Magic Squares in India

  • Takao Hayashi
Living reference work entry
The oldest datable magic square in India occurs in Varāhamihira’s encyclopedic work on divination, Bṛhatsaṃhitā (ca. AD 550). He utilized a modified magic square of order four in order to prescribe combinations and quantities of ingredients of perfume. It consists of two sets of the natural numbers 1–8, and its constant sum ( p) is 18 (Fig. 1). It is, so to speak, pan-diagonal, that is, not only the two main diagonals but also all “broken” diagonals have the same constant sum. Utpala, the commentator (AD 967), also points out many other quadruplets that have the same sum.


Central Column Arithmetical Progression Thirteenth Century Common Difference Sanskrit Text 
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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Doshisha UniversityKyoto CityJapan