Ancient Egyptian Mathematics
The Egyptian numeration system, developed over 5,000
years ago, is one of the earliest known systems of writing
numbers. It was used primarily for administrative and practical
purposes such as trade, architecture, and land measurement.
This system is particularly notable for its use of hieroglyphic
symbols, which represented different numerical values.
Hieroglyphic writing, system
that employs characters in the
form of pictures. Those
individual signs, called
hieroglyphs, may be read as
pictures, symbols for objects,
or sounds.
britannica.com
The Egyptian Numeration System
Hieroglyphic numerals. Table 1 shows Egyptian hieroglyphic numerals
and some of their ideographic meanings [Allen, 2001a, Williams,
2002c, Aleff, 2003, Bertin, 2003].
(Kovalerchuk, 2007)
(Kovalerchuk, 2007)
(Kovalerchuk, 2007)
Practical Applications of the Egyptian Numeration System
The Egyptian numeration system was essential for many aspects of daily
life, particularly in:
Architecture: Calculating dimensions and quantities of materials for
constructing monumental buildings such as pyramids and temples.
Agriculture: Measuring and distributing land and harvests, often recorded in
hieroglyphic texts on walls or papyrus.
Trade and Taxation: Keeping records of goods traded and taxes collected,
ensuring that economic transactions were accurately documented.
Learning check!! 4
31
152, 123
2,010
2,303
Learning check!!
What is one similarity the Egyptian number system has
with our system?
Which do you think is more efficient and which is more
intuitive?
Rhind Papyrus and the Moscow Papyrus
• the most important mathematical documents
from ancient Egypt
• they provide valuable insights into the
mathematics practiced by the ancient Egyptians,
including arithmetic, geometry, and algebraic
problems
The Rhind Mathematical Papyrus
•Date: Circa 1650 BCE
•Location: The British Museum, London
•Description: The Rhind Mathematical Papyrus is one of ancient
Egypt's most extensive mathematical texts. It was discovered in
Thebes and purchased by Alexander Henry Rhind in the 19th
century, which is why it bears his name. The papyrus contains a
variety of mathematical problems and their solutions, demonstrating
how the Egyptians performed arithmetic operations and solved
practical problems.
Example from the Rhind Papyrus:
Problem Statement: "A quantity added to a quarter of that quantity equals 15. What is the
quantity?“
Solution:
1
The problem essentially asks to solve the equation x+ x=15
4
• Multiply through by 4 to eliminate the fraction: 4x+x=60
• Combine like terms: 5x=60
60
• Solve for x: x= =12
5
The Moscow Mathematical Papyrus
Date: Circa 1850 BCE
Location: The Pushkin State Museum of Fine Arts, Moscow
Description: The Moscow Mathematical Papyrus is another important
Egyptian mathematical text. It is slightly older than the Rhind Papyrus and
contains 25 problems with solutions. The problems in this papyrus focus on
more practical applications, including geometry and volumes of solids.
Example from the Moscow Papyrus:
Problem: Volume of a Pyramid
Problem Statement: The problem asks for the volume of a truncated
pyramid (frustum), which has a square base and top, with different side
lengths.
Solution: The ancient Egyptians used the following formula, which is
quite advanced for the time:
1
• V= h(𝑎2 + ab + 𝑏 2 )
3
• Where V is the volume, h is the height, a is the side length of the
bottom square, and b is the side length of the top square.
Babylonian Numerals
The Babylonians inherited the Sumerian style of writing on clay
tablets.
Babylonian Numerals
arithmetic was positional and sexagesimal based on 60 with
symbols for 1, 10, 60, 600, 3600, 36000, and 216000. We
follow a simplified notation from [Allen, 2001b] where V is
used for 1 and for 10. In this notation
Because 734110 = 222160 = (2)602 + (2)60 + 21
The Babylonians' contributions to mathematics, particularly their
development of a positional number system, their early use of a
placeholder for zero, and their base-60 system, have had a lasting
impact on the modern number system and mathematical practices. Their
work laid the groundwork for many of the mathematical concepts that
are now fundamental to the way we understand and use numbers today.
From the way we measure time and angles to the algebraic methods we
use in problem-solving, the influence of Babylonian mathematics is
deeply embedded in our everyday lives.
