Ramanujam number is a number game of cubic numbers

 

Ramanujam number is a number game of cubic numbers

How did we see the Pythagorean Theorem? It means that certain square numbers can be viewed as the addition of two square numbers. If you raise the question whether we can see a similar pattern in cubic numbers, you will arrive at the concept of Ramanujam number. Here you only want to see if you can find a number as the addition of two cubic numbers rather than the cubic number as the addition of two cubic numbers.

In that way the Ramanujam number is like a discovery made from the superposition of square numbers.

Ramanujam had special powers at numbers. He had an amazing ability to calculate numbers in his mind.

Once his mentor Professor Hardy came to see him and expressed the impression that his car number 1729 was not to his liking. Ramanujam then showed that number as the addition of two cube numbers. And that too in two ways. That's why the number is known as Ramanujam number.

How Ramanujam expressed 1729 as the addition of two cubic numbers in two ways,

1729 = 13 + 123 = 93 + 103

Here 1729 is not the only cubic number. But it can be expressed in two ways as the addition of two cubic numbers. This is what Ramanuja showed.

It's almost like Pythagorean numbers, isn't it, with one difference. Like its next version. This way you can jump from one invention to another.

That leap is to think about how a property that applies to square numbers changes a little more or less for cubic numbers. Ramanujam too could have thought like that. At the end of that idea Ramanujam could have found the number.

Among some of the discoveries about square numbers, a mathematician named Kapreker thought differently and discovered some numbers. These numbers are called Kapreker numbers. Let's know a little about them. It will help you to understand how you can continue your thinking in numbers. It may even help you make a new discovery in mathematics.

Now let's look at the Kaprekar numbers.

The square of 45 will be 2025. Seperate 2025 as 20 and 25 and add these numbers you get result of 45. The square of 45 is 2025. i.e, 45² = 2025. Such an invention was made by Kabrekar. That means it can be referred to as fun in numbers.

Similarly the square of 297 will be 88209. If you seperate that number as 88 and 209, you get a sum of these numbers as 297. 88209 is the square of 297. i.e, 297² = 88209. This is also a Kabrekar number.

There are many such Kabrekar numbers. You find out.

I think your mathematical curiosity has taken off by now.

When you look at the numbers in different ways, you can find a variety of discoveries. I think you understand by now that those inventions are math lessons for you on various topics.

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