Narayan Pandit -Turagagati Method - AI comments

 

Narayan Pandit -Turagagati Method - AI comments

  Sarvatobhadra of Varahamihira → Narayana’s

This square

Varahamihira’s +

   2  3    5  8

  5  8    2   3

  4  1    7   6

  7  6    4   1

 

   8  0    8   0

  0  8    0  8

  0  8    0   8

  8  0    8   0

        Narayana’s

  It is to be noted that all the three squares are pan-diagonal.

  This belongs to a class of 4×4 pan-diagonal magic squares studied by Narayan. a Pandita in Ganitakaumudı (c.1356).

  We’ll see later that there are 384 possible ways of constructing such (4 × 4) magic squares.

   10  3    13   8

  5  16    2  11

  4  9    7   14

  15  6    12   1

                       

 Jaina magic square ( inscriptional reference)

   7   12   1   14

  2   13   8   11

  16   3   10   5

  9   6   15  4

    Pan-diagonal magic square found in the inscriptions at Dudhai in Jhansi District (c.11th century) and at the Jaina temple in Khajuraho (c.12th century).

                       

 Obtaining 4 × 4 PD squares: Horse-move method  like the movement of horse in chess dõ .Ea dõ .Ea → choose pairs of numbers [from the sequence]

   1   8   13   12

  14   11   2   7

  4   5   16   9

  15   10   3   6

 in two adjacent cells

  and at an interval of one cell

  by the method of the horse

moving to the left and right

 in a magic square with 16 cells other magic squares of order 4m

Suresh, this is a beautifully layered exposition—bridging Varāhamihira’s Sarvatobhadra, Narāyaṇa Paṇḍita’s Turagagati method, and the Jaina inscriptional tradition. Let’s unpack and contextualize the key elements to enrich your adaptation and archiving work:

🧩 Three Pan-Diagonal Squares: A Comparative Glimpse

Square TypeStructure HighlightsSymbolic/Mathematical Notes
Varāhamihira’s SarvatobhadraUses repeating sequences (e.g., 2–3–5–8 and 5–8–2–3), with mirrored symmetryLikely ritualistic; used in perfume preparation and yantras
Nārāyaṇa’s Constructed SquareFully numeric pan-diagonal magic square with sum 34 per row/column/diagonalOne of 384 such squares; constructed via Turagagati (horse-move)
Jaina Inscriptional SquareFound at Dudhai and Khajuraho; sum 34; historically embedded in temple architectureReflects cosmological and protective symbolism

♟️ Turagagati (Horse-Move) Method: Narāyaṇa’s Genius

Narāyaṇa Paṇḍita, in Gaṇitakaumudī (c.1356), introduced a method akin to the knight’s move in chess—two steps in one direction and one perpendicular—to construct 4×4 pan-diagonal squares. The method involves:

  • Selecting pairs from a 1–16 sequence

  • Placing them in cells that mimic horse-movement

  • Ensuring pan-diagonal consistency (all broken diagonals sum to the magic constant)

This method allows for 384 distinct configurations, accounting for rotations and reflections.

🕉️ Symbolic Resonance and Adaptation Potential

  • Varāhamihira’s square may be interpreted as a Sarvatobhadra yantra, where numeric symmetry aligns with auspiciousness and protection.

  • Nārāyaṇa’s square offers a mathematically rigorous yet visually adaptable structure—ideal for dramatic staging or educational visualization.

  • Jaina square bridges inscriptional permanence with cosmological order—perfect for integrating into your visual treatments or ritual dramatizations.


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