Indian Mathematicians And Their Contributions

Ramanujan

    He was born on 22nd of December 1887 in a small village of Tanjore district, Madras. He failed in English in Intermediate, so his formal studies were stopped but his self-study of mathematics continued. He sent a set of 120 theorems to Professor Hardy of Cambridge. As a result he invited Ramanujan to England.
    Ramanujan showed that any big number can be written as sum of not more than four prime numbers.
    He showed that how to divide the number into two or more squares or cubes.
    When Mr Litlewood came to see Ramanujan in taxi number 1729, Ramanujan said that 1729 is the smallest number which can be written in the form of sum of cubes of two numbers in two ways, i.e. 1729 = 93 + 103 = 13 + 123 since then the number 1729 is called Ramanujan’s number.
    In the third century B.C, Archimedes noted that the ratio of circumference of a circle to its diameter is constant. The ratio is now called ‘pi ( Π )’ (the 16th letter in the Greek alphabet series)
    The largest numbers the Greeks and the Romans used were 106 whereas Hindus used numbers as big as 1053 with specific names as early as 5000 B.C. during the Vedic period.

ARYABHATA

    Aryabhatta was born in 476A.D in Kusumpur, India.
    He was the first person to say that Earth is spherical and it
revolves around the sun.
    He gave the formula (a + b)2 = a2 + b2 + 2ab

    He taught the method of solving the following problems:

BRAHMAGUPTA

    Brahma Gupta was born in 598A.D in Pakistan.
    He gave four methods of multiplication.

    He gave the following formula, used in G.P series

a + ar + ar2 + ar3 +……….. + arn-1 = (arn-1) ÷ (r – 1)

    He gave the following formulae :

Area of a cyclic quadrilateral with side a, b, c, d= √(s -a)(s- b)(s
-c)(s- d) where 2s = a + b + c + d
 Length of its diagonals =

SHAKUNTALA DEVI

ShakuntalaDevi was born in 1939.    In 1980, she gave the product of two, thirteen digit numbers within 28 seconds, many countries have invited her to demonstrate her extraordinary talent.
    In Dallas she competed with a computer to see who give the cube root  of 188138517 faster, she won. At university of USA she was asked to give the 23rd root of
91674867692003915809866092758538016248310668014430862240712651642793465704086709659

32792057674808067900227830163549248523803357453169351119035965775473400756818688305
 620821016129132845564895780158806771.

She answered in 50 seconds. The answer is 546372891. It took a UNIVAC 1108 computer, full one minute (10 seconds more) to confirm that she was  right after it was fed with 13000 instructions.
Now she is known to be Human Computer.

BHASKARACHARYA

   He was born in a village of Mysore district.    He was the first to give that any number divided by 0 gives infinity (00).
    He has written a lot about zero, surds, permutation and combination.
    He wrote, “The hundredth part of the circumference of a circle seems  to be straight. Our earth is a big sphere and that’s why it appears to be flat.”
    He gave the formulae like sin(A ± B) = sinA.cosB ± cosA.sinB

Source: http://www.icbse.com/indian-mathematicians

அல்ஜீப்ரா என்ற பெயர் எப்படி வந்தது?

 அல்ஜீப்ரா என்ற சொல் "அல் - ஜபர்" (al-jabr) என்ற  அராபிய மொழி மருத்துவ குறிச்சொல்லில் இருந்து வந்தது. "அல் - ஜபர் " என்ற சொல்லுக்கு உடைந்த பாகங்களை மீண்டும் சேர்த்தல் என்பது பொருள் ஆகும்.

http://www.keetru.com/index.php?option=com_content&view=article&id=22316:2012-12-12-22-29-17&catid=44:general&Itemid=123

Algebra was invented by the Muslim mathematician Al-Khwarizmi in the book he wrote in 

820 AD. Algebra is the Arabic word (aljabr) for "equation", and the word "algorithm" comes from the author's name, Al-Khwarizmi. He is rightly known as "the father of Algebra". 

