Permutations and Oblong Numbers in the <i>Theravāda-vinaya</i>: A New Intersection of Buddhism and Indian Mathematics

Abstract

Within the context of Indian religions, Jainism has long been recognized for its extensive use of permutations and combinations. However, the application of these principles within Buddhist scriptures has received relatively little scholarly attention. This paper introduces a new example of the specific application of permutations and combinations in Buddhist scriptures. In this paper, we focus on the first saṅghādisesa rule in the Theravāda-vinaya, which lists a series of element sets and arranges these elements according to a certain pattern known as “ten-roots” (mūla), and we discover that these arrangements form a regular numerical sequence, called “oblong numbers”. Moreover, similar patterns with different quantities are also found in the fourth Pārājika and the fifth saṅghādisesa rules. This indicates that the compilers of the Theravāda-vinaya did not use this mathematical knowledge without basis. Interestingly, we also found the use of this sequence in the Bakhshālī manuscript. Therefore, in this article, after summarizing and verifying the arrangement rules of the Theravāda-vinaya, we discuss whether the oblong numbers were influenced by Greek mathematics.

Keywords

• Buddhism and mathematics
• <i>Theravāda-vinaya</i>
• permutation
• oblong numbers