Number Theory

    

The Magic Squares of Khajuraho, Durer and the Golden Proportion

Authors: Andrey V. Voron

Based on the theoretical analysis of 4×4 pandiagonal squares, their "structure" features are shown: the invariants of the structure of 4×4 pandiagonal squares are pairs of numbers equal in sum to one of the two Fibonacci numbers — 13 or 21. It is revealed that any variant of the set of six digits of the Durer square and similar 4×4 pandiagonal squares, forming a continuous symmetric configuration, is equal in total to the integer 51. A geometric figure "cube in a cube" is constructed, which has the properties of the "golden symmetry" of 4×4 pandiagonal squares. All the numbers of the diagonals of the cube have the properties of "golden symmetry" (two numbers form in one case the total number 13, in the other — 21), and all planes having 4 angles (numbers) both the inner and outer squares of the geometric figure form a total of the Fibonacci number — 34.

Comments: 4 Pages.

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Submission history

[v1] 2024-08-25 12:43:39

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