The volume contains selected articles presented in the ZOOM conference on History of Mathematics in Jain Literature, December 2020, and also contains articles invited by the editors on specific topics. The main objective for the conference was to bring to the attention of historians in mathematics that there is a plenty of literature written by monks and scholars in Jaina literature that contains elements of arithmetic, algebra and geometry, independent of discoveries by other cultures in the past. The talks and the discussions at the conference highlighted a need for a volume that can be recommended as a reference book for a course on History of Mathematics in the Departments of Mathematics and Education in colleges and universities. This is our hope that the present volume would fill up the gap on the lack of knowledge of past Jaina contributions.
Author(s): Surender K.l Jain, S. G. Dani
Publisher: World Scientific
Year: 2022
Language: English
Pages: 246
City: Singapore
Contents
Preface
Introduction
Article 1. Decimal Numerals and Zero in Ancient Jaina Literature
1.1. Introduction
1.2. All Numbers Expressed in Words (No need of zero)
1.3. The Decimal and Non-decimal Scales of Counting
1.4. The Place-value Method of Counting and Recording, and the Case of Anuyoga-dvara-sutra
1.5. Triloka-Prajnapti and Some Other Early Works
1.6. After Tiloya-pannatti and Upto About 850 CE
References and Notes
Article 2. Evolution and Development of Mathematical Ideas through Jaina Scriptures
2.1 Decimal System with Place Value
2.2. The Concept of Zero with Place Value
2.3. Sarvanandı.
2.4. Jinabhadra.
2.5. Square-roots and Compound Fractions.
2.6. The Number Field: Z+.
2.7. Ordinals and Cardinals.
2.8. Integer Partitions.
2.9. Temporal Scale. Analogy Measures (Upamamana).
2.10. Occupancy Problem in Probability Theory: (r balls in n cells)
2.11. The Geometry and Mensuration of a Circle and Concentric Annuli.
2.12. Beginnings of Algebra
2.13. Emergence of Binomial Coefficients. Six-fold Increase/Decrease.
2.14. Binomial Coefficients and Power Expansion.
2.15. Combinatorics.
2.16. Logarithms (base 2).
2.17. Pre-Calculus.
2.18. Algebraic Symbolism (Artha-sandrsti).
2.19. Conclusion.
Acknowledgements
Abbreviations
References
Article 3. Geometry in Ancient Jaina Works; a Review
3.1. Introduction
3.2. Geometry in Early Jaina Works
3.2.1. Circumference of a circle
3.2.2. On the choice of the value √10
3.2.3. Chords and arrows
3.2.4. Chords and arcs
3.2.5. Area formulae
3.3. Jaina Geometry in Later Phases
3.3.1. Srıdhara and the volume of a sphere
3.3.2. Vırasena and the volume of a conical frustrum
3.3.3. Mahavıra on the quadrilaterals
3.3.4. Mahavıra, on curved figures and the ayatavrtta
3.3.5. T.hakkura Pheru
3.4. In Place of Conclusion
Acknowledgements
References
Article 4. Partitions of Numbers Described in Bhagavatı Sutra
4.1. Introduction
4.2. Partitions as Found in the Bhagavatı Sutra
4.3. Results and Discussion
4.4. Concluding Remarks
Abbreviation and Notation
Acknowledgments
References
Article 5. Concept of Infinity in Jaina Literature
5.1. Introduction
5.2. Classification of Numbers
5.3. Classification of Infinity
5.4. Asankhyata and Ananta
5.5. Conclusion
Acknowledgement
References
Article 6. Geometry in Mahavıracarya’s Ganitasarasangraha
6.1. Introduction
6.2. Trilaterals and Quadrilaterals
6.3. Circles
6.4. Areas of Some Special Curves
6.5. Area Bounded by Circles
6.6. Elongated Circle (Ayatavrtta)
6.7. Conchiform
6.8. Hexagon
6.9. Sphere
6.10. Area of Convex and Concave Spherical Segment
6.11. Ring
6.12. Conclusion
Acknowledgements
References
Article 7. Kuttıkara Equations in Mahavıracarya’s Ganitasarasangraha
7.1. The Kuttaka: An Introduction
7.2. Kuttaka and its Types
7.2.1. Vallika Kuttıkara
7.2.2. Visama Kuttıkara
7.2.3. Sakala Kuttıkara
7.2.4. Suvarna and Vicitra Kuttıkara
7.3. Aryabhata’s Approach and Kuttaka
Acknowledgment
References
Article 8. Series Summations in Srıdhara and Mahavıra’s Works
8.1. Introduction
8.2. Formation of Peculiar Series
8.3. The Srıdhara-Mahavıra Series
8.4. Epilogue and Concluding Remarks
References
Article 9. Cryptography and Error-Detection in Siribhuvalaya
9.1. Introduction
9.1.1. Recent scholarship
9.1.2. Organization of this paper
9.2. The Structure of the Siribhuvalaya
9.3. Decrypting a Cakra
9.3.1. Examples
9.4. Encryption (Encoding) Method
9.5. Error Detection at the End of Each Chapter
9.6. Multiple Languages
9.7. Related Concepts in Modern Cryptography
Acknowledgments
References
Article 10. Jain Syllogism and Other Aspectsof Jain Logic with Applications to Statistical Thinking
10.1. Introduction
10.2. Materials and Methods
10.3. Results and Discussion
10.3.1. Five-fold Jain syllogism( /Pancavayavavakya)
10.3.2. History and development of the five-fold Jain syllogism
10.3.3. Five-fold syllogism in Bayesian terminology
10.3.4. Conditional predication principle (Syadvada)
10.3.5. Conditional (non-absolute) holistic principle(Anekantavada)
10.3.6. Turing and ‘enigmatic statistics’
10.4. Conclusion
Acknowledgment
References
Article 11. Zero in the Early Svetambara Jaina Works
References
Article 12. Jaina Mathematical Sources since the Eighth Century
12.1. Introduction
12.2. Unpublished Non-Canonical Jaina Mathematical Texts
12.3. Published Jaina Non-Canonical Works
References
Appendix
