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
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 Type | Structure Highlights | Symbolic/Mathematical Notes |
|---|---|---|
| Varāhamihira’s Sarvatobhadra | Uses repeating sequences (e.g., 2–3–5–8 and 5–8–2–3), with mirrored symmetry | Likely ritualistic; used in perfume preparation and yantras |
| Nārāyaṇa’s Constructed Square | Fully numeric pan-diagonal magic square with sum 34 per row/column/diagonal | One of 384 such squares; constructed via Turagagati (horse-move) |
| Jaina Inscriptional Square | Found at Dudhai and Khajuraho; sum 34; historically embedded in temple architecture | Reflects 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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