**3D Hyperbolic Tiling and Horosphere Cross Section**

Vladimir Bulatov,

Shapeways

Joint AMS/MAA meeting

San Diego, January 10, 2018

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# Category: Geometry

## Vladimir Bulatov – ShapeWays – Hyperbolic Tiling

**3D Hyperbolic Tiling and Horosphere Cross Section**

## Dynamic Symmetry – Phylotaxis – Oleh Bodnar

## Softology – DLA – LBM – Snowflake – Cellular Automata

## Spirals – Logarithmic – Fermats – Archimedean & Hyperbolic Spirals

## Number and Magnitude

## Caroline Series – Hyperbolic Geometry, Perspective and Time

## Jason Davies – Mappings and Geometries

## Eyvind Earle – Illustrator – Natural

## Ken Wheeler – The Missing Secrets of Magnetism – Theoria Apophasis

## Robert Lawlor – The Geometry of the End of Time – Kali Yuga

Vladimir Bulatov,

Shapeways

Joint AMS/MAA meeting

San Diego, January 10, 2018

The term dynamic symmetry was for the first time applied by the American architecture researcher J. Hambidge to a certain principle of proportioning in architecture . Later this term independently appeared in physics where it was introduced to describe physical processes that are characterized by invariants. Finally, in the given research the term dynamic symmetry is applied to regularity of natural form-shaping that in terms of origin also appears not to be connected with Hambidge’s idea, and, moreover, appearance of this term in physics. However, all the three variants are deeply interconnected in terms of their meaning which we are going to show.

At first, we point out strategic similarity of Hambidge’s and our researches. This is a well-known historical direction which in the field of architecture and art is motivated by the search for harmony regularities and, thus, is aimed at studying the objects of nature. Usually architects take interest in the structural regularities of natural form-shaping and, particularly, in the golden section and Fibonacci numbers which are regularities standing out by their intriguing role in architectural form-shaping. It is not accidentally that architects who do researches so frequently pay attention to botanical phenomenon **phyllotaxis** which is characterized by these regularities.

**DYNAMIC SYMMETRY IN NATURE AND ARCHITECTURE**

Continue reading “Dynamic Symmetry – Phylotaxis – Oleh Bodnar”

We have lost the relationship between Number and Form or Number and Magnitude as the Ancient Greeks called their Forms.

A few years ago a Revolution in Mathematics and Physics has started. This revolution is caused by Geometric Algebra.

In Geometric Algebra the Ancient Theories of Euclid and Pythagoras are reevaluated.

Numbers are Scalar (Quantum) Movements of Geometric Patterns and not Static Symbols of Abstractions that have nothing to do with our Reality.

Movements and not Forces are the Essence of Physics.

The basic rule Movement = Space/Time (v=s/t) shows that Time and Space are two Reciprocal 3D-Spaces. Our Senses Experience Space and not Time.

The Simple Rule N/N=1/1=1 balances the Duals of Space and Time. One Unit Step in Space is always Compensated by One Unit Step in Time.

When we Look with our Eyes and not with our Mind we can See that Space looks very different from what we Think it is. In Our Space Parallel Lines meet at Infinity.

Around 1400 during the Renaissance Painters started to look at Space with their own Eyes and discovered the Rules of Perspective Drawing.

Between 1600-1800 Perspective Theory changed from a Theory of Art to a Theory of Mathematics called Projective Geometry.

It took 400 Years before a few Mathematicians realized that Projective Geometry was the Foundation of Mathematics and it took another 100 years before Projective Geometry started to influence Physics.

In 1908 Hermann Minkowski discovered that Einstein’s Theory of Special Relativity could be analysed using Projective Geometry. Minkowski created a 4D Space-Time Metric Geometry in which he added one Time Dimension.

Many experiments now show that 4D-Space-Time is not sufficient to incorporate what Time Really is.

Continue reading “Caroline Series – Hyperbolic Geometry, Perspective and Time”

**Reviewer:** robstawithlove – favoritefavoritefavorite – October 9, 2016

**Subject:** A New Theory of Everything and Lots of Pain

The implications of this book have been reverberating rather uncomfortably in my mind for days. The literary standard and academic tone are as jarring as its emphatically repeated message to reject the bulk of quantum theory, general relativity, the standard particle model of physics and much of accepted cosmology. Yet, the proposition that emerges is groundbreaking, if taken into proper consideration.

Ken Wheeler draws upon ancient philosophy and the work of Faraday, Maxwell, Heaviside, Steinmetz and Tesla in formulating the premise that the prime cause for all of the known forces emanate from perturbations of the Ether, which is non-physical and existent in counter-space, that was widely accepted and necessary in the work of the listed innovators and that has roundly been rejected by the advent of quantum mechanics. What follows is an experiential/experimental analysis of the relationship between dielectricity and magnetism as expressed in geometry and interacting forces, leading to somewhat of a definition of both, and their relationship to electromagnetism.

Once established and defined, this relationship is then extended to redefine the nature and observed effects of ferromagnetic, diamagnetic and radioactive elements, conductors (dielectric reflectors), insulators (dielectric capacitors) and superconductors before addressing the toroidal structure of galaxies, molecular bonds, the hydrogen atom, gravity and light itself.

It would therefore be fair to say that the content is an inversion of physics as we know it, but yet accords well with other non-standard contemporary postulates that seek to unite physics with consciousness, science with ancient philosophy, the fractal-holographic view of the universe or even an information-based theory of physics (although I suspect that the author may be as disparaging of some of these proponents as much as Einstein or Feynman). If correct, the work may provide more substance to some of the mathematically abstract and empirically unproven forces or entities that make up our current cosmological view, such as dark energy and dark matter (hypothesised to explain observable effects) and may serve to flesh out the work of physicists and cosmologists in investigating black holes and their effects, amongst others.

A serious drawback in the writing, is the unfortunate tendency of the author to make frequent statements of opposition – many of which lead to contradiction. These are damaging to the core content of the work, which is more than sufficient in quality in both its investigations and findings to be plausible and worthy of serious consideration. Mr. Wheeler’s style and approach makes it manifestly clear that he is not an academic, an apologist or a politically motivated physicist with his eyes on a prize. It is also clear that the book has not been edited or spruced up by a publisher. While this may alienate certain readers before the substance of the book emerges, I find these qualities to be indicators of sincerity, both with regards to the investigation and to the frustration felt with the state of established physics. Simultaneously, I am concerned that the author’s supposition of opposition can only engender further exclusion from consideration, which is a travesty when considering the amount of work and time that have been committed to this transmission of knowledge.

My conclusion is that this book is of great value to those who are able to cast literary prejudice aside, those who are not too attached to a dogmatic view of physics or its luminaries, those who are comfortable with unlearning (even temporarily) what has become “established fact” and in particular those who seek to act upon knowledge rather than discuss it at length in “appropriate forums”. To paraphrase C.G. Jung: “There is no coming to consciousness without pain”. This would be just the book for that.

(Uncle Fester warning btw ‘^)