HISTORY OF ALGEBRA

Topics: Quadratic equation, Decimal, Algebra Pages: 25 (1228 words) Published: April 14, 2015
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.
• This is illustrated by a specific example, rather
than by abstractly describing its successive
steps.
• The starting point could be relations involving
specific numbers and the unknown, or its
square, or systems of such relations

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.
• This is illustrated by a specific example, rather
than by abstractly describing its successive
steps.
• The starting point could be relations involving
specific numbers and the unknown, or its
square, or systems of such relations

THE SEARCH OF “EQUATION”
• Greek Mathematics
• Proportion Theory, Elementary Arithmetic
• Greek mathematics was the discovery by the
Pythagoreans around 430 B.C. that certain ratios
among pairs of magnitudes do not correspond to
simple ratios among whole numbers.
• Proportions became a main tool of mathematics
in general.

THE SEARCH OF “EQUATION”
• Greek Mathematics
• The Greeks would state this in as strictly verbal
fashion.
• Even shorthand expressions, such as the much later
A:B :: R:S.
• The theory of proportions provided significant
mathematical results, yet it could not lead to
deriving.
• A main feature of Greek mathematics is that
comparisons or simultaneous
• manipulations can only be made among magnitudes
of the same kind

THE SEARCH OF “EQUATION”
• Diophanthus
• original methods for solving problems that in retrospect may be seen as linear or quadratic
• A problem whose solutions are all negative was called by him “absurd”.
Diophantus solved specific problems using ad-hoc
methods convenient for the problem at hand; he did not
• provide general methods suitable for some “standard” cases.

THE SEARCH OF “EQUATION”
• Diophanthus
• first to introduce some kind of...
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • The History of Algebra Essay
  • History of Classical Algebra Essay
  • history of algebra Essay
  • History of Algebra Essay
  • Essay about History of Algebra
  • history Essay
  • History of Algebra Essay
  • History of Algebra Essay

Become a StudyMode Member

Sign Up - It's Free