle <rdisalle@uwo.ca>

space and time: the hole argument

http://plato.stanford.edu/entries/spacetime-theories/    Absolute and Relational Theories of Space and Motion  Nick Huggett <huggett@uic.edu>  Carl Hoefer <carl.hoefer@ub.edu>

Dr. Claus Kiefer. Institut für Theoretische Physik Universität zu Köln … 0221 470-4300 (secretary). Fax: 0221 470-2189. E-mail: kiefer@thp.uni-koeln.de

http://people.bu.edu/gorelik/cGh_FirstSteps92_MPB_36/cGh_FirstSteps92_text.htm