Ancient Mathematics: Triangles in Egypt


L-BBE, CC BY 3.0 <https://creativecommons.org/licenses/by/3.0>, via Wikimedia Commons
The Great Pyramid of Giza

Have you ever wondered what the very first math equations looked like? Or how ancient civilizations did things like measure distances, count numbers, and compute algebra without modern tools like rulers and calculators? When you see pictures of the Egyptian pyramids--or maybe you’ve even seen them for yourself!--have you ever thought, “How on earth did people build that?”


If so, you’re not the only one! Even still today, historians and scientists are baffled by the massive size and precision of the pyramids. But thanks to some manuscripts left behind, we can piece together the kind of math the ancient Egyptians might’ve used when building complex structures like the Great Pyramid of Giza.

 

Why study ancient math?


We often think of scientific discoveries as being linear, meaning that whoever is credited with first coming up with a concept must have been the only one to have ever thought of it. But the truth is, many different cultures throughout history learned about things like the Pythagorean Theorem long before they got the names we recognize today.


People from ancient civilizations had a lot of the same problems we have now--they needed to measure land, divide resources, build sturdy structures, and track the changing seasons and weather. These practical matters are what inspired the first, ancient mathematicians to create their own number systems and arithmetic. It can be hard to imagine a kind of math that looks different from what we learn in schools today. But luckily, ancient cultures left behind a lot of artifacts and documents that we can learn from!

One of the incredible things about math is that its rules and principles mostly stay the same throughout history. This means that the math used by ancient peoples is, at its core, the same math we use today. We’ll take a closer look at how concepts like the Pythagorean Theorem were used across the world. As we’ll find out, there are many instances where mathematical concepts were “discovered” around the same time in completely different parts of the world!


Why is it important to learn about the history of mathematics? Well, it can help us gain an appreciation for the ways math has brought humanity together. Some people call math the “universal language,” because it can be shared across all cultures regardless of the barriers of different languages and dialects.

 

The Right Angle for Sturdy Buildings


The kind of ancient mathematics we’ll look at in this post comes from Egypt between the years 3000-2000 B.C.E. This was around the time of the very first recorded mathematics historians have ever found. Even though it was so long ago, many ancient civilizations were incredibly advanced and created all kinds of art, music, science, writing, and architecture. One of the most awesome examples of ancient Egyptian math is the Great Pyramid of Giza.

A closer look at the blocks used to build the Great Pyramid of Giza
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Building houses, shelters, temples, and gathering spaces is an important part of any community. Just like modern day construction workers you see along the street, Ancient Egyptians learned that they needed to construct perfect right angles to ensure the stability of their buildings, including the pyramids. If you’ve ever tried to build a sand castle, Lego house, or played with wooden blocks, you know that crooked towers fall over easily.




Egyptian builders found a way to reliably measure right angles by using whole numbers. And, knowingly or unknowingly, they made use of the Pythagorean triple: 3, 4, 5. Let’s take a look at what this means!

 

(Pre-) Pythagorean Theorem


The Pythagorean Theorem is a rule about the way the three sides of a right triangle are related to each other. Remember that a right triangle is one with a perfectly straight corner measuring 90°.

The longest side--the diagonal side--of a right triangle is called the hypotenuse. If you measure the lengths of all three sides of a right triangle, there’s a special relationship between those three measurements. The square of one side’s length plus the square of the other side’s length is equal to the square of the hypotenuse’s length.

Together, the group of lengths a, b, and c are called a Pythagorean triple. One example of a Pythagorean triple is a=3, b=4, and c=5:


Ancient Egyptians used this group of Pythagorean triples to measure out right angles. They would tie knots in a piece of rope to create 3, 4, and 5 equal spaces. Three people would then hold each corner of the rope and form a right triangle! By carrying this rope tool across fields and construction sights, the ancient Egyptians could make sure everything was neat and orderly.


 

A Modern Perspective


It’s fascinating to see how some of the world’s first mathematicians started to make sense of concepts we are so familiar with today. We sometimes take for granted our understanding of triangles, but it was once part of groundbreaking discoveries.


As you continue your study of math, you might notice that the ways you learn about geometry in school are both similar to and totally different from how ancient Egyptians kept track of their work. But when we look at the history of mathematics as a whole, we can see the beautiful ways that different people came to understand the same ideas. It truly is all connected into our united human experience!


In the next post we’ll dive deeper into how Ancient Egyptians understood fractions. In the future we'll learn about the differences between ancient analysis methods and modern proof strategies that use newer concepts like irrational numbers and integrals. In the meantime, keep an eye out for evidence of ancient wisdom coming through in our everyday life--you might just find that mathematical intuition isn’t so mysterious after all!


Credits:

Images courtesy of Wikimedia Commons

Written by Nicole Naporano

Edited by Madelyn Leembruggen

 

Explore the usefulness of triangles with these activities!


Define (5-15 minutes): Types of Triangles


Expand (10-20 minutes): Can you come up with another example of a Pythagorean triple? How many examples can you find?


Interact (15-30 minutes): Make your own knotted string like the example in the post! What can you measure with it?


Explore (30-60 minutes): Gather examples of geometry from cultures across the globe.