A holographic representation of three-dimensional J9 Space

This paper is an exploration of the numeric and visual properties of a square numerical grid containing 81 elements ("J(9) Space"). J(9) Space has been derived from the standard multiplication grid through the calculation of digital roots. Nested within J(9) Space are eight smaller square grids. A three-dimensional representation of J(9) Space has been created from the two-dimensional numerical grid, displaying the highly symmetrical properties contained within it. The three-dimensional representation is fundamentally a collection of two-dimensional triangular polygons that create a surface in three-dimensional space. J(9) Space appears to be a fundamental part of the framework of the number system and has some interesting mathematical features. This paper also summarises the recording of a three-dimensional printed model of J(9) Space as a denisyuk reflection hologram. This is an artistic impression of the model using a volume holographic technique. The author who has contributed the mathematical concept (Prashant Jadav) suggests that the use of digital roots to develop three-dimensional models from well-known mathematical tools is a new method by which to create and visualise structures within the number system.