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  • Non-periodic tiling

    From Gerald Kelleher@21:1/5 to All on Wed Sep 6 13:50:43 2023
    https://imgur.com/gallery/UV2tvOJ

    Although over a half lifetime ago, I am still protective of that representation for although it contains the 4 angles of the tiling plus 216 degrees, nobody can really read it and what it represents.

    https://www.projectrhea.org/rhea/images/e/e3/Rhombic.jpg

    https://www.mrbertman.com/images/figure1.png

    I thought people would recognise what is familiar in the diagram both old and new but it turns out that like everything else, the challenges of inspiration do not come easy to those who have forgotten geometry and that harmony that runs through creation.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Gerald Kelleher@21:1/5 to All on Sun Sep 10 00:58:11 2023
    The fully developed feature is Chi-Rho with the foundations in the golden triangle-

    https://www.geogebra.org/resource/sxEMtV6q/0DTICmpFzNPJWEDy/material-sxEMtV6q.png

    The three remaining angles are in proportion to 4, 3 and 2 thereby completing the arrangement of non-periodic tiling as 36°, 72°, 108° and 144°.

    Many artists, and notably Kepler in astronomy, tried to work this geometry into their perspectives as the geometric proportion known as Phi. Although the subject receives a dry expression in mathematical terms, it is so enjoyable and satisfying for those
    who permit creation to express itself in geometry rather than non-geometric treatments found in equations and suchlike.

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

    The approximation of 1.618033.. is 1.62 so just as 432° is 1.2 times 360°, then the expansion of 1.62 by doubling it gives meaningful numbers in timekeeping and geometry at large scales.

    1.62 - 3.24 - 6.48 - 12.96 -25.92 - 51.84

    25 - 30 - 36 - 43.2 - 51.84

    The angle of inclination of the Great Pyramid is 51.84 ° incorporating a triangle, and square with a high Phi content. Perfect for those who can enjoy geometry at this level of consideration without favour or fact to this era that is always trying to
    mesh geometry with timekeeping.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Gerald Kelleher@21:1/5 to All on Thu Sep 14 02:47:32 2023
    The conditions for life across the Universe would retain the geometric feature of Phi proportion just as the Pi would be the same on every other planet. It may be fine for mathematical theorists to go on a misadventure with geometry for the last number
    of centuries and especially 100 years ago, however, it prevents appreciation of the connection between humanity and their surroundings at small and large scales. For those unfamiliar with the Phi proportion of the golden ratio, there are any number of
    websites out there with some more relevant than others-

    https://www.adobe.com/creativecloud/design/discover/golden-ratio.html

    Just as the geometry of DNA within animate life is made up of four chemicals that say nothing without a broad perspective, the four angles of non-periodic tiling likewise become lost in a world of abstract mathematics that would look like an indulgence
    to 21st-century eyes or, at least should it should these days.

    https://www.projectrhea.org/rhea/images/e/e3/Rhombic.jpg

    What is 432° in simplicity is 360° in diversity and multiplicity hence it delights those who find the Universal appeal in the geometry. The sullen and dour will see nothing.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Gerald Kelleher@21:1/5 to All on Thu Oct 12 23:46:26 2023
    Long before fullerenes and a combination of hexagons and pentagons, the geometry of non-periodic tiling with its four angles suggested a combination of hexagonal and pentagonal geometry encapsulated by an encompassing value of 432°. The structure is
    neither entirely pentagonal nor hexagonal but a balance between the two.

    https://imgur.com/gallery/UV2tvOJ

    The association between terrestrial science and objects beyond our planet on a larger scale, whether the spirals of a galaxy, the structure of a solar system, a supernova star or other features yet to be discovered made themselves known and become
    connected in a specific but diverse way. As this geometry encompasses animate and inanimate existence, it is more important than trying to isolate chemicals for the conditions of life on Earth let alone elsewhere in the cosmos.

    The dizzying array of geometric features is delightful within the normal language of space at a local level or large scale even in an era when a section of humanity tries to combine geometry with timekeeping for some contrived spectacle only appealing to
    themselves and others who know no better.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)