A holographic representation of three-dimensional J9 space

Prashant Jadav; Vivian Amos; Martin Richardson

doi:10.1117/12.2510707

1 March 2019 A holographic representation of three-dimensional J₉ space

Prashant Jadav, Vivian Amos, Martin Richardson

Proceedings Volume 10944, Practical Holography XXXIII: Displays, Materials, and Applications; 109440D (2019) https://doi.org/10.1117/12.2510707
Event: SPIE OPTO, 2019, San Francisco, California, United States

Abstract

This paper is an exploration of the numeric and visual properties of a square numerical grid containing 81 elements (“J₉ Space”). J₉ Space has been derived from the standard multiplication grid through the calculation of digital roots. Nested within J₉ Space are eight smaller square grids. A three-dimensional representation of J₉ 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. J₉ 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 J₉ 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.

Citation Download Citation

Prashant Jadav, Vivian Amos, and Martin Richardson "A holographic representation of three-dimensional J₉ space", Proc. SPIE 10944, Practical Holography XXXIII: Displays, Materials, and Applications, 109440D (1 March 2019); https://doi.org/10.1117/12.2510707

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