Announcement

Collapse
No announcement yet.

The Golden Tractate of Hermes Trismegistus applied to electromagnetism

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • MonsieurM
    replied
    this is fun ................. List of Elements of the Periodic Table - Sorted by Groups (periodic table columns) ..... meet Group 13 .... guess what some of those we talked about quite a bit in this thread and others :

    5 10.811 Boron B 2300 2550 2.34 1808 13 [He] 2s2 2p1 8.298

    13 26.9815 Aluminum Al 660 2467 2.7 8.07 1825 13 [Ne] 3s2 3p1 5.9858

    31 69.723 Gallium Ga 30 2403 5.91 1875 13 [Ar] 3d10 4s2 4p1 5.9993

    49 114.818 Indium In 157 2000 7.31 1863 13 [Kr] 4d10 5s2 5p1 5.7864

    81 204.3833 Thallium Tl 303 1457 11.85 1861 13 [Xe] 4f14 5d10 6s2 6p1 6.1082



    Last edited by MonsieurM; 09-01-2012, 08:32 PM.

    Leave a comment:


  • MonsieurM
    replied
    Originally posted by MonsieurM View Post

    THE CODE OF CARL MUNCK, AND ANCIENT GEMATRIAN NUMBERS - PART ONE

    Carl listed some of the Gematrian numbers with their "Alpha" or "Word" meanings in the newsletter -

    (let you do Harmonic Math )

    144 = Light

    288 = Double light, the Kingdom of Heaven.

    432 = Consecration (also the square root of the classical speed of light, 186624 miles per second). Several Biblical references are also tied to it; Luke 8:15, Revelation 2:17, etc.

    396 = Classical earth radius (3960 miles).

    576 = Prophecy and Gospel. ( HM 5 + 13 )

    864 = Time (2) the source of light and life, (3) Most Holy.

    1152 = Witness (576 x 2). Biblical references include Luke 14:26, Revelation 3:12, 12:11 and 19:9.

    1296 = Circle of space (360 x 60 x 60). 1296 was also Plato's favorite number.

    1548 = Priest of God.

    1728 = A-flat in music.

    2304 = False Christs and False prophets (1 Cor. 14:22, Mark 13:12).

    3168 = Lord Jesus Christ.

    3888 = New Jerusalem (Rev. 21:2, 1 Cor. 12:27, Luke 8:21, etc.).

    5184 = Victory over the beast (Rev. 15:2).



    hang on a sec ....... ..... if

    a fractal construct has an 'efficient function', it has a fractal ergonomy to them, they function on multiple levels and in multiple dimensions:
    then we can derive from the above mystic numbers some kind of combination of elements from Walter Russel's ( and Lao ) Table of Elements




    we can also use the standard Table of Elements :

    List of Elements of the Periodic Table - Sorted by Atomic Number

    see 369 "transmutation" here : http://www.energeticforum.com/psychi...tml#post206715

    let's try

    144 = Light



    at first glance we have :

    60 144.24 Neodymium Nd 1010 3127 7.01 1885 101 [Xe] 4f4 6s2 5.525



    Neodymium - Wikipedia, the free encyclopedia

    Another chief use of neodymium is as the free pure element. It is used as a component in the alloys used to make high-strength neodymium magnetspowerful permanent magnets[3]. These magnets are widely used in such products as microphones, professional loudspeakers, in-ear headphones, and computer hard disks, where low magnet mass or volume, or strong magnetic fields are required. Larger neodymium magnets are used in high power versus weight electric motors (for example in hybrid cars) and generators (for example aircraft and wind turbine electric generators).[4]
    Last edited by MonsieurM; 09-01-2012, 08:02 PM.

    Leave a comment:


  • MonsieurM
    replied
    was mentioned by David icke

    This version was taken from the Lawful Path
    Extracts

    Paranoia Magazine, Fall 2003 (Issue 33) with Hartford Van Dyke, who they believe is the author

    David Icke with Jack Blood -16th August 2012 Part 2 of 2 - YouTube

    Silent Weapons for Quiet Wars

    The following document is taken from two sources. The first, was acquired on a website (of which I can't remember the address) listing as its source the book titled Behold A Pale Horse by William Cooper; Light Technology Publishing, 1991. The second source is a crudely copied booklet which does not contain a copyright notice, or a publishers name. With the exception of the Forward, the Preface, the main thing that was missing from the first source was the illustrations. As we began comparing the two, we realized that the illustrations, and the accompanying text (also missing from the first) made up a significant part of the document. This has now been restored by The Lawful Path, and so far as I know, is the only internet copy available complete with the illustrations.

