Srinivasa ramanujan Life and wo FROM: KAVYA AND AKANKSHA
Srinivasa Ramanujan
Jan 16, 2015
dis was actually made by me and my frnd akanksh tanwar for maths interschool competition
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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
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