A Periodic Table of Geometries

My studies have brought me to investigate a variety of geometries. I consider the premise of a ‘periodic table’ of geometry, which would act a multi-dimensional tool for the illustration of the range of geometric foundations which underly natural phenomena and theoric situations. This table would include ‘uni-dimensional’ structures of point, line, polygon, arc and function (slope), which would then stratify as multiple dimensions as simple geometry are compared with each other. This would lead to both archemedian and platonic primitives as well as a range of complex geometies arising from graph functions. Polar parametic graphing can allow differentiation of cardiods and lissajous geometries in this area as specific vectors of dimensional stratification. Similarly, archimedian geometries have ‘higher’ forms in geodesics (Buckballs, etc) and in this, structural tensegrity could plot the vector of another dimension. Recursion itself would also add its own dimension to the table as fractal functions are incorporated. Pi, phi, e (etc), being transcendental, would become the table’s only constants as all other fixed numbers would loose their relevancy except in references as variables. (randomly fixed, transitively constant?) Phi and others would open the door into non-euclidean spaces and klein forms, elliptic and hyperbolic geometries could begin to make headway toward hypercubes, tesseracts and other n-dimensional concepts.

Tabulation of such information could be used by most scientific fields as a bridge between abstract equations and the reality of natural phenomena. However, if ‘dimensions’ of geometry were added in a simple and visually intuitive enough manner, the basic geometries could be conveyed even in grade school classes along with traditional mathematical methods, smoothing the gaps between high school, college, applied sciences and research sciences. Because of the visual nature of geometry it may also help bridge the gap between ‘art’ and ‘science’. The focus would be on visualization of these forms so they could be codified.

§Those who live in the Sun

their shapes and structure-proportions were much like us. their spine was different ins one way. They did a kind of yoga that is based on high-D math. It was one of my first exposures to extremely high-dimensional mathematics. I saw a Periodic Table of Geometries that I still use to navigate the terrain of maths. I didn’t look to see if they were projecting the information to me, or if I caught a glimpse of their operations. They can move into the earth field through doorways they construct, which are based on the geometric math of their yoga when such is used to build a ‘curtain’ of some kind. I know I learned enough that it is where I am going to be eventually because I saw where I will live. They do many kinds of activities, but how deep within the sun they do them is related to the governance-like importance of why to do them there. It’s maybe like if words had 7+ meanings, and each meaning could redefine some part of reality based on where you said it, but the ‘word’ is also a mix of body movement and thoughts. (maybe the ‘prana bindu’ inspiration?)


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