    We have no first-hand knowledge that this document is genuine, however many of the concepts contained herein are certainly reasonable, important, and bear strong consideration.

    If anyone has additional knowledge about the source of this document; has better copies of the illustrations than the ones posted here; has any missing pieces to this document, or has any comments which can improve upon the quality of this document, we will appreciate your comments. ----The Lawful Path
    Summary

    Economics is only a social extension of a natural energy system. It, also, has its three passive components. Because of the distribution of wealth and the lack of communication and lack of data, this field has been the last energy field for which a knowledge of these three passive components has been developed.

    Since energy is the key to all activity on the face of the earth, it follows that in order to attain a monopoly of energy, raw materials, goods, and services and to establixh a world system of slave labor, it is necessary to have a first strike capability in the field of economics. In order to maintain our position, it is necessary that we have absolute first knowledge of the science of control over all economic factors and the first experience at engineering the world economy.


    In order to achieve such sovereignty, we must at least achieve this one end: that the public will not make either the logical or mathematical connection between economics and the other energy sciences or learn to apply such knowledge.

    This is becoming increasingly difficult to control because more and more businesses are making demands upon their computer programmers to create and apply mathematical models for the management of those businesses.
    Forward (From Bill Cooper's "Behold a Pale Horse." )
    Preface
    Silent Weapons for Quiet Wars
    Security
    Historical Introduction
    Political Introduction
    Energy
    Descriptive Introduction of the Silent Weapon
    Theoretical Introduction
    General Energy Concepts
    Mr. Rothschild's Energy Discovery
    Apparent Capital as "Paper Inductor
    Breakthrough
    Application in Economics
    The Economic Model
    Industrial Diagrams
    Three Industrial Classes
    Aggregation
    The E-model
    Economic Inductance
    Inductive Factors to Consider
    Translation
    Time Flow Relationships and Self-destructive Oscillations
    Industry Equivalent Circuits
    Stages of Schematic Simplification
    Generalization
    Final Bill of Goods
    The Technical Coefficients
    The Household Industry
    Household Models
    Economic Shock Testing
    Introduction to the Theory of Shock Testing
    Example of Shock Testing
    Introduction to Economic Amplifiers
    Short List of Inputs
    The Personal Paper Trail
    Habit Patterns -- Programming
    National Input Information
    Short List of Outputs
    Table of Strategies
    Diversion, the Primary Strategy
    Diversion Summary
    Media Schools Entertainment Work
    Consent, the Primary Victory
    Amplification Energy Sources
    Logistics
    The Artificial Womb
    The Political Structure of a Nation - Dependency
    Action/Offense
    Responsibility
    Summary
    System Analysis
    The Draft
    Enforcement
    Factor I
    Factor II - Father
    Factor III - Mother
    Factor IV - Junior
    Factor V - Sister
    Factor VI - Cattle

    Leave a comment:


  • MonsieurM
    replied
    you should watch the following doc .... will open your eyes to the world :

    SECRET OF THE SEVEN SISTERS - DESERT STORMS AND FORTUNES (2011) LEGENDADO 1/4 - YouTube

    Leave a comment:


  • MonsieurM
    replied
    Freezing magnetic monopoles: How dipoles become monopoles and vice versa

    Magnetic monopoles, entities with isolated north or south magnetic poles, weren't supposed to exist. If you try to saw a bar magnet in half, all you succeed in getting are two magnets, each with a south and north pole. In recent years, however, the existence of monopoles, at least in the form of "quasiparticles" consisting of collective excitations among many atoms, has been predicted and demonstrated in the lab. Now Stephen Powell, a scientist at the Joint Quantum Institute (JQI) and the University of Maryland, has sharpened the theoretical framework under which monopoles can operate
    "Steady flows of magnetic monopoles are apparently impossible," Powell said, "but transient currents have been demonstrated, and one could imagine creating an alternating current, the magnetic equivalent of AC electricity." This so-called 'magnetricity' might be exploited for designing new kinds of high-density data storage.

    The laws of electromagnetism predict a great symmetry between electric and magnetic forces. This equality does not extend, however, to isolated magnetic "charges." Isolated electric charges, in the form of electrons, are of course quite common. Such charges attract or repel each other with a force inversely proportional to the square of the distance between the charges. A positive charge and a negative charge can team up to form a neutral electric dipole. The situation in magnetism seems different: dipoles yes, monopoles no.

