✅ Mode of Submission: Online XI/XII VEP - Online project submission link, 2025-26
Mode of Submission: Online XI/XII VEP - Online project submission link, 2025-26
Ancient Egyptian
Ancient Egyptian Geometry
Geometry and
and Early
Early
Trigonometry
Trigonometry
Introduction– Math in Ancient
Egypt
Ancient Egypt thrived along the Nile from ~3000 BCE.
Mathematics developed from practical needs – building, surveying, calendars.
No symbols like today; math was written using hieroglyphs and on papyrus.
Main sources:
Rhind Mathematical Papyrus
Moscow Papyrus
Focus: Geometry in real life – not theory
Basic Geometric Ideas
Egyptians knew how to calculate:
Area of rectangle = length × width
Area of triangle = ½ × base × height
Volume of cylinder/cone (approximate
methods)
Used unit fractions (like 1/2, 1/3)
Rope stretchers used ropes tied in 12 parts to
form right triangles (3-4-5 rule)
Geometry in Architecture – The
Pyramids
Pyramids like Khufu (Giza) required advanced geometry.
Used a concept called Seked – horizontal run per 1 cubit of rise
(similar to cotangent).
Seked helped calculate the slope of pyramid sides.
The Great Pyramid aligns almost perfectly with cardinal
directions – precise planning!
Land Surveying with Geometry
Nile floods wiped out field boundaries yearly.
Surveyors (called rope stretchers) used
geometry to re-measure land.
Redrew square and triangular plots using fixed
rope lengths.
Helped in land tax, ownership, and fairness in
farming
Geometry in Astronomy and
Temples
Temples and pyramids were aligned with celestial bodies.
Egyptians tracked stars (especially Sirius) to predict Nile flooding.
Used shadow lengths (like a sundial) to measure time and angles.
Calculated star risings and temple orientations using early geometry.
Early Trigonometric Concepts – Seked
Though not formal trigonometry, Egyptians used Seked as a slope measure.
Seked = run per rise = cotangent of the angle
Example: A seked of 5 palms per cubit means a gentler slope than 3 palms.
Used it to build sloped walls, ramps, and pyramid sides.
Trigonometry developed later in Greece, but Egypt used similar practical ideas.
Rhind Mathematical Papyrus
Written by scribe Ahmes (~1650 BCE), based on
older sources.
Contains over 80 problems – fractions, equations,
and geometry.
Example problems:
Calculate the area of a field
Find height of a pyramid given base and seked
Shows Egyptians' logical and procedural thinking in
solving math problems
Practical Applications and Legacy
Geometry helped in:
Architecture – Pyramids, temples
Land division – post-flood surveying
Astronomy – tracking stars, solstices
Laid foundations for future civilizations like the Greeks.
Egyptians showed math can be powerful even without modern
symbols
Conclusion
Ancient Egypt used practical geometry in daily life, not theory-based.
Their concepts like seked showed early understanding of slopes and angles.
Through architecture, astronomy, and surveying, they built a lasting legacy.
Egyptian math reminds us: real-world problems inspire great math ideas.
Mathematical knowledge was applied in building wonders like the Great
Pyramid, which still stuns modern engineers.
Land surveying techniques developed to restore boundaries after Nile floods
reflect advanced applied mathematics.
Thank You
Thank You
