Srinivasa Ramanujan

Srinivasa ramanujan Life and works

FROM: KAVYA AND AKANKSHA

Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.

INTRODUCTION

He was born on 22nd December. 1887 in a small village in Tamil Nadu named erode in his grandmother’s house

He offered alternative method of solving the same questions in an easier way, to the teacher and took half the time to finish his maths examinations.

One of the greatest reasons of his success is that he didn’t waste his time and used it judiciously.

HIS WORKS

CYCLICITY

The last digits of the exponents of all numbers have cyclicity i.e. every Nth power of the base shall have the same last digit, if N is the cyclicity of the number.

21 ends with 222 ends with 423 ends with 824 ends with 625 ends with 226 ends with 427 ends with 8 And so on,

31 ends with 332 ends with 933 ends with 734 ends with 135 ends with 336 ends with 937 ends with 7And so on,  

CYCLICITY OF 2CYCLICITY OF 3

NUMBER CYCLICITY1 12 43 44 25 16 17 48 49 2

C YCLICITY

TABLE

USE OF CYCLICITY Unit digit for 359

We know that the cyclicity of 3 is 4. 59 ÷ 4 The remainder will be 3. So, the unit digit for 359 will be same as the Unit digit for 33 i.e. “7"

1729Hardy Number

13+123=172993+103=1729

HARDY NUMBERSWhile travelling in taxi hardy noticed it’s numbers ,1729 . He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was declared a dull number.Ramanujan denied it saying that it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.

Magic Square•A magic square is a square in which all the Column, rows and diagonal add up to a magic number •The magic number in the magic square refers to a number which we get after adding all the numbers in a row column or diagonal

22 12 18 8788 17 09 2510 24 89 1619 86 23 11

139 139 139 139

=139 =139= 139

= 139

= 139

= 139

22 12 18 8788 17 09 2510 24 89 1619 86 23 11

RAMANUJAN’S MAGIC SQUARE

22 12 18 8788 17 09 2510 24 89 1619 86 23 11

RAMANUJAN’S MAGIC SQUARE

MADE BY:

AKANKSHA AND

KAVYA