What Is The Ramanujan Magic Square?

While math, as a subject might be strenuous and arduous, its wonders never fail to leave us flabbergasted. One such magical math square was created by Srinivasa Ramanujan, who was an Indian mathematician. This magical square is a matrix of numbers in which every row, column and diagonal add up to the same number. 

Mathematician, Ramanujan created a Magic Square: one of its kind fascinating mathematical objects that has a deep and mysterious history that has been so far unmanageable for researchers and mathematicians to decipher. Knowing and learning about this magic square can be helpful and rewarding for students. 

Therefore, in this blog post, we will explore the origins of the Ramanujan Magic Square, its properties, and much more. We will also discuss some applications of the Ramanujan Magic Square in mathematics. Explore more below.

What is unique about Ramanujan magic square?

Ramanujan magic square is a special kind of magic square that was invented by the Indian mathematician Srinivasa Ramanujan. It is a 3×3 grid in which each of the nine cells contains a number from 1 to 9, and each row, column, and diagonal have the same sum.

What makes Ramanujan magic square unique is that it can be generated by starting with any 3×3 magic square and adding or subtracting the same number from each cell. This means that there are an infinite number of possible Ramanujan magic squares! It is said that he discovered this method while working on his famous notebook.

There are many things that make this method of creating magic squares unique.

  • It uses a different approach than most other methods. Rather than using algebra or arithmetic, Ramanujan’s method relies on geometry. This makes it more visually appealing and easier to understand. It also has the benefit of being able to create larger magic squares than other methods.
  • Another thing that makes Ramanujan magic square unique is the way it is constructed. Most other methods of creating magic squares use a fixed layout. This means that the numbers in the square are arranged in a specific way. Ramanujan’s method, on the other hand, uses a flexible layout. This allows for more creativity and variety in the construction of the square.
  • Lastly, Ramanujan magic square is unique because it can be used to create different types of magic squares. Most other methods can only be used to create one type of magic square. This flexibility makes Ramanujan’s method much more powerful and versatile.

Pros and cons

While the magic square leaves the students surprised initially, the educators must also inculcate the positives and drawbacks that come with Ramanujan’s magic square. Some of which are: 


  • it is more visually appealing and easier to understand than other methods.
  • It is also more flexible, allowing for more creativity in the construction of the square.
  • it can be used to create different types of magic squares.


  • It is not a massively-known method, making it used restrictively.
  • Because it is less familiar, it may be harder to explain to others.
  • Because it relies on geometry, it may be difficult to extend to higher dimensions.

Despite these cons, the pros of the Ramanujan magic square make it a very powerful tool. 

Ramanujan magic square: History, concept, and its use, decoded

Ramanujan’s method was first published in 1917 in his paper “On certain arithmetical functions”. Since then, it has been used to create some truly amazing magic squares.

Some of the most famous examples of others using this concept in math include:

1. The Lo Shu square

The Lo Shu square

This is a 3×3 magic square that has been used in China for over 4000 years. It is said to have been discovered by the legendary Emperor Yu, who saw it on the back of a turtle. The Lo Shu square is also known as the Ramanujan-Nagell magic square, as it can be generated using Ramanujan’s method. It served the purpose of city planning, designing tombs, and temple design for architectural matters. The magic square was essentially used here to designate spaces of political and religious importance.

2. The Durer magic square

The Durer magic square

Dürer’s magic square is a magic square with magic constant 34 used in an engraving namely- Melancholia I by Albrecht Dürer It is a 4×4 magic square that the German artist created by Albrecht Durer in 1514. It is said to be his most famous work of art, and it hangs in the Louvre museum in Paris.

3. The Perfect Magic Square 

In 2006, a team of mathematicians from the University of Tokyo used Ramanujan’s method to create a new type of magic square. This square is known as the “perfect” magic square, as it contains all of the possible numbers that can be used in a 3×3 magic square.

The Ramanujan magic square can be used by anyone who wants to create a magic square. However, it is most often used by mathematicians and magicians. This is because it is a very versatile method that can be used to create a wide variety of magic squares. The findings of the same can be found in Ramanujan’s notebook.

That’s it..

And they profoundly once said, “If patterns of numbers can create a symphony, Ramanujan is the Beethoven of number theory.” Ramanujan magic square is a very powerful tool that can be used to create a wide variety of magic squares. It is perfect for those who want to create beautiful and intriguing magic squares. However, if you are interested in creating your own magic square, then Ramanujan’s method is definitely worth considering.

Leave a Comment