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A General Impression of Geometry
We have been so accustomed to such colossal edifices that it seems we have forgotten to pause in wild-eyed awe and ask, “How were such magnificent monuments built during ancient times?” The answer is geometry.
Geometry, or the mathematics that deals with the measurement of and relationship between lines, points and figures, is as ancient as mankind itself. The earliest evidence of geometry can be traced back to the Indus Valley during the Bronze Age Civilization. Primitive human beings of that era were discovered to have a fairly impressive knowledge of obtuse triangles – a triangle where one of the interiors angles is more than 90 degrees.
Fast-forward to Ancient Greece. Euclid, a mathematician commonly referred to as the “Father of Geometry,” wrote The Elements, which is considered by many as an influential–if not the leading--textbook on geometry. The history of geometry would be incomplete without mentioning Pythagoras, the Greek philosopher who has been credited for discovering the equation, a2 + b2 = c2 or what we commonly refer to as the Pythagorean Theorem.
The Ancient Greeks may seem to have pioneered the study and application of geometry, but even hundreds of years before these celebrated thinkers were born, another venerable civilization has been diligently utilizing this field of mathematics – The Ancient Egyptians.
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A Journey to Eqypt
The science of ancient Egyptian architecture, art and culture includes an appreciation of geometry. The Rhind Mathematical Papyrus, which was named after the Scottish Antiquarian Alexander Rhind, was unearthed during an excavation in Thebes and was dated back to around 1550 B.C. It reveals to us just how much the Egyptians had thoroughly grasped the concepts of geometry. This manuscript is short of being a treatise on the mathematical solutions to practical problems encountered in public works. It enumerates problems with their respective suggested answers in the form of numerical operations and geometrical shapes.
Although geometry during this period was still on the empirical side, the Egyptians were slowly able to make remarkable precision in approximations. They were able to calculate the area of a square, trapezoid, triangle, circle, the height and angles of a pyramid and even the volume of a cylinder. And as the Egyptians perfected their understanding of geometry, a new pursuit began toward the “sacred.”
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What's Sacred About Geometry?
The Egyptians desired to create harmony in everything around them. The balance and symmetry of their ancient structures–from the pyramids and temples, to statues and obelisks–are testimonies to the Egyptian’s standard for harmony. This standard is translated into Sacred Geometry, the geometry employed in their sacred architecture.
The primary principle behind this is the relationship between progression and proportion. This series of progression and proportion, occurring naturally in the universe (e.g. in the number of layers in a chambered nautilus or petals of a flower) is evident in Egypt’s buildings and design. This series, dubbed in the west as the Fibonacci Series starts with the numbers 2 and 3. To complete the series, the first 2 digits are added to come up with the succeeding number of the series in such a way that any number is the sum of the immediately two preceding numbers. The series, therefore, appears in this fashion: 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610…
Aside from this sacred series, there is also the “sacred ratio” or the “golden ratio” applied extensively to hieroglyphs, pyramids and other monuments. The golden ratio is approximately a mathematical constant of 1.6180339887. It is often symbolized by the Greek letter Phi (Φ).
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Experts in Geometry
The Ancient Egyptians were able to translate into tangible form their ethereal aspiration for harmony in the graceful and elegant structures that they left behind. Like poetry you can touch, the beauty and grandeur eternally captured in these ancient structures have not only stood the test of time but have certified the expertise of Ancient Egyptians in the field of geometry.