    But new ideas and new experiments have changed the conventional thinking. First, experiments with cold electrons flowing in a two-dimensional sheet could, under the action of powerful magnetic fields, be coaxed into moving in circular orbits. These orbits in turn seem to interact to produce quasiparticles which have a charge equal to a fraction of the conventional electron charge. This was called the fractional quantum Hall effect. Could there be an analog for magnetic dipoles? Could circumstances allow the existence of isolated (or fractional) magnetic poles?

    Recent experiments and Germany and France point to this possibility in so called "spin ice," a solid material made of the elements dysprosium (Dy), titanium (Ti), and oxygen (O). The basic building block of these materials is a pair of tetrahedral groupings, with (typically) two Dy atoms (each of which acts like a tiny dipole magnet of its own) pointing out of each tetrahedron and two pointing in. This is analogous to the orientation of hydrogen atoms in water ice, hence the name "spin ice."

    Leave a comment:


  • MonsieurM
    replied
    with the previous post in mind ....the sbb coil can also then be used like the coil below

    [QUOTE]Pasadena (USA) - NASA scientists have developed a new type of amplifier for electrical signals. The device can be used for a variety of applications, for example, to study distant stars, galaxies and black holes but also to explore the quantum world and the development of quantum computers.

    from : http://www.energeticforum.com/agricu...o-culture.html

    Originally posted by Stealth
    I talked with a man recently and he showed me his garden. Above each tomato plant was a coil of copper wire, wound as a cone, small end down, supported by a wooden stake. Neither end of the copper wire was connected to anything. He had 9 turns of wire in each coil, wound counterclockwise. The tomatoes where had the coils above them were far larger and had many more tomatoes than those which didn't. This arrangement evidently was drawing electricity from the atmosphere. Even though we had two weeks of no rain, the ones under the coils seemed to conserve moisture better and was far healthier. Good Luck. stealth
    thank you Stealth .... a personal experience is worth a thousand theories

    if i may ask did it look like this ...... the coils that is :






    ------------------------------------------------- a little repost from http://www.energeticforum.com/psychi...l-antenna.html

    found some research on water and quantum properties:

    Cooperative and Coherent Water

    Cooperative hydrogen-bonding between molecules gives rise to energetically favourable three-dimensional network of supramolecular clusters in liquid water under ambient conditions, resulting in long-range dipole correlation and quantum coherence Dr. Mae-Wan Ho
    info on quantum coherence:


    http://en.wikipedia.org/wiki/Coherence_(physics)

    Positive Electricity Zaps Through Water Chains

    Water bound on surfaces of proteins and membranes conducts positive electricity, and could enable cells and tissues to intercommunicate rapidly and efficiently. Dr. Mae-Wan Ho

    Can Water Burn?


    The case of salt water that can be ignited when exposed to a radio frequency beam and what it could tell us about the structure of water Dr. Mae-Wan Ho
    Is Water Special?

    Quantum Physics Makes Water Different

    If So plus Water on the Sun info, then it explains this:

    Apparently the Russian scientist Alexander Chizhevsky, who proposed and thoroughly researched links between solar activity and biological response, found that bacteria in water responded to solar flares instantaneously, as opposed to the 8.3 minutes it should take for the photon bombardment to elicit a response."
    and this:

    Redon files: Quantum Entanglement in Photosynthesis and Evolution

    Recently, academic debate has been swirling around the existence of unusual quantum mechanical effects in the most ubiquitous of phenomena, including photosynthesis, the process by which organisms convert light into chemical energy.
    and finally:

    Chengdu Organic Chemicals Co. Ltd., Chinese Academy of Sciences

    "Quantum Water" Discovered in Carbon Nanotubes

    Chengdu Organic Chemicals Co. Ltd., Chinese Academy of Sciences


    A new quantum state of water found in carbon nanotubes at room temperature could have important implications for life...
    ...That's a big deal. Reiter and co chose carbon nanotubes because they are an analogue of the conditions water faces when passing through living systems, through ion channels in cell membranes, for example. Biologists have long known that flow through these channels is orders of magnitude greater than conventional fluid dynamics predicts. Perhaps this new state of quantum water is the reason why.
    enjoy

    link:

    Physics and Physicists: Quantum Physics Makes Water Different

    New Science of the Organism - Water

    Leave a comment:


  • MonsieurM
    replied
    I was a bit surprised to see the following

    grenz|wissenschaft-aktuell: Astrophysiker entwickeln den fast perfekten Signalverstärker

    google translated:

    Pasadena (USA) - NASA scientists have developed a new type of amplifier for electrical signals. The device can be used for a variety of applications, for example, to study distant stars, galaxies and black holes but also to explore the quantum world and the development of quantum computers.

