Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 – Part 1

137th Birth Anniversary of S. Ramanujan,
December 22, 1887-April 26, 1920

National Mathematics Day, India – December 22

Part 1: Recreation of Number on 1729
Part 2: Magic Square

This paper brings representations of 1729, a famous Hardy-Ramanujan number in different situations. These representations are of crazy-type, single digit, single letter, Selfie-type, running expressions, selfie fractions, equivalent fractions, Triangular, Fibonacci, fixed digits repetitions prime numbers patterns , Pythagorean triples, palindromic-type, polygonal-type, prime numbers, embedded, repeated, etc. Ideas toward magic squares are also extended. Some quotes and historical notes on Ramanujan’s life are also specified.

This work brings magic squares connected with S. Ramanujan’s life and with Hardy-Ramanujan number 1729. There are three different types of magic squares. The first type is based on some historical years of S. Ramanujan’s life. The second type is with magic sum as 1729. In this case the magic squares constructed are of orders 7, 13, 14 and 19. The \textbf{third type} is magic squares based on Pythagorean tripes where the number 1729 is one the entry. In this case the magic squares constructed are of orders 6, 7, 11 and 19.

It is revised and extended version of author’s previos work. Below is a link of this work for download.

• Inder J. Taneja, Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729, Zenodo, December 20, 2024, pp. 1-127, https://doi.org/10.5281/zenodo.14538297
  • Site links:
    • Part 1: Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 – Part 1 (old site)
      Part 1: Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 – Part 1 (new site)
    • Part 2: Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 – Part 2 (old site)
      Part 2: Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 – Part 2 (new site)

Below are the itens that we worked with representations of the Hardy Ramanujan Number 1729

1. Magic Squared On Ramanujan’s Life Numbers
2. Single Digit Representations and Patterns
3. Single Letter Representations and Pattern
4. Crazy and Pyramid-Type Representations
5. Same Digits Both Sides
6. Same Digits Power-Plus
7. Same Digits: Factorial-Power
8. Narcissistic-Type Representation
9. Power Representations
10. Fibonacci Sequence Representation
11. S-gonal Values
12. Polygonal Numbers
13. Selfie-Fractions
14. Equivalent Fractions
15. Pythagorean Triples and Patterns
16. Pandigital-Type Pythagorean Triples
17. Upside-Down and Mirror Looking
18. Special Representations
19. Numbers from 1 to 1729 in Terms of 1729-9271
20. Running Equality Expressions
21. Selfie Representations
22. Fixed Digits Repetitions Prime Patterns
23. Embedded Palindromic Prime Patterns
24. Magic Square Type Palprimes
25. Palindromic Prime Numbers
26. Two Color Pattern Designs for 17-29
27. Magic Squares with 1729 – See second part

Single Digit Representations and Patterns

Single Letter Representations and Pattern

Crazy and Pyramid-Type Representations

Same Digits Both Sides

Same Digits Power-Plus

Same Digits: Factorial-Power

Narcissistic-Type Representation

Power Representations

Fibonacci Sequence Representation

S-gonal Values

Polygonal Numbers

Selfie-Fractions

Equivalent Fractions

Pythagorean Triples and Patterns

Pandigital-Type Pythagorean Triples

Upside-Down and Mirror Looking

Special Representations

Numbers from 1 to 1729 in Terms of 1729-9271

Running Equality Expressions

Selfie Representations

Fixed Digits Repetitions Prime Patterns

Embedded Palindromic Prime Patterns

Magic Square Type Palprimes

Palindromic Prime Numbers

Two Color Pattern Designs for 17-29

References

• Inder J. Taneja, 2019 In Numbers, Zenodo, December 31, 2019, pp. 1-27, http://doi.org/10.5281/zenodo.2529103.
• Inder J. Taneja, 2020 In Numbers: Mathematical Style, Zenodo, December 31, 2019, pp. 1-37, http://doi.org/10.5281/zenodo.3596193.
• Inder J. Taneja, 21 Mathematical Highlights for 2021, Zenodo, December 26, 2020, pp. 1-75, http://doi.org/10.5281/zenodo.4394408.
• Inder J. Taneja, Hardy-Ramanujan Number – 1729, Zenodo, December 22, 2021, pp. 1-106, https://doi.org/10.5281/zenodo.5799640.
• Inder J. Taneja, Mathematical Beauty of 2022, Zenodo, December 26, 2021, pp. 1-78, https://doi.org/10.5281/zenodo.5805264.
• Inder J. Taneja, 23 and 2023 in Numbers and Patterns, Zenodo, December 22, 2022, pp. 1-51, https://doi.org/10.5281/zenodo.7473340.
• Inder J. Taneja, Mathematical Representations of the Last Day of the Year 23 Written American Style: 12.31.23 (123123), Zenodo, December 19, 2023, pp. 1-13, https://doi.org/10.5281/zenodo.10405771
• Inder J. Taneja, Mathematical Aspects of 24 and 2024, Zenodo, December 19, 2023, pp. 1-40, https://doi.org/10.5281/zenodo.10406530.
• 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.

Part 2: Magic Squares

Please see the second part