Activity 1: Comparative Study of Ancient Mathematical Civilizations
CATEGORY Ancient Egypt Ancient Babylonia Comparison / Insights
Numeration - Base-10 (decimal) - Base-60 - Babylonian system
System system (sexagesimal) system was more advanced
- Used hieroglyphs - Used cuneiform and abstract (with place
- No concept of zero - Had place value value)
- No place value - Placeholder symbol - Egyptian system was
for missing numerals simpler, more visual,
and suited for daily
practical uses
Practical Uses - Building - Trade and urban - Both used math in
construction (e.g., planning daily life
pyramids) - Arithmetic, algebra, - Egypt focused on
- Land surveying and geometry for physical applications
- Resource administration - Babylon used math
management - Astronomy and for complex
- Astronomy for calendar predictions calculations and
agriculture and systemic management
calendars
Mathematical - Rhind Papyrus - Plimpton 322 (c. - All were educational
Documents (c. 1650 BCE): 1800 BCE): tools for solving real
arithmetic, Pythagorean triples, problems
geometry early number theory - Egyptian docs: written
- Moscow Papyrus - Written in cuneiform on papyrus, focused
(c. 2000–1800 using base-60 on geometry and
BCE): volume, area fractions
- Babylonian doc: clay
tablet, early algebra
and number theory
Legacy in - Inspired decimal - Legacy of - Both laid the
Modern Math system sexagesimal system foundation of modern
- Contributions to in time and angle mathematics
Euclidean measurement - Egypt; practical
geometry - Influenced algebra, geometry and
- Early trigonometry, and measurement
understanding of astronomy - Babylon; abstract
fractions and math, algebra, and
measurement astronomical models
Numeration Systems
The Ancient Egyptians developed a base-10 (decimal) numeration system, which was likely
inspired by the human hand's ten fingers. Numbers were written using hieroglyphic
symbols that represented units, tens, hundreds, and so forth. This made the system intuitive
and easy to apply for everyday calculations. However, it had major limitations: it lacked a
concept of zero and place value, which made writing and interpreting large numbers
cumbersome. For instance, the number 48 would be written using four symbols for ten and
eight individual strokes for one.
In contrast, the Babylonians created a much more advanced base-60 (sexagesimal)
numeration system. This allowed them to handle fractions and divisions with greater
flexibility, which was especially useful in astronomy, geometry, and timekeeping. Their
writing system, known as cuneiform, used wedge-shaped marks on clay tablets. A
significant breakthrough in their numeral system was the concept of place value—the
position of a symbol determined its actual value. Although they initially lacked a symbol for
zero, they later used a placeholder to indicate absence of a value in a position, enabling
more precise calculations.
This comparison shows that while Egypt’s system was visually straightforward and ideal for
basic, practical calculations, Babylonia’s numeration method was more sophisticated and
laid the groundwork for the modern positional numeral system.
Practical Applications of Mathematics
In Ancient Egypt, mathematics was primarily applied to solve real-world problems such as
constructing buildings, measuring land, managing resources, and organizing calendars
for agriculture. The architectural precision seen in the construction of pyramids and temples
is a clear example of how geometry was used practically. Land surveying after Nile floods
and distributing food also demanded reliable arithmetic skills.
Babylonian mathematics, while also rooted in practical needs, extended to a more complex
urban environment. The Babylonians used arithmetic and algebra not just for trade and
commerce, but also for designing cities, managing legal contracts, and making astronomical
predictions. Their approach was more systematic and abstract, aiming not just to describe
the world, but to understand and predict it.
Thus, although both civilizations relied on math for functionality, Egyptian math was rooted
in tangible, physical applications, whereas Babylonian math incorporated more
advanced thinking, suitable for systemic management and scientific pursuits.
Mathematical Documents and Records
Our understanding of ancient mathematics is enriched by the surviving mathematical
documents from both civilizations. Two of the most significant texts from Egypt are the
Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus. The Rhind
Papyrus, dating to around 1650 BCE, contains 84 problems ranging from arithmetic and
geometry to early algebraic reasoning. It was likely a training manual for scribes,
demonstrating applications such as calculating land areas and dividing food. The Moscow
Papyrus, from around 2000–1800 BCE, focuses on volume and geometry, including a
famous problem on computing the volume of a truncated pyramid—showing their grasp of
3D measurement and construction.
From Babylonia, the most famous artifact is Plimpton 322, a clay tablet dating to around
1800 BCE. Written in cuneiform using the base-60 system, it contains a list of Pythagorean
triples, proving that the Babylonians understood relationships in right-angled triangles over
a thousand years before Pythagoras. Although it lacks modern algebraic notation, it
reflects a deep understanding of number theory and geometry.
While differing in format and emphasis—papyrus scrolls in hieratic script for Egypt, clay
tablets in cuneiform for Babylonia—all these texts were educational, practical, and
systematic. They reflect how mathematics was taught and used to solve real-life problems
in construction, measurement, and even astronomy.
Legacy in Modern Mathematics
The influence of Egyptian and Babylonian mathematics is still evident in modern times. From
Egypt, we inherited the decimal system—the foundation of our current number system.
Their practical geometry laid the groundwork for Euclidean geometry, and their
techniques in measurement, area, and volume remain fundamental in engineering and
construction today.
Babylonian contributions are even more pronounced in abstract and scientific areas. Their
sexagesimal system is still used in timekeeping (60 minutes in an hour, 60 seconds in a
minute) and angular measurement (360 degrees in a circle). Their work in algebra, solving
quadratic and cubic equations, and applying math to astronomy directly influenced future
mathematical thought in Greek, Islamic, and Western traditions.
In essence, Ancient Egypt contributed the foundation of applied mathematics, useful in
daily life, architecture, and trade. Ancient Babylonia advanced mathematical theory,
enabling complex computations, abstract reasoning, and scientific modeling. Together, these
civilizations laid the cornerstones of modern arithmetic, geometry, algebra, and even time
systems.
SECTION: BSE 1-M
SUBJECT: HISTORY OF MATHEMATICS
MEMBERS: RAMILLANO, ADRIAN
BAGAY, IVYLUZ
TIBAY, MARY ROSE
CASAYURAN, RON HOLLEY
