Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares – Part 1

Part 1: Mathematics of 25 and 2025 in Numbers
Part 2: Mathematics of 25 and 2025 in 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 whole work availabe online:

• 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 is divided in two parts. One on recreation of numbers and another on Magic squares. See the links as given below:
  • Site Links:
    • Part 1: Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares – Part 1 (new site) or
      Part 1: Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares – Part 1 (old site)
    • Part 2: Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares – Part 2 (new site) or
      Part 2: Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares – Part 2 (old site)

This is also appeared in the newspaper “The Guardian”.
Can you solve it? All you need to know about 2025

Part 1: Mathematics of 25 and 2025 in Numbers

Below are around 25 items that we worked in this part.

1. Crazy Representations with Multiple Choices
2. Pyramid-Type Representations
3. Single Digit Representations and Patterns
4. Single Letter Representations and Patterns
5. Running Equalities Expressions
6. Pythagorean Triples and Patterns
7. Selfie Representations and Patterns
8. Selfie Fractions and Patterns
9. Equivalent Expressions
10. Narcissistic-Type Representations and Patterns
11. Semi-Selfie Representations
12. Amicable-Type Pattern
13. Power Representations
14. Square-Power Patterns
15. Power-Plus-Minus Equality Expressions
16. Fatorial-Power Equality Expressions
17. Fibonacci-Triangular Equality Expressions
18. Factorial-Fibonacci-Triangular Equality Expressions
19. Embedded Prime Patterns
20. Fixed Digits Repetitions Prime Patterns
21. Palindromic-Type Patterns and Expressions
22. 0 to 200 Numbers in Terms of 2025-5202
23. Upside-Down and Mirror Looking
24. Three Color Representations for Each Month
25. Magic Square – See Part 2.

Crazy Representations with Multiple Choices

Pyramid-Type Representations

Single Digit Representations and Patterns

Single Letter Representations and Patterns

Running Equalities Expressions

Pythagorean Triples and Patterns

Selfie Representations and Patterns

Selfie Fractions and Patterns

Equivalent Expressions

Narcissistic-Type Representations and Patterns

Semi-Selfie Representations

Amicable-Type Pattern

Power Representations

Square-Power Patterns

Power-Plus-Minus Equality Expressions

Fatorial-Power Equality Expressions

Fibonacci-Triangular Equality Expressions

Factorial-Fibonacci-Triangular Equality Expressions

Embedded Prime Patterns

Fixed Digits Repetitions Prime Patterns

Palindromic-Type Patterns and Expressions

0 to 200 Numbers in Terms of 2025-5202

Upside-Down and Mirror Looking

Three Color Representations for Each Month

References

Inder J. Taneja, Work on Recreation of Numbers – Recreating Numbers and Magic Squares