HISTORY OF ALGEBRA
HISTORY OF ALGEBRA
M AT H 1
WHAT IS ALGEBRA?
• Denotes various kinds of mathematical ideas and techniques
• more or less directly associated with formal manipulation of abstract symbols and/or with finding the solutions of an equation. HISTORICAL OBJECTIVES
1. attempts to deal with problems devoted to finding the values of one or more unknown quantities.
2. the evolution of the notion of number
3. the gradual refinement of a symbolic language THE SEARCH OF “EQUATION”
• Egyptian Mathematics
Egyptian mathematical texts known to us dated from about 1650 B.C.
• They attest for the ability to solve problems equivalent to a linear equation in one unknown
• Later evidence, indicates the ability to solve problems equivalent to a system of two equations in two unknown quantities
THE SEARCH OF “EQUATION”
• Babylonian and Egyptian Mathematics
• Throughout this period there is no use of symbols; problems are stated and solved verbally, like in the following, typical example:
THE SEARCH OF “EQUATION”
• Method of calculating a quantity, multiplied by 1 1/2 added 4 it has come to 10.
What is the quantity that says it?
Then you calculate the difference of this 10 to this 4. Then 6 results.
Then you divide 1 by 1 1/2. Then 2/3 result.
Then you calculate 2/3 of this 6. Then 4 results.
Behold, it is 4, the quantity that said it.
What has been found by you is correct.
THE SEARCH OF “EQUATION”
• Babylonian Mathematics
• cuneiform texts preserved in clay tablets.
Babylonian arithmetic was based on a wellelaborated, positional sexagesimal system
(base 60).
• BUT, no consistent use of zero.
• A great deal of Babylonian mathematics consists of tables: multiplication and reciprocal tables, squares, square and cube roots (though no cubes), exponentials and others.
THE SEARCH OF “EQUATION”
• Babylonian Mathematics
• Beside tables, there are problem texts involving the computation of an unknown number.
• These texts explain a procedure to be followed in order to find the number.
M AT H 1
WHAT IS ALGEBRA?
• Denotes various kinds of mathematical ideas and techniques
• more or less directly associated with formal manipulation of abstract symbols and/or with finding the solutions of an equation. HISTORICAL OBJECTIVES
1. attempts to deal with problems devoted to finding the values of one or more unknown quantities.
2. the evolution of the notion of number
3. the gradual refinement of a symbolic language THE SEARCH OF “EQUATION”
• Egyptian Mathematics
Egyptian mathematical texts known to us dated from about 1650 B.C.
• They attest for the ability to solve problems equivalent to a linear equation in one unknown
• Later evidence, indicates the ability to solve problems equivalent to a system of two equations in two unknown quantities
THE SEARCH OF “EQUATION”
• Babylonian and Egyptian Mathematics
• Throughout this period there is no use of symbols; problems are stated and solved verbally, like in the following, typical example:
THE SEARCH OF “EQUATION”
• Method of calculating a quantity, multiplied by 1 1/2 added 4 it has come to 10.
What is the quantity that says it?
Then you calculate the difference of this 10 to this 4. Then 6 results.
Then you divide 1 by 1 1/2. Then 2/3 result.
Then you calculate 2/3 of this 6. Then 4 results.
Behold, it is 4, the quantity that said it.
What has been found by you is correct.
THE SEARCH OF “EQUATION”
• Babylonian Mathematics
• cuneiform texts preserved in clay tablets.
Babylonian arithmetic was based on a wellelaborated, positional sexagesimal system
(base 60).
• BUT, no consistent use of zero.
• A great deal of Babylonian mathematics consists of tables: multiplication and reciprocal tables, squares, square and cube roots (though no cubes), exponentials and others.
THE SEARCH OF “EQUATION”
• Babylonian Mathematics
• Beside tables, there are problem texts involving the computation of an unknown number.
• These texts explain a procedure to be followed in order to find the number.
References: • Corry, L. (n.d.). History of Algebra. Retrieved April 15, 2015, from Tel-Aviv University: http://www.tau.ac.il/~corry/publications/articles/p df/algebra%20EB.pdf Hiskey, D. (2010, December 10). WHERE THE WORD “ALGEBRA” CAME FROM. Retrieved April 15, 2015, from http://www.todayifoundout.com/index.php/2010/12/ the-origins-of-the-word-algebra/