Ancient Egyptian Mathematics By Caroline Blundell Overview

1
Ancient Egyptian Mathematics

• By Caroline Blundell

2
Overview

• Egyptian Numerals
• Sources
• Arithmetic Operations
• Egyptian Fractions
• An Egyptian Problem
• Interesting Facts
• Conclusion

3
Egyptian Numerals
For example 1326
4
Hieratic Numerals
5
Egyptian Mathematical Calculations

• The Rhind Mathematical Papyrus
• The Moscow Papyrus

6
Egyptian Addition
equals
Example 1452 Add
79
1531
7
Egyptian Multiplication

• Example
• 19 x 23

• Two columns.
• Double numbers.
• Use subtraction.
• Add corresponding numbers.

19 16 3 3 2 1 1 1 0
437
368 46 23
8
Egyptian Division
Example 1125 / 25
1125 800 325 325 200 125 125 100
25 25 25 0
1 4 8 32
45
9
Egyptian Fractions

• Vulgar Fraction A fraction that has a
  numerator that is not one.

• Unit Fraction - A fraction that has a numerator
  of one.

5/7
1/7

• Egyptian Fraction Sum of unit fractions with
  different denominators.

5/7 1/2 1/7 1/14
Example 5/7 5/7 1/2 3/14 To solve 3/14,
look at the divisors of 14 14, 7, 2, 1
5/7 1/2 (2 1)/14 5/7 1/2 1/7 1/14
10
Egyptian Fractions

• Can become laborious, however..

The Egyptians cheated!

• On the Rhind papyrus there is a table that lists
  the Egyptian fractions for 2/n, where n is an odd
  number from 3 - 101.

11
Egyptian FractionsNotation

• Was used to represent a fraction, and is
  pronounced R.

• R represents the numerator of one, and whatever
  is underneath is the denominator.

Example
Special Cases
1/2
1/3
1/10
2/3
3/4
12
Problem 14 in The Moscow Papyrus
13
Problem 14 on The Moscow Papyrus
Square the numbers 2 and 4, then add to the sum
of these squares the product of 2 and 4.
Multiply this by 1/3 of 6.
Behold it is 56, you have found it correctly
22 42 (2 x 4)
6/3
V h/3 a2 ab b2
14
Mathematical Facts About The Great Pyramid

• 20 years to build
• Approx 2 million blocks of stone
• Was 481ft (145.75m) high but has lost 30ft (10m)
  off its top

• The perimeter divided by 2x its height is pi.
• When using the Egyptian unit of measurement the
  perimeter is 365.24 - the amount of days in the
  year.
• The height x 10 to the power of 9 gives
  approximately the distance from the earth to the
  sun.

15
Summary Of Egyptian Maths

• Not well suited for arithmetical calculations.
• Built around addition.
• Communicated by example rather than principle.
• Lack of surviving documents.

QUESTIONS?