    "This amplifier our abilities of different things being measured to redefine" the team leader Jonas Zmudzinas Jet Propulsion Laboratory (JPL) and professor explained at the California Institute of Technology (Caltech), that its development to date in the journal "Nature Physics" has described.

    An amplifier is a GERAT that increases the strength of weak signals. This amplifier play a fundamental role in general in a variety of scientific measurements and electronics. "For many applications, the current amplifier are perfectly adequate," says Peter Day by JPL. "For a variety of scientific applications, the technologies are available, however, a significant limitation dar."


    as it is an SBB Coil used in Orgone devices we have discussed way back




    Originally posted by boguslaw View Post
    Wyniki Szukania w Grafice Google dla http://www.educate-yourself.org/dc/IM2011coils%20321.jpg



    Tesla said that in those SHAPES is encoded key to Universe, meaning to every force in nature.

    6 and 9 are pancake coil in opposite directions
    3 is a center tapped coil

    also known as SBB coils, one of my favorite coil


    thanks boguslaw for the info, did not know that

    How to make an SBB coil

    and the one twisted, is i think a Mobius Sbb coil, check out this post : http://www.energeticforum.com/144488-post36.html



    coil info

    ------------------------------ the weird thing is that it was posted in

    Crop Circle at Chalk Pit, nr Wootton Rivers, Wiltshire. Reported 2nd August* 2012.

    Last edited by MonsieurM; 08-06-2012, 01:29 AM.

    Leave a comment:


  • MonsieurM
    replied
    from: http://www.energeticforum.com/renewa...tml#post203235

    Originally posted by nat1971a View Post
    Just in case you miss it. Pages 115-116 of the book (page number 138-139 of the pdf). The mass matching of the coils is described on page 115 at the bottom.

    "the weight on this helix happened to be precisely the same as that of the coil.....the shock was almost too intense..."
    this is some great news nat1971a ... thank you for bringing it ti light .... closing another gap in figuring out Tesla's Puzzle

    an similar pattern






    Rotating Earth
    Over the course of an evening, the stars appear to move in the night sky. This movement, however, is not the stars changing position, but rather Earth rotating on its axis. This image faces north, with Polaris, the north star being the brightest trail closest to the center of the light paths.



    --------------------------

    Originally posted by nat1971a View Post
    For info on Telsa's shock waves....


    From "The Free Energy secrets of cold electricity" Peter Lindemann
    Tesla searched the literature to find references to this radiant energy but he could not find much...........No such reference was found, except in the surreptitious observations of two experimenters. In one case, Joseph Henry..........Scientific writings of Joseph Henry : Henry, Joseph, 1797-1878 : Free Download & Streaming : Internet Archive

    Start reading pages 108-145 Scientific writings of joseph henry volume 1
    Article Titled "contributions to electricity and magnetism no III."

    It is quite obvious that Tesla read this document as it also refers to mass matching the primary with the secondaries..It's all there...shocks and all. If you read up more on joseph henry you will also find he attached an elevated capacitance with ground connection. Tesla's radiant energy system is more or less joseph henry's system.

    Leave a comment:


  • MonsieurM
    replied
    for those interested in the Norwegian Spiral

    Hessdalen Live TV, page 1

    Greetings ATSers

    Project Hessdalen, a scientific endevour in trying to learn more about a recurring luminous aerial phenomena in Norway, has set up a new live streaming server. It streams from three different cameras. The streams also work on the iPad which is a plus for many.
    we have talked about it before

    link to the doc

    The Portal - The Hessdalen Lights Phenomenon - FULL - YouTube





    one more thing :

    Hessdalen - Wikipedia, the free encyclopedia







    = 62 + 47 + 35 = 144 = 81 = HM 9 ( number 144 is important see Bruce Cathie )

    = 11 + 11 + 17 = 39 = 12 = HM 3

    Leave a comment:


  • MonsieurM
    replied
    remember we discussed the Leon Cathedral León Cathedral - Wikipedia, the free encyclopedia






    = 42 + 35 + 58 = 135 = HM 9
    = 5 + 7 = 12 = HM 3

    from http://www.energeticforum.com/psychi...tml#post181828






    Leave a comment:


