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Ancient Egyptian Mathematics

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by

Laura J

on 9 December 2013

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Transcript of Ancient Egyptian Mathematics

Ancient Egyptian Mathematics
Addition and Subtraction
Numerical Characters
1
10
100
1,000
10,000
100,000
1,000,000
Reading Numbers
Lower numbers are written in front of higher numbers
Start at the top when there is more than one row of numbers
These processes simply required counting glyphs much like our base ten system
You simply collect all symbols of a single type and replace any ten of those symbols with a symbol of the next higher order
and
is equal to
Multiplication and Division
The Basics
is 12,204
is 1,100,020
Applying This System
Modern Applications
12x12=48+96=144
12 = 1100 in base 2
Modern Applications
Computers multiply and divide the same way Egyptians did!!

Humans operate in base 10. Computers operate in base 2, they only know the symbols 0 and 1.

1, 2, 3, 4 = 1, 10, 11, 100
Multiplying by 2 in binary is easy.
Add 0 on end like x10 in base 10.
1 = 1
2 = 10
4 = 100
8 = 1000

24 = 1 1000
48 = 11 0000
96 = 110 0000

1100 x 1100 = 1 1 0000
+ 1 1 0 0000
-------------
1001 0000
Background Information
The Rhind Papyrus
dates from approximately 1650 B.C.E.
It remains one of the best sources of ancient Egyptian maths
The papyrus lists the practical problems encountered in administrative and building works
contains arithmetic, algebraic, geometric and fraction problems

A Base-10 System
Ancient Egyptian mathematics use a
base 10 system

similar to our current mathematical system.
However, their characters, or glyphs, were represented by images, not numerals.
What did the Egyptians use Math for?
Measuring time
Measuring straight lines
Calculating level of Nile floodings calculating areas of land
Counting money, taxes
figuring out the numbers of days in the year (And they came quite close!)

This might seem complicated but we've seen it before
Multiplication and division use the counting glyphs.
To multiply two numbers, you need to understand
the double or the half of the integer.

1 35

2 70

4 140

8 280
(x2)
Let's Try - What is 35 times 11?
We will double 35 and 1
at the same time
until the multiples of 1 reach 11
1+2+8 = 11
35+70+280 = 385
Now Let's Replace the Integers with Glyphs!
Let's Try 35 times 11
(x2)
(x2)
(x2)
(x2)
(x2)
35 times 11 = 385
1
2
4
8
or
35
70
140
280
or
11
385
god with arms raised
lotus
finger
tadpole or frog
single stroke
cow hobble
coiled rope
One More Time
12 times 24 = 288
1 24
2 48
4* 96*
8* 192*
4 + 8 = 12
96 + 192 =
It works!
288
Addition and subtraction were a process of
grouping and regrouping.
Fractions
They used fractions like 1/2 and 1/4
but to make fractions like 3/4, they added pieces
3/4 = 1/2 + 1/4
Egyptians used fractions by adding pieces
For example, to write 2/5, they wrote 1/3 + 1/15
Written record of Egyptian factions goes back to the Rhind Papyrus
never
They repeated the same fraction twice when adding
The Ancient Egyptians used a number system based on
unit fractions
They used fractions of the form 1/n
Any other fraction had to be represented by
a sum of such fractions
(or reciprocals)
A fraction written as a sum of distinct unit fractions is called an
Egyptian Fraction
by Becca Chang and Laura Micetich
Full transcript