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Recreational Mathematics Magazine

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Mathematical Citation Quotient (MCQ) 2016: 0.05

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Digital Root Patterns of Three-Dimensional Space

Chia-Yu Lin
Published Online: 2016-04-14 | DOI: https://doi.org/10.1515/rmm-2016-0002


In this study, we define vedic cube as the layout of each digital root in a three-dimensional multiplication table. In order to discover the geometric patterns in vedic cube, we adopt two methods to analyze the digital root in a three-dimensional space. The first method is floor method, which divides vedic cube into several X-Y planes according to different Z values (floors) to analyze the geometric characteristics on each floor. The second method is symmetric plane method, which decomposes vedic cube by its main and secondary symmetric planes.

Keywords: Digital root; pattern; vedic square; vedic cube; symmetry


  • [1] Abas, S. J., Salman, A. S. Symmetries of Islamic geometrical patterns, World Scientific, Singapore, 1995.Google Scholar

  • [2] Balmond, C. Number 9, Prestel, Munich, 1998.Google Scholar

  • [3] Balmond, C. Element, Prestel, Munich, 2007.Google Scholar

  • [4] Balmond, C. Crossover, Prestel, Munich, 2013.Google Scholar

  • [5] Balmond Studio. 2012. http://www.balmondstudio.co.in/pavilions_images/serp2002_3.jpgGoogle Scholar

  • [6] Balmond Studio. 2013. http://www.balmondstudio.com/work/serpentine-pavilion-2002/Google Scholar

  • [7] Bunyard, D., Brine, A. “Islamic art: Vedic square”, Micromath, 1988.Google Scholar

  • [8] Coxeter, H. S. M. Regular Polytopes, Dover, New York, 1973.Google Scholar

  • [9] Ghannam, T. The Mystery of Numbers: Revealed Through Their Digital Root (2nd Edition): Unraveling the Hidden Design of the Universe through The Digital Root of Numbers, CreateSpace, North Charleston, SC, USA, 2012.Google Scholar

  • [10] Jones, L. “Mathematics and Islamic art”, Mathematics in School, 18(4), 32-35, 1989.Google Scholar

  • [11] Lu, P. J., Steinhardt, P. J. “Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture”, Science, 315(5815), 1106-1110, 2007.Web of ScienceGoogle Scholar

  • [12] The British Library Board. Mamluk Qur’an, 2015. http://www.bl.uk/onlinegallery/sacredtexts/mamlukquran.html Google Scholar

About the article

Published Online: 2016-04-14

Published in Print: 2016-03-01

Citation Information: Recreational Mathematics Magazine, Volume 3, Issue 5, Pages 9–31, ISSN (Online) 2182-1976, DOI: https://doi.org/10.1515/rmm-2016-0002.

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© 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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