Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares

This work brings numerical and magics squares representations for 25 and 2025 in different ways. The number representations are of crazy-type, pyramid-type, single digit, single letter, running numbers, Triangular, Fibonacci, palindromic-type, prime numbers, embedded prime patterns, repeated digits prime patterns, selfie, semi-selfie, narcissistic, etc. Some interesting patterns for 25 and 2025 are also included in the work. The magic square representations are of there are three types. One is universal  magic squares with 25 and 2025. By universal, we understand that the magic square is upside-down  and mirror looking. In this case, we have constructed magic squares of orders 3, 4, 5, 6, 7, 8, 9 and 10. The second types of magic squares are with magic sums 25. In this case, there are only three types of magic squares, i.e., of orders 5, 10 and 25. The third type is magic squares with magic sum 2025. In this case, the magic squares constructed are of orders 3, 5, 6, 9, 10, 15, 18 and 25. In second and third type we have used the sequential entries with positive and/or negative numbers.

Below is a link of work for download:
Inder J. Taneja, Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares, Zenodo, December 20, 2024, pp. 1-94, https://doi.org/10.5281/zenodo.14533193.

Whole work can be downloaded from the above link. Total there are twenty-four itens aborded in this work. These itens are represented individually for 25 and/or 2025 in different frames.

1. Crazy Representations.
2. Single Digit Representations and Patterns.
3. Single Letter Representations and Patterns.
4. Running Equalities Expressions.
5. Embedded Palindromic Prime Patterns.
6. Pythagorean Triples and Patterns.
7. Selfie Representations.
8. Narcissistic Type Representations.
9. Power Representations.
10. Permutable Bases and Powers.
11. Selfie Fractions and Patterns.
12. Equivalent Fractions.
13. Power-Plus-Minus Equalities.
14. Factorial-Power Equalities.
15. Fixed Digits Repetitions Prime Patterns.
16. Amicable Numbers.
17. Semi-Selfie Representations.
18. Palindromic-Type Patterns.
19. Power Pattern.
20. Upside-Down and Mirror Looking.
21. Magic Squares.
22. 25 and 2025 in Magic Squares.
23. Four-Colors Patterns.
24. Numbers 1 to 200 in Terms of 2025-5202.

1. Crazy Representations

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