# Palindromic Magic Square (விகடகவி மாயச் சதுரம்)

A palindrome is “a word, phrase, or sequence that reads the same backwards as forwards“, example madam

We have come up with a new idea of forming palindrome magic square with special feature of repeated numbers along the diagonals!

This is a sample 5 x 5 Palindrome Magic Square. We have also done the same for higher orders including 7 x 7, 11 x 11, and so on! Happy exploring!!

Note: விகடகவி மாயச் சதுரம் in Tamil means Palindrome Magic Square

# Srinivasa Ramanujan – 100-by-100 Biography Magic Square

## Ramanujan and Magic Squares

Srinivasa Ramanujan had a special affinity toward numbers. His taxi-cab number (1729) incident is popular. A Mathematician without parallel, he made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. His works have been collected and analyzed throughout the world

Incidentally, in the opening page of the first Ramanujan’s notebook, there begins by working out a 3 x 3 Magic Square!

Having worked on a variety of special Magic squares ourselves, we could not think of a greater tribute to Srinivasa Ramanujan than this!

### Summary

This is one of the biggest number puzzles we have done so far! This Biography Magic Square summarizes the important events that happened in the life of Sri Srinivasa Ramanujan.

The important dates in the life of Srinivasa Ramanujan were compiled from various sources. These dates were taken two digits at a time, representing either the date of the month or the month or the first/second half of the four-digit year.      As an example, Ramanujan’s date-of-birth 22-12-1887, is taken as four separate entries as    22    12    18 and 87. In short, Ramanujan’s entire life history is reproduced here, from his birth to till date in  Ramanujan-style.

### Construction

Important dates from Ramanujan’s life were collected and these were then arranged horizontally in a row, from left to right. This row would form the top row of this biography magic square. The rest of the magic square is constructed after assembling this row.

This magic square has the properties of a conventional magic square, namely the sum of the entries along each row/column/diagonal sum up to the same magic-sum 2183.

– starting from left to right, or, from top to bottom, we have embedded magic squares of orders 4 x 4 , 8 x 8, 12 x 12, 16 x 16, 20 x 20, and then in increased orders of 25 x25, 30 x 30, 36 x 36, 42 x 42, 49 x 49, 56 x 56, 64 x 64, 72 x 72, 81 x 81, 90 x 90, and finally 100 x 100. This is thus a cascade of magic-squares-inside-a-magic-sqaure!

Thus the total 100 x 100 Ramanujan Biography Magic square will contain the following 184 smaller magic squares of sizes as listed below:

Size of Magic Square      Number of such Magic Squares                       Total Entries

4 x 4  Magic squares          25             25   ( 4 x 4 )           =       400   squares

5 x 5  Magic squares          20             20   ( 5 x 5 )           =       500   squares

6 x 6  Magic squares          24             24   ( 6 x 6 )           =       864   squares

7 x 7  Magic squares          28             28   ( 7 x 7 )           =     1372   squares

8 x 8  Magic squares          32             32   ( 8 x 8 )           =     2048   squares

9 x 9  Magic squares          36             36   ( 9 x 9 )           =     2916   squares

10 x 10  Magic squares     19             19 (10 x 10 )          =     1900   squares

Total                                         184  (Different sized squares)   10,000   Squares

### Sidenote

We have constructed a smaller 16 x 16 version of this Biography Magic Square with fewer details, which you can find here.

This was earlier published in an article “A Unique Novel Homage to the Great Indian Mathematician” in the March 2013 (Volume 23, Pg 146-147) Mathematics Newsletter published by the Ramanujan Mathematics Society. (download free).

# DIAMOND inlaid Magic Square

This is a DIAMOND Magic-Square wherein all the ODD-numbers are inside the Diamond shape. (Magic-Total is 65)

[table id=diamond_inlaid_5x5 /]

# 30 x 30 Magic Squares inside a Magic Square

The above is a 30 x 30 Magic Squares inside a Magic Square

This is a special construction of a Magic Square wherein we start with a small Magic Square (centermost one in the figure) and added rows and columns around it, ensuring that we have a Magic Square at each stage. This Magic Square has been color-coded to make the Magic Squares clearer.

From the center Yellow coloured is a 4 x 4 Magic square with a total of 1802 in all vertical, Horizontal and in both diagonals. When combininng with the blue coloured sqauare,  that 6 x 6  will give a totl of 2703.  Further it will expand to 8 x 8 , 10 x 10 etc… and finally it will become 30 x 30 with a grand total of 13515.

I have done this Magic squares inside the magic square from 5 x 5,     6 x 6, 7 x 7, …….198 x 198, 199 x 199 and 200 x 200.  In the 200 x 200 Magic squares inside a magic square all the numbers from 1 to 40,000 are used and the row total will be 4,00,00,100.  Also I am  planning to do it upto 1500 x 1500.

Definitely, it is a gift given to me by Almighty.  I thank the Almighty for giving me the idea, guided me to work, and helped me to complete it with much difficulties.

# SWASTIKA Magic Square

This is a special Magic Square called as the SWASTIKA Magic Square. All odd numbers are inside the SWASTIKA SYMBOL. (The Magic-Total is 65)

[table id=swastika-5×5 /]

You can find more special Magic-Squares here

# Srinivasa Ramanujan – 16×16 Biography Magic Square

This Biography Magic Square summarizes the important events that in the life of Sri Srinivasa Ramanujan.

How it was constructed:

Important dates in the life of Ramanujan were taken, two digits at a time, representing either the date or the month or the first or second part of the four-digit year. As an example, Ramanujan’s birth-day 22-12-1887 is taken in four separate entries as 22 12 18 87. These were then laid out in the top of the Magic Square, in the first column. Then, a complete Magic Square was built on top of these numbers, with the following additional feature : each  square indicated by a separate color (in this case, there are 4 such 4×4 sub-sqaures), which are magic squares themselves!