Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 – Part 2

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

Part 1. This part 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.

Part 2. 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 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)

Part 2: Magic Square

Below are the itens that we worked with magic squares on Hardy Ramanujan Number-1729

1. Magic Squared On Ramanujan’s Life Numbers
   • Hardy-Ramanujan Number-1729: Magic Squares of Order 4
   • Magic Squares of Order 4
   • Magic Squares of Order 5
2. Magic Squares with Magic Sum 1729
   • Magic Squares of Order 7
   • Magic Squares of Order 13
   • Magic Squares of Order 14
   • Magic Squares of Order 19
3. Pythagorean Triples and with Entry 1729
   • Magic Squares of Order 6
   • Magic Squares of Order 7
   • Magic Squares of Order 11
   • Magic Squares of Order 19
4. References

Magic Squared On Ramanujan’s Life Numbers

Hardy-Ramanujan Number-1729: Magic Squares of Order 4

Magic Squares of Order 4

Magic Squares of Order 5

Magic Squares with Magic Sum 1729

Magic Squares of Order 7

Magic Squares of Order 13

Magic Squares of Order 14

Magic Squares of Order 19

Pythagorean Triples and with Entry 1729

Magic Squares of Order 6

Magic Squares of Order 7

Magic Squares of Order 11

Magic Squares of Order 19

References:

1. Inder J. Taneja, Block-Wise Magic and Bimagic Squares of Orders 12 to 36, Zenodo, February 1, 2019, pp. 1-53, https://doi.org/10.5281/zenodo.2555343.
2. Inder J. Taneja, Block-Wise and Block-Bordered Magic and Bimagic Squares of Orders 10 to 47. Zenodo, January 14, 2021, pp. 1-185, https://doi.org/10.5281/zenodo.4437783
3. Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – I, Zenodo, August 18, 2020, pp. 1-81, https://doi.org/10.5281/zenodo.3990291.
4. Inder J. Taneja, Bordered Magic Squares with Order Square Magic Sums, Zenodo, January 20, 2020, pp. 1-26, https://doi.org/10.5281/zenodo.3613690.
5. Inder J. Taneja, New Concepts in Magic Squares: Double Digits Bordered Magic Squares of Orders 7 to 108, Zenodo, August 09, 2023, pp. 1-30, https://doi.org/10.5281/zenodo.8230214.
6. Inder J. Taneja, New Concepts in Magic Squares: Cornered Magic Squares of Orders 5 to 81, Zenodo, August 09, 2023, pp. 1-27, https://doi.org/10.5281/zenodo.8231157.
7. Inder J. Taneja, Striped Magic Squares of Even Orders 6, 8, 10, 12 and 14, Zenodo, November 10, 2023, pp. 1-34, https://doi.org/10.5281/zenodo.10107355.
8. Inder J. Taneja, Figured Magic Squares of Orders 6, 10, 12, 14 and 16 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, November 29, 2022, pp. 1-31, https://doi.org/10.5281/zenodo.7377674.
9. Inder J. Taneja, Inder J. Taneja, Generating Pythagorean Triples and Magic Squares: Orders 3 to 31, Zenodo, May 28, 2021, pp. 1-153, https://doi.org/10.5281/zenodo.4837491.
10. Inder J. Taneja, Sequential Pythagorean Triples and Perfect Square Sum Magic Squares, Zenodo, June 21, 2021, pp. 1-595, https://doi.org/10.5281/zenodo.5009204.
11. Inder J. Taneja, Representations of Hardy-Ramanujan Number-1729, Zenodo, December 18, 2024, pp. 1-65, http://doi.org/10.5281/zenodo.14511547.
12. Inder J. Taneja, Magic Squares and Hardy-Ramanujan Number-1729, Zenodo, December 18, 2024, pp. 1-21, https://doi.org/10.5281/zenodo.14511561.