By Team Aakash Byju's | 21st December 2022

National Mathematics Day:  5 Key Contributions by Ramanujan to Maths

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Srinivasa Ramanujan has contributed a lot to solving mathematical analysis, number theory, infinite series, etc. Here are his top 5 contributions.

This number is known as the Ramanujan number. The mystery behind this number is that :

The smallest natural number is expressed as the sum of two cubes, in two different ways. 1729 = 1   + 12   or 1729 = 9  + 10

3

3

3

3

1729

Ramanujan found a formula for infinite series for π, that helped in an accurate approximation of π.

Infinite Series of π

1

(4k)! (1103+26390k)

(k!)

4

π

=

2√2

9801

k = 0

(396)

4k

The n    Ramanujan prime  number is the least integer  R   , for which there are at least n primes between x &  x  , for all  x ≥ Rn.

Ramanujan Prime

The first five Ramanujan primes are 2, 11, 17, 29, 41

th

n

2

f(a,b)

a

=

n=-∞

2

n(n+1)

b

2

n(n-1)

Ramanujan beautifully represented the generalised form of the Jacobi triple product as

Ramanujan Theta Function

Ramanujan Magic Squares

He created a 3×3 square such that each cell is filled with unique numbers from 1-9 & the sum of numbers in each row, each column, and in each diagonal will be equal.

4

3

8

9

2

5

7

6

1

15

15

15

15

15

15

15

15