  • MonsieurM
    replied
    Chemists discover new type of molecular bond near white dwarf stars

    have found that some molecules can form and hold together due to extremely high magnetic fields. As they write in their paper published in the journal Science, their calculations suggest that such molecules likely exist near white dwarf stars.
    Because atoms could align with the magnetic field
    ------------------------- just reminded me of; of course it is not as powerful, but maybe the same process happens in the following article ( as above so below )


    remember the following image when we discussed : Francis E. WILKINSON -- High Frequency Transformations

    Francis E. WILKINSON

    High-Frequency Transformations



    [IMG][/IMG]

    Leave a comment:


  • MonsieurM
    replied
    The Astronomist: The Universe and Life is asymmetric: Chirality

    The Universe and Life is asymmetric: Chirality

    The shadow of symmetry haunts physics. Symmetry is invoked to understand nature concisely, but broken symmetry is invoked to understand nature completely. Physics is filled with examples of shattered symmetries: there is more matter than antimatter, neutrinos only come in the left handed spin flavor, and quantum processes break symmetries constantly, but nature also violates symmetry in chemistry and biology in a very clever manner. Chemistry and biology are subjects I do no normally touch upon, but I am intrigued by the curious circumstance of life on Earth: many molecules are not superimposable upon their mirror images, a property called chirality, and life on Earth has a preference for these chiral mirror configurations. Physics and life is inherently asymmetric.

    That something is not identical to its mirror image is a property known as chirality. Hands (etymologically the word chirality is derived from the Greek word for hand), spiral galaxies, and the DNA helix are all examples of chiral objects chirality in biochemistry. I want to ask what makes life chiral, why is life chiral, and how did life become chiral. In order to supplement my limited knowledge of the subject I interviewed a world expert and author of over twenty papers on the subject, Robert Compton, who I must give a deep thanks to for being willing to answer my silly questions.
    read on .....

    It is important to accept that the concept of symmetry is tinted by the human notion of harmonious or aesthetically pleasing forms, but the strict mathematical interpretation of symmetry relies upon metrics of geometry. To this end many seemingly symmetric forms in the living natural world are actually examples of broken symmetries: spiral tree trunks, the human form, and sea shells (which generally only coil in one particular direction according to species). The remarkable thing is that this macro asymmetry can be traced back to a micro asymmetry in the chemistry of life. The arrangement of atoms in a molecule defines the function of that molecule, but even molecules with the same chemical configuration can behave differently as in the case of chiral molecules which are like mirror images of the same molecule that come in 'left' and 'right' handed forms. The great asymmetry of life is that all living organisms on Earth almost exclusively utilize the left handed (or levorotatory) configuration for amino acids and the right handed (or dextrorotatory) configuration for sugars belonging to DNA or RNA.

    COHERENCE AT ANY LEVEL IS COHERENCE AT ALL LEVELS.

    An orderly arrangement between wave lengths establishes a connection between frequencies and fields. But for this connection to last, it must resonate to all frequencies and fields. This can only be accomplished through the resonate structure of golden mean pathways. a harmonic cascade effect

    Last edited by MonsieurM; 07-18-2012, 02:52 PM.

    Leave a comment:


  • MonsieurM
    replied
    was thinking Orgone Chamber + Aluminum and found the following

    Wilhelm Reich -- Orgone -- Collected articles

    Orgone Products: Orgone Cloudbuster & Chembuster. The Only Mini Cloudbuster & Chembuster on the net!

    Orgone Chembuster / CloudBuster addition of Quartz crystals ( if all his quartz was left chiral he'll get more effects ) into the Orgone mix I do use the crystals, Quartz, amethyst, tourmaline, jade and turquoise.Aluminum
    I think Aluminum should be used but in a specific Manner .... more like Ighina the Italian Tesla


    -------------------------

    Study Demonstrates Gravity Determines Handedness of Molecular Screws | Chemistry | Sci-News.com

    Published: Mar 5th, 2012

    Study Demonstrates Gravity Determines Handedness of Molecular Screws


    Researchers have for the first time demonstrated that gravity plays a role in the formation of molecular aggregates, and that it can even be used to make them right-handed or left-handed.
    Many chemical and biochemical substances exist in the form of one of two structures that are the exact mirror-image of one another. However, no one could explain exactly how these images originally formed.