A Brave Puzzle

This square has eleven letters missing, which you have to replace:

 Every row, column AND the main diagonals contain all the letters in the word "BRAVE".


http://www.mathsisfun.com/puzzles/a-brave-puzzle.html

Sudoku Types - Continued....

Flower Sudoku

                   Flower Sudoku consists of five Sudoku puzzles, similar to Samurai Sudoku. However, these puzzles overlap each other more than in Samurai. The center grid is covered by the remaining sub-puzzles.



Futoshiki

            Futoshiki - also known as "Hutoshiki" or "Unequal"- is a logical math puzzle played on a square grid. The objective of Futoshiki is to enter numbers from 1 to 5 (or whatever the grid dimension is) in each column and each row.
            In addition, inequality constraints are given between some of the cells, indicating that one cell must be higher or lower than its neighbour.



Girandala Sudoku
    Girandola Sudoku is a Sudoku variant. It contains an extra group of nine marked cells. This group must also contain the numbers 1 through 9. 


 

Hoshi Sudoku
      It contains six large triangles. The numbers 1 to 9 must be placed into the cells of each large triangle. Every line of any length - even uncontinous - must contain every number not more than once.



Killer Sudoku
        This Sudoku variant , also called as  "Killer Sudoku", "Sums Sudoku", "Samunamupure" or "Kikagaku Nampure". The puzzle contains sub-regions with specified sums. No number can be repeated within a sub-region.

 

 Mathdoku

Mathdoku - also known as "CalcuDoku" or "Square Wisdom" - is a logical math puzzle. The objective of Mathdoku is to fill the grid with the numbers 1 to 9 (or whatever the grid dimension is) such that each row and each column contains only one instance of each number.
In addition, each outlined group of cells contains digits which achieve a specified result using the specified mathematical operation (+, -, ×, ÷). Unlike Killer Sudoku, numbers can repeat within a group of cells.

 

Samurai Sudoku
          "Samurai Sudoku" or "Gattai-5 Sudoku". It contains five grids, one in the center and 4 overlapping each corner of the central one. The numbers 1 to 9 must be placed correctly for all the five puzzle grids.

 

 

 

 

 

 

 

 

Sudoku X

This Sudoku variant is called "Sudoku X", "Diagonal Sudoku" or "Kokonotsu". In Sudoku X the main diagonals must also contain the digits 1 through 9.



Tripledoku

Tripledoku  contains three 9×9 grids. The numbers 1 to 9 must be placed correctly for all of the three grids. 



Twodoku

Twodoku", "Sensei Sudoku" or "DoubleDoku". It contains two 9×9 grids. The numbers 1 to 9 must be placed correctly for both grids.

 

Windowku

This Sudoku variant is called "Windoku", "Four-Box Sudoku" or "Hyper Sudoku". The puzzle contains four additional 3×3 regions that must contain the numbers 1 through 9.

Sudoku

    Source: www.sudoku-puzzles.net 
     Sudoku - also known as "Number Place" - is a logic-based, combinatorial number-placement puzzle. The aim of Sudoku is to enter a number from 1 through 9 in each cell of a grid, most frequently a 9×9 grid made up of 3×3 subgrids. Each row, column and region must contain only one instance of each number.
       There are 19 different types of Sudoku.

• Sudoku
• Argyle Sudoku
• Asterisk Sudoku
• Binario
• Butterfly Sudoku
• Center Dot Sudoku
• Easy as ABC
• Even-Odd Sudoku
• Flower Sudoku
• Futoshiki
• Girandola Sudoku
• Hoshi Sudoku
• Killer Sudoku
• Samurai Sudoku
• Mathdoku
• Sudoku X
• Tripledoku
• Twodoku
• Windowku

Sudoku
     Sudoku - also known as "Number Place" - is a logic-based, combinatorial number-placement puzzle. The aim of Sudoku is to enter a number from 1 through 9 in each cell of a grid, most frequently a 9×9 grid made up of 3×3 subgrids. Each row, column and region must contain only one instance of each number.

