# GoldenRatio Artwork

### general-radius-formula icosahedron dodecahedron 20 faces 12 vertices 12 faces 20 vertices public birthday ⊙2012 ⊘12 ⊖20 public birthplace www.phimath.net category uncertified original mathematics discovered by hieronymous-le-clochard ### Socrates: I know that I know nothing.

MathGroupies: I know that we know, nothing new. >>>> Oh, really, please let them explain the introduction of unit-radius for doe-radi-formula and ike-radi-formula.

Don't be shy, send me your opinion.

# isaac-pacl-report studies since 2008

### considers the original isaac material without third-party internet hoax photos ### phiman uses pentagonometry

This simple statement is the overall conclusion of many occasional studies of isaac-pacl-report symbols, the pentras. With the help of that paper hieron discovered the magic of pentagonometry. The new knowledge of ike-doe-radi-formulas are a good and helpful entry point for pentagonometry.

One thing you should keep in mind: hieronymous is rather an artist or a science fiction writer, than a professional mathematician. All calculations have a clear mathmatical background: GoldenRatio (= φ = phi) based numbers. The most favourable analytical way to describe pentagons is GoldenRatio based. All geometrical constructions of regular pentagons pass by a GoldenRatio construction.

During history of humanity a lot of science fiction has become reality. Humans flying to mars is still a science fiction today, maybe a reality in 100 years. Radio, TV, Phones, Computers, Robots, electric Lights, Photos were all science fiction 200 years ago, a reality today. Pentagonometry is a personal science fiction of hieron, maybe a reality in 20 years. Pentagonometry is so vast, that a single man cannot bring it up, but an internet community has a good chance.

### The introduction of belief-levels

To structure beliefs of different categories the community will introduce belief-levels. On the highest level we have placed idea, means any idea, of any quality, pure fiction, fantasy, mathematical ideas (inspirations). An idea doesn't need any argumentation, but if we find arguments, the idea can become a guess. With more and better arguments a guess can become an opinion, then conviction, and finally with a wideley accepted proof among mathmaticians, a mathematical (scientific) belief. All statements start on the idea level, but not all ideas will flow down to common mathematical belief. Two extreme examples: [idea]doe-radi-formula, [idea]isaac-pacl-report graphic was created by a mathematician. Within the community the doe-radi-formula jumps very fast and easily to the mathematical level, simply because some short calculations proof mathematical correctness. The second idea will need good arguments to reach the guess-level in a community. And maybe a distinction between community belief and private belief would be useful. phi := [opinion] a transcription of the greek letter φ which established as default symbol for GoldenRatio;
phimanity := [idea] a supraintelligent extraterrestrial civilization. humanity analog phimanity
phiman := [idea] an individual of phimanity. human analog phiman
phimath := [idea] the mathematics of phiman
pentagonometry := [guess] pentagon-related generalization of trigonometry, a goldenRatioMathematics
pentra := [idea] pentagonometric character.

definitions and [belief-levels] by hieronymous-le-clochard, 2012 0108

birthday of this website: www.phimath.net
birthday of first icosahedron & dodecahedron radius formula worldwide attention: unrevised material, never seen by any mathematician, nor an English lector

Mathematical aspect: A single recursion is responsible for all radii, responsible for both, ikeRadi and doeRadi. for ikeRadi the recursion goes: GoldenRatio^n -GoldenRatio^(n+2) → -GoldenRatio^(n+1), For doeRadi the recursion goes: GoldenRatio^n + GoldenRatio^(n+1) → GoldenRatio^(n+2), and this is just an algebraic exchange of two terms referencing the same recursionEquation.

A quick & dirty explanation would be:
ike&doeRadi are normedSubranges @ phiRecursions. (phi=GoldenRatio)