Beejank using Casting out 9 and Casting out 11- A Comparative Analysis

Authors

  • Komal Asrani Department of CSE, BBDNIIT, Ayodhya Road, Lucknow, 226024, Uttar Pradesh, India. Author https://orcid.org/0009-0002-8256-0599
  • Kailash Vishwakarma Department of Physics, BN PG College, Rath, Hamirpur, 210431, Uttar Pradesh, India. Author
  • Deepak Asrani Department of CSE, Graphics Era Deemed University, Clement Town, Dehradun, 248002, Uttarakhand, India Author

DOI:

https://doi.org/10.31305/rrjiks.2026.v3.n1.013

Keywords:

Beejank, Ancient Mathematics, Casting out 9, Casting out 11

Abstract

Beejank is one of the basis operations used in ancient Indian mathematics for verification of arithmetic operations. The popular definition of Beejank quotes it as the process of summing its digits repeatedly until a single digit is obtained. However, we dive in depth and explore two popular approaches of calculating Beejank- Casting out 9 and Casting out 11. The detailed understanding of both the approaches is discussed. Further, comparison of casting out 9 and 11 is done for various arithmetic operations and identify the suitability for verification of results. Constraints of both the approaches have been summarized.

Author Biographies

  • Komal Asrani, Department of CSE, BBDNIIT, Ayodhya Road, Lucknow, 226024, Uttar Pradesh, India.

    Komal Asrani received her B.E(Electrical) from GEC, Bilaspur and M.S from BITS,Pilani. She completed her Ph.D.(Computer Science) from UPRTOU, Allahabad. She also completed her Diploma in Vedic Mathematics. Presently, she is serving as Professor in the Dept. of Computer Science & Engg, BBDNIIT, affiliated to AKTU Lucknow and possess an overall experience of 26 years. Besides her current role as Professor, she has been actively contributing to the promotion of Vedic Mathematics and Indian Knowledge Systems (IKS) through lectures, workshops, and conferences across India. As a resource person and invited speaker, she has delivered sessions in Faculty Development Programmes, National and International conferences, and training camps. Beyond conferences, she has conducted workshops and camps in universities, colleges, and schools, including Bundelkhand University, CCS University Meerut, Manav Rachna University, and Bharat Uday Gurukul, Hamirpur. She has also contributed to UGC curriculum design discussions at Galgotia University. Her talks have spanned diverse themes such as the application of Vedic Mathematics in cryptography, computer science, and engineering, as well as its relevance to modern education. She has also engaged audiences through online webinars organized by IIT Patna, IIIT Pune, Regional Science Centres, and Vidya Bharati. Besides these platforms, she has consistently aimed to bridge ancient wisdom with modern applications, making Vedic Mathematics more accessible to students, teachers, and researchers, while strengthening the presence of IKS in contemporary academic discourse through her YouTube channel which lists more than 150 videos.

  • Kailash Vishwakarma, Department of Physics, BN PG College, Rath, Hamirpur, 210431, Uttar Pradesh, India.

    Dr. Kailash Vishwakarma is a distinguished physicist, educationist, and scholar of Vaidik Science. He served as Professor and Head of the Department of Physics and later as Principal of B.N.P.G. College, Rath, Hamirpur (U.P.), affiliated with Bundelkhand University. He earned his B.Sc. (1980), M.Sc. (Physics, 1982), and Ph.D. (Physics, 1987) from University of Allahabad. With nearly four decades of academic experience, Dr. Vishwakarma has published over 90 research papers in Physics and more than 50 papers on Vaidik Vigyan. He has authored over 35 books, supervised 11 Ph.D. scholars and 10 M.Phil. scholars, and successfully completed several major and minor research projects. A sought-after speaker, he has delivered invited lectures at universities, IITs, IIITs, research institutions, and international forums across India and abroad. Since 1989, he has actively promoted Vaidik Ganit through workshops and training programs. His notable honors include the Madhav Ganit Puraskar (2023) and the Acharya Prafulla Chandra Rai Vigyan Samvardhan Samman (2025).

  • Deepak Asrani, Department of CSE, Graphics Era Deemed University, Clement Town, Dehradun, 248002, Uttarakhand, India

    Deepak Asrani is a distinguished academician and technology professional with over 30 years of combined experience in academia, industry, and software development. He is currently serving as Professor, Computer Science & Engineering, and Dean (Academics) at Graphic Era Deemed University, Dehradun. He holds a Ph.D. in Computer Science & Engineering, along with M.Phil. (Computer Science), M.S. (Software Systems), and B.E. (Electronics & Telecommunication). His research interests include Database Management Systems, Data Warehousing, Data Analytics, Networking, Java, and Object-Oriented Analysis & Design and ancient Indian Knowledge Systems. Dr. Asrani has published several research papers in reputed journals and international conferences, guided numerous undergraduate and postgraduate projects, and is currently supervising doctoral research. He has played a pivotal role in NBA accreditation, academic administration, and curriculum development. A recipient of multiple NPTEL Elite certifications, he has also delivered expert lectures and actively contributes to outcome-based education, research, and faculty development initiatives.

References

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Published

2026-06-30

Issue

Vol. 3 No. 1 (2026): Research Review Journal of Indian Knowledge Systems [JAN-JUN 2026]

Section

Articles

How to Cite

Asrani, K., Vishwakarma, K., & Asrani, D. (2026). Beejank using Casting out 9 and Casting out 11- A Comparative Analysis. Research Review Journal of Indian Knowledge Systems, 3(1), 119-131. https://doi.org/10.31305/rrjiks.2026.v3.n1.013