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37 lines
1.2 KiB
Python
37 lines
1.2 KiB
Python
"""
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Dürer's Melancholia I Magic Square — Verification Script
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From issue #31. Albrecht Dürer's 4×4 magic square (1514), as documented in §166.
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The bottom row reads 4, 15, 14, 1 — but the year 1514 appears as [15, 14] in positions
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[0,1] and [0,2] of the bottom row (columns 2 and 3, value 15 and 14).
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Magic constant: 34. PHI = FOUR = 34.
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Reference: INDEX.md §166, figures/durer-square.md
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"""
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import numpy as np
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magic_square = np.array([[16,3,2,13],[5,10,11,8],[9,6,7,12],[4,15,14,1]])
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def check():
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target = 34
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print("Row sums: ", magic_square.sum(axis=1))
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print("Column sums: ", magic_square.sum(axis=0))
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print("Main diagonal: ", np.trace(magic_square))
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print("Anti-diagonal: ", np.trace(np.fliplr(magic_square)))
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# 2x2 sub-square sums
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sums = []
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for i in range(3):
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for j in range(3):
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sums.append(magic_square[i:i+2, j:j+2].sum())
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print("2x2 sub-square sums:", sums)
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print("Unique 2x2 sums:", len(set(sums)))
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print("All equal target 34:", all(s == target for s in [
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*magic_square.sum(axis=1), *magic_square.sum(axis=0),
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np.trace(magic_square), np.trace(np.fliplr(magic_square))
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]))
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if __name__ == "__main__":
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check()
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