 

Argyle Sudoku
              This "Argyle Sudoku" is a Sudoku variant  . It contains additional marked diagonals that must also contain the digits 1 through 9 exactly once.

 

 Asterisk Sudoku
            It contains an additional area of nine specially marked cells. Those nine cells must also contain the digits 1 to 9 exactly once.

 

Binario
       Binairo - also known as "Binary Puzzle", "Takuzu" or "Tohu wa Vohu" - is a logical puzzle played on a square grid. The objective of Binairo is to fill the grid with the numbers 1 and 0. Each row and each column must be unique.
          In addition, there have to be as many "1" as "0" in every row and every column (or one more for odd sized grids) and no more than two cells in a row can contain the same digit.



Butterfly Sudoku
        The puzzle consists of four 9×9 grids. The numbers must be placed correctly for all four grids.

 

Center Dot Sudoku
             The central cells of each region form an extra region that must also contain the numbers 1 through 9.This is called Center Dot Sudoku.



Easy as ABC

           Easy as ABC - also known as "ABC End View" or "Last Man Standing" - is a logical puzzle played on a square grid. The objective of Easy as ABC is to fill the grid with the letters A through G (or whatever the grid dimension is). Each row and each column must contain only one instance of each letter. The clues outside the grid show which letter comes across first from that direction.



Even-Odd Sudoku
            In this variant white cells must contain odd digits and gray cells must contain even digits.

History of Sudoku

                    The history of Sudoku puzzles likely has it roots in the mathematical concept of Latin Squares.Leonhard Euler, a Swiss mathematician, in the 1780's developed the idea of arranging numbers in such a way that any number or symbol would occur only once in each row or column. Latin Squares is used in statistical analysis.
                    Sudoku rules add the restraint that each region may only have the numbers (or symbols) occurring but once. Howard Garns, an architect from Indianapolis, is credited with creating this rule when he developed the puzzle we know as Sudoku.
                    Dell Magazines published the puzzle under the name of Number Place for over 25 years. It is a staple of Dell Magazines to this day. You can find Number Place in Dell Collector's Series.
Presently Dell Magazines publishes several Sudoku puzzle books with such titles as Dell Original Sudoku, Dell Extreme Sudoku, and Dell Maximum Sudoku to name a few.
                    Sudoku is definitely an American invention, but the name isn't. Introduced into Japan by Nikoli under the name of 'Suuji wa dokushin ni kagiru' roughly translating to mean the numbers must be unmarried or single. Thankfully the name has been shortened to Sudoku.The history of Sudoku continues to expand. Wayne Gould, a retired Hong Kong judge, author of Su Doku The Official Utterly Addictive Number-Placing Puzzle,  first encountered the puzzle in a Tokyo book store.
He began to create his own puzzles and was soon addicted like the rest of us. He introduced his puzzles to The Times, a British newspaper, as Su Doku. His puzzles first appeared there on November 12, 2004.

Mathematics

Mathematics is a science, or class of sciences, which treats of the exact
relations existing between quantities or magnitudes, and of
the methods by which, in accordance with these relations,
quantities sought are deducible from other quantities known
or supposed; the science of spatial and quantitative
relations.

       - Webster's 1913 Dictionary

The Pythagoreans invented the term mathematics, from the Greek word mathema, which meant “science.”

Why do we need to learn Mathematics??

       The technologies that we use in our day to day life, and the emerging new technologies, are all based on Mathematics.So, In order to master those technologies, we need Mathematics. Mathematics is not just the numbers....it is about the patterns too.

What are patterns?? Patterns are a theme of the recurring events or objects. A toddler tries to separate blocks of different colors.For example, blue block from a red block.The separation is a pattern. The multiples of five end in either zero or five.This is a pattern.The higher - grade students learn from Algebra to Calculus.These constitute lots of functions,which is the pattern of how one number changes to other.