pati-ganita

mathematics

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July 17, 2026

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Pati-ganita is a term from ancient Indian mathematics that refers to arithmetic and mensuration. It literally translates to "board-computations," referencing the practice of performing calculations on a dust board or sandbox. This field encompassed fundamental arithmetic operations such as addition, subtraction, multiplication, division, squaring, square-root extraction, cubing, and cube-root extraction.1

Pati-ganita also included techniques for solving problems related to mixtures, series, plane and solid geometry, and the geometry of shadows. It provided formulas for calculating areas, volumes, interest, and solving proportions, as well as quadratic equations and permutations. Mathematicians like Brahmagupta and Shridhara made significant contributions to pati-ganita, laying the groundwork for what would become arithmetic and algebra in Indian mathematics.123

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Indian mathematics
The changing structure of mathematical knowledge
…at the emerging distinction between pati-ganita (arithmetic; literally “board-computations” for the dust board, or sandbox, on which calculations were carried out) and bija-ganita (algebra; literally “seed-computations” for the manipulation of equations involving an unknown quantity, or seed); these were also called “manifest” and “unmanifest” calculation, respectively, alluding to the types…
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…at the emerging distinction between pati-ganita (arithmetic; literally “board-computations” for the dust board, or sandbox, on which calculations were carried out) and bija-ganita (algebra; literally “seed-computations” for the manipulation of equations involving an unknown quantity, or seed); these were also called “manifest” and “unmanifest” calculation, respectively, alluding to the types…
Read More