Narayan Pandit - 8x8 Magic Square - AI Comment

 Narayana outlines the folding method for samagarbha magic squares as follows:

Narayana's Example 2: 8x8 Magic Square with Sum 260

In this case, Narayana takes 1, 2, 3, 4, 5, 6, 7, 8 as the first sequences and 0, 1, 2, 3, 4, 5, 6, 7 as the second sequence. The sum of the first sequence is 36. Subtracting this from 260 gives 224.

This, when divided by 28, which is the sum of the second sequence, gives 8 as the factor. Thus the product sequence will be 0, 8, 16, 24, 32, 40, 48, 56.

Now the chadya and chadaka squares are given in Fig. 4. The process of folding leads to the pan-diagonal magic square as shown in Fig. 5.

Suresh, this example from Narāyaṇa Paṇḍita’s Bhadragaṇita chapter is a masterclass in mathematical elegance and symbolic choreography. Let’s walk through the 8×8 pan-diagonal magic square construction using the Samputavidhi (folding method), and explore its deeper implications for your adaptation work.

🧮 Step-by-Step Breakdown: Narāyaṇa’s Example 2

1. Sequences Defined

• Mūlapankti (Base Sequence): $1,2,3,4,5,6,7,81,\; 2,\; 3,\; 4,\; 5,\; 6,\; 7,\; 8$ → Sum = 36

• Parāpankti (Secondary Sequence): $0,1,2,3,4,5,6,70,\; 1,\; 2,\; 3,\; 4,\; 5,\; 6,\; 7$ → Sum = 28

2. Magic Sum (Phala):

$$S=260\Rightarrow \text{Guṇa (Factor)}=\frac{260-36}{28}=8S\; =\; 260\; \backslash Rightarrow\; \backslash text\{Guṇa\; (Factor)\}\; =\; \backslash frac\{260\; -\; 36\}\{28\}\; =\; 8$$

3. Guṇapankti (Product Sequence):

Multiply each term of Parāpankti by 8 → $0,8,16,24,32,40,48,560,\; 8,\; 16,\; 24,\; 32,\; 40,\; 48,\; 56$

🧩 Constructing the Chadya and Chadaka Squares

🔷 Chadya (Covered Square):

• Constructed by repeating rows of the Mūlapankti horizontally

• First 4 rows: direct sequence

• Last 4 rows: reversed sequence

🔶 Chadaka (Coverer Square):

• Constructed by repeating columns of the Guṇapankti vertically

• First 4 columns: direct sequence

• Last 4 columns: reversed sequence

🌀 Folding Rule: Samputavidhi

The final magic square $MM$ is formed by folding Chadaka over Chadya:

$$M(i,j)=\text{Chadya}(i,j)+\text{Chadaka}(n-1-i,j)M(i,\; j)\; =\; \backslash text\{Chadya\}(i,\; j)\; +\; \backslash text\{Chadaka\}(n\; -\; 1\; -\; i,\; j)$$

This vertical reflection and addition yield a pan-diagonal 8×8 magic square with all rows, columns, and diagonals summing to 260.

🎭 Symbolic and Dramatic Resonance

• The folding mimics Namaste—a gesture of union, symmetry, and reverence.

• The sequences represent ascending and descending energies, merging to form cosmic balance.

• The square itself becomes a mandala of harmony, ideal for visual staging or ritual dramatization.

🔍 For Deeper Study

You might enjoy . It includes examples, diagrams, and comparative insights that could enrich your visual treatments and digital archiving.

Would you like to co-construct a symbolic grid or animation that dramatizes this folding process? We could map each sequence to musical phrasing, lighting cues, or character dynamics in your adaptation.

 

 

Fig. 5. 8x8 Magic Square with Sum 260

References:

[1]Ahmed, M., Algebraic Combinatorics of Magic Squares, arXiv:math/0405476 [math.CO]. [2]Ahmed,MayaMohsin.,DemystifyingBenjaminFranklin’sOther8-Square,Recre ationalMathematicsMagazine,vol.4,no.7,2017,pp.21-27. [3]Ahmed,M.,Howmanysquaresarethere,Mr.Franklin?:ConstructingandEnumer atingFranklinSquares,Amer.Math.Monthly,Vol.111,2004,394–410. [4]Ahmed,M., Unraveling the secret of BenjaminFranklin: ConstructingFranklin squaresofhigherorder,arXiv:1509.07756[math.HO]. [5]Andrews,W.S.,MagicSquaresandCubes,2nd.ed.,Dover,NewYork,1960. [6]Datta,B.andA.N.Singh,MagicSquaresinIndia.RevisedbyK.S.Shukla,Indian JournalofHistoryofScience,27,1991,51ˆ A¡V120. [7] Pandita,N.,TheGanitaKaumudi,EditedbyShastri,M.D.,PrincessofWalesSaras vatiBhavanatexts,Benares,1942. [8] Pasles,P.C.,The lost squaresofDr.Franklin:BenFranklin’smissingsquaresand thesecretof themagiccircle,Amer.Math.Monthly,108,(2001),489-511.