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Maths in Ancient Civilisations
Long before calculators, algebra, or modern notation, ancient peoples were using mathematics to understand the world around them. From the movement of the stars to the layout of cities, early civilisations developed their own number systems, measurement methods, and geometric principles – often for deeply practical reasons.
These mathematical beginnings weren’t just about trade or building; they shaped culture, religion, and science. Here’s how three of the world’s great ancient civilisations used maths to build the foundations of everything we know today.
Ancient Egypt - Measuring the World by the Nile
The Egyptians used mathematics as a tool of daily life – for farming, architecture, and the afterlife. Their approach was visual and practical, but remarkably advanced for its time.
- Used a base-10 system written in hieroglyphs – the same principle our number system follows today.
- Invented early fractions, often with unit fractions like 1/2, 1/3, 1/4 to divide food and land fairly.
- Measured land using geometry, especially after annual Nile floods erased boundaries.
- Used “ropesmen” – surveyors who stretched knotted ropes to create right angles for construction.
- Calculated the volume of granaries and storage jars using simple formulas for cylinders and pyramids.
- Developed approximate values for π (pi) when building circular structures and columns.
- Recorded mathematical problems and solutions in the Rhind Papyrus (c. 1650 BCE) – one of the oldest maths texts.
- Used arithmetic in pyramid design, ensuring perfect alignment and slope ratios.
- Applied geometry to religious symbolism, such as the triangular form representing cosmic harmony.
- Divided the day into 12 daylight and 12 night hours, creating one of the first 24-hour time systems.
Babylon (Mesopotamia) - The Mathematicians of Clay and Stars
The Babylonians were masters of number and astronomy. Using clay tablets and styluses, they built one of the earliest place-value systems and developed mathematics far beyond practical use.
- Created a base-60 (sexagesimal) number system, still used today for time and angles.
- Used positional notation, meaning the value of a number depended on its position – the forerunner of our modern system.
- Recorded vast tables of squares, cubes, and reciprocals, effectively creating the world’s first mathematical reference books.
- Solved quadratic and cubic equations, showing algebraic reasoning centuries before algebra was named.
- Used Pythagorean triples (like 3, 4, 5) over a thousand years before Pythagoras himself.
- Developed sophisticated calendars and predicted eclipses using numerical cycles.
- Measured land and built structures using ratio-based geometry, not fixed units.
- Calculated interest and compound interest in trade and loans – showing early financial mathematics.
- Used maths in astrology and celestial mapping, blending science and belief.
- Recorded everything on durable clay tablets, many of which survive – giving modern historians a window into early algebra.
Ancient China - Patterns, Balance, and Practical Innovation
Mathematics in ancient China blended logic, philosophy, and engineering. The Chinese valued harmony and proportion – ideas reflected in their mathematical systems.
- Used counting rods to represent numbers and perform arithmetic – a visual, physical form of calculation.
- Employed a decimal place-value system centuries before it reached Europe.
- Compiled their mathematical knowledge in The Nine Chapters on the Mathematical Art (c. 100 CE), a text that shaped East Asian mathematics for over a millennium.
- Solved simultaneous linear equations using matrix-like arrangements, a concept far ahead of its time.
- Applied maths to engineering and irrigation projects, including canal design and flood control.
- Created magic squares and numerical patterns that represented harmony and cosmic balance.
- Used geometry in architecture, emphasising balance and symmetry in city planning.
- Calculated areas, volumes, and taxes, showing maths as a key part of governance.
- Explored negative numbers as early as the Han Dynasty – a concept Europe resisted for centuries.
- Used mathematical reasoning in music theory, linking ratios to the tuning of instruments and the philosophy of order.
