Transcript Egyptian Maths

EGYPTIAN MATHS
OVERVIEW
In ancient Egypt Mathematics was
mainly studied for its applications to the
problems of everyday life. In Egypt and
Mesopotamia over 2000 years b.C.
(perhaps 5000) the need to solve
problems no longer marks the birth of
elementary Arithmetic as a Science. At
these
ancient
civilizations
simply
counting objects was no longer sufficient
to meet daily needs. Tax`s problems,
irrigation,
land
measurement,
construction of levees, canals, pyramids
complex, require appropriate institutions
with which to work and rules for the
calculation.
To redraw the boundaries of fields after
the annual Nile floods are needed skilled
surveyors, requires the use of bricks which is
calculated the amount needed before embarking on
a building, the harvest is divided between the
farmer, the state, the priestly class.
The first evidence of the
use of Mathematics from the
Egyptians date back to the Old
Kingdom, with an inscription that
records the achievements of war,
using the numbering system
which will be used throughout the
Egyptian History. Also in the first
dynasty was widespread practice
to confirm the use of geometric
concepts.
SOURCES, NUMERALS, MULTIPLICATION
AND DIVISION
A witness to the
remarkable development of
Mathematics at these people, we have
received a lot of Babylonian clay
tablets inscribed with cuneiform
characters and some Egyptian
papyri.
Unlike Mesopotamian
civilization, the amount of the
mathematical texts come to us from
Ancient Egypt is rather limited,
because of the difficulty of
preservation of the papyri
themselves, so it is possible that
actual knowledge of Egyptian
Mathematics are still undervalued .
Among those papyri who
provide us with more information
are Ahmes papyrus, the papyrus of
Moscow and the roll of skin.
The papyri testify that the
ancient Egyptians used a decimal
system for writing numbers,
though numbers in the names of
the trace remains of a primitive
stage in which it was adopted a
system based on five. The system,
which has remained essentially
stable for the duration of the
Egyptian civilization, involved the
use of seven basic hieroglyphs,
each representing a power of ten,
from 100 to 106. Each symbol was
repeated from one to nine times,
adding the value of all the signs,
we obtain the desired number.
This
system
is
not
positional, although the figures
were usually written in order from
the largest value to the smallest
one. Additionally there is no
symbol for zero.
1
1000
10
1000
0
1000000
100
100000
HOW EGYPTIANS DID MULTIPLICATIONS
For example, how they did
23 x 17=?
1
2
4
8
16
23
46
92
184
368
solution
23
+
368
391
HOW EGYPTIANS DID DIVISIONS
For example, how they did
276 : 23 =?
4
+8
12
1
2
4
8
23
46
92
184
solution
92
+184
276
Symbols were formed by Egyptians. They
started using symbols (small draws) to
build easily pyramids and temples.
They have also created hieroglyphs.
Nowadays it helps us understanding
Egyptians’ numeral system.
Egyptian mathematics also wrote papyrus.
Rhind Papyrus and Moscow Papyrus are
the most important elements from their
civilization.
Some years later, they started measuring
farmlands. It was really difficult using just
integers, so, they invented a new type of
number: factionary
number.
Today, we use fractions every time we
want calculate or divided something.
today, we use fractions every time we
want calculate or divided something.
ALGEBRA
The Arithmetic arises from problems, through the problems it evolves. From
practical needs are the encouragement to research, but sometimes the
intellectual curiosity, for enjoyment, take the hands of the scribe, and so
are also fixed problems completely independent from concrete issues.
The Egyptians knew and used the correct formula to find the area of
rectangles, triangles, trapezoids and volume of the pyramid and truncated
pyramid.
The Egyptians did not use a symbolic notation for algebraic problems and to
express their equations, even though they had a clear conception of the
entities involved and in particular the concept of unknown.
The mathematical texts received by us contain numerous examples of
linear equations.
The ancient Egyptians were able to solve quadratic equations, problems
that were contained almost all geometric in nature, and the resolution of
the equation was then only an internal passageway of the problem.
Solving a quadratic equation
always involves the
calculation of square roots. In
the papyri the result of the
root is written directly and are
never the steps of the
calculation, it is likely that the
scribes did use of appropriate
tables containing the roots of
whole numbers and fractions,
but none of these boards has
come down to us.
Then, in the Rhind papyrus
have survived three examples
of Arithmetic progressions,
denoted by the word “των”
meaning "common difference".
EGYPTIAN
MATHEMATICIANS
From 3000 BC to 300 BC. The most important authors were:
•Ahmes
was the Egyptian scribe who
wrote the Rhind Papyrus - one of the
oldest known mathematical documents.
•Joseph
is one of the authors who gives
some of the measurements of the Great
Pyramid which make some people
believe that it was built with certain
mathematical constants in mind.
•Robins
argues against both the golden
ratio or π being deliberately involved in
the construction of the pyramid.
Example:
•When we look to a clock we use it. It is said a quarter
to/past… (¼).
•We also can say: I just eat ½ of pizza.
•Or even when we analyze something: 1/3 of population
is unemployed.
•And all the time we divide something: Divide these
candies for the five kids (1/5).
•We are constantly using fractions nowadays, it is very
important because it is a simple way to calculate
something without worrying with integers numbers.