    Now, researchers from the Nijmegen High Field Magnet Laboratory (HFML), the Netherlands, the CNR-IPCF Institute in Messina, Italy, and the University of Messina, have demonstrated that a combination of gravitational and rotational forces may play a role.


    Non-chiral porphyrins, shown with green blocks, can form screw-shaped chiral structures. The rotation (red arrows) and gravity (green arrows) determine whether left- or right-handed screw structures are formed (N. Micali et al)


    -------------- from: http://www.energeticforum.com/renewa...tml#post153750

    Solid-state physics: Golden ratio seen in a magnet

    The golden ratio has been spotted in a magnetic compound. (principle of correspondence )
    Access : Solid-state physics: Golden ratio seen in a magnet : Nature

    ------------------------------------



    from The Avalon Foundation :|: Research - Examination of Apparent Transient Weight Changes In Accelerated Chiral Crystals

    All of the identified crystals may be considered chiral in nature, and generally seemed to have values higher than sucrose for rotatory power at typical sodium wavelengths of light. Among these candidates are:

    Alpha quartz (found in nature as nearly equal populations of left and right hand crystals)
    Lithium Iodate (expensive, though well studied)
    Single crystal tellurium (being readily available in bulk, but expensive in single crystal form)
    Gamma selenium (grown from solution)
    Cinnabar (Mercuric Sulphide - highly toxic)
    Tourmaline
    Rochelle Salt


    The clear winner from this list, for our purposes, was alpha quartz! Good quality natural quartz points are readily available, and large cultured specimens are available as well for modest prices. The SiO4 ion is well studied and the alpha quartz lattice has long been characterized for dimensions and properties. Alpha quartz has been cited as having a sodium line optical activity of between 23 and 25 degrees per mm.
    Last edited by MonsieurM; 07-18-2012, 03:01 PM.

    Leave a comment:


  • MonsieurM
    replied
    Just linking Pattern

    those " wires" on the Tori don't they resemble the Mobius Wire ( sort of )



    from: http://www.energeticforum.com/psychi...tml#post172524

    a fractal construct has an 'efficient function', it has a fractal ergonomy to them, they function on multiple levels and in multiple dimensions:
    If you understood the above statement , you'll understand the following

    Originally posted by MonsieurM View Post
    just on a side note: the double spiral water closely resembles the double mobius coil mentioned earlier

    Step 1

    2 wires of six feet each to be made into 2 mobius wires (you end up with 2 mobius wires that are 1/4 the length of 6 feet )coiled at 45 degrees (see how to build a mobius coil Mobius Coil Tutorial )







    enjoy the experimentation

    COHERENCE AT ANY LEVEL IS COHERENCE AT ALL LEVELS.
    An orderly arrangement between wave lengths establishes a connection between frequencies and fields. But for this connection to last, it must resonate to all frequencies and fields. This can only be accomplished through the resonate structure of golden mean pathways
    . a harmonic cascade effect

    Leave a comment:


  • MonsieurM
    replied
    Mathematics: First-ever image of a flat torus in 3D

    Just as a terrestrial globe cannot be flattened without distorting the distances, it seemed impossible to visualize abstract mathematical objects called flat tori in ordinary three-dimensional space. However, a French team of mathematicians and computer scientists has succeeded in constructing and visually representing an image of a flat torus in three-dimensional space. This is a smooth fractal, halfway between fractals and ordinary surfaces. The results are published in PNAS.



    Image showing the isometric embedding of a square flat torus in 3D space, seen from the outside (above) and from the inside (below). Different oscillation waves, called corrugations, can be distinguished. Together, the corrugations form an object that resembles a fractal and has a rough appearance
    In the 1950s, Nicolaas Kuiper and the Nobel laureate John Nash demonstrated the existence of a representation of an abstract mathematical object called flat torus, without being able to visualize it. Since then, constructing a representation of this surface has remained a challenge that has finally been met by scientists in Lyon and Grenoble.

    On the basis of the Convex Integration Theory developed by Mikhail Gromov in the 1970s, the researchers used the corrugation technique (oscillations). This reputedly abstract mathematical method helps to determine atypical solutions to partial differential equations. This enabled the scientists to obtain images of a flat torus in 3D for the first time. Halfway between fractals and ordinary surfaces, these images show a smooth fractal.

    These findings open up new avenues in applied mathematics, especially in the visualization of the differential equations encountered in physics and biology. The astounding properties of smooth fractals could also play a central role in the analysis of the geometry of shapes.

    Leave a comment:

Working...
X