Throughout this year I have discovered that almost every great civilization in the world has had a
way to estimate area. Since the beginning of development, people have needed to estimate area
for many different reasons. Whether it was estimating the area of an oddly shaped field or
deciding how big a structure needed to be to hold a certain amount of material they have had
some formula or system to find it out. Math was extremely important for religion where alters
had to be built to very specific specifications. Often only the upper classes were able to learn the
wonders of math and geometry. The information was not given to everyone like it is today. The
elite or select few where the ones making all the discoveries, it was a privilege and the work they
did is what we base our systems off of today. From the ancient Babylonians to the sophisticated
Greeks, Chinese and Middle Easterners, their knowledge is evident in their buildings and
monuments. The most interesting thing I have learned is that they all found some estimation of
pi. Pi was extremely useful for a number of reasons, it was widely used in astronomy and this
also helped with navigation. It was used to calculate areas of circles and cylinders and had many
more practical applications.
The Babylonians where more or less the pioneers of their time. They were masterminds
at finding areas and understood the important of mathematics. From Artifact 1 it is evident that
they had some knowledge of geometry. They developed a number system that was completely
their own and used a base of sixty. This is unlike our system which is a base ten; their
mathematical system was a wise choice because many numbers can easily go into sixty. This
would allow them to work with circles and triangles which have three-hundred and sixty degrees
and one-hundred and eighty degrees respectively. We also know that they were well aware of
methods such as completing the square. The formulas derived from these methods are still used
today.
The Greeks were an extremely remarkable society that learned how to approximate the
area for pi. In Artifact 2 it is shown that they used this approximation to find the area of complex
shapes such as cylinders and spheres. In Artifact 3 it is shown that Archimedes approximated pi
1
to equal 3 1/7 or 3.142857. He also found the equation 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 3 7 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟and this was
extremely important. With this he could find how much fence is needed to secure a field or stone
to secure the walls of a city. This was a huge advance for the Greek civilization.
By the third century C.E there was a fairly accurate reading for pi. Artifact 4 states that in
the writing “Nine Chapters” pi was written to be greater than 3 and about 3.14. A couple hundred
years later the estimate became 3.1415926. This is an accurate estimation and is basically the
same estimation calculators’ use today. The estimation was found by Zu Chang Zhi who used a
24,576 sided polygon to create an object that was circle like. By doing so he came up with the
most accurate estimation so far. This extremely precise estimation aloud for better engineering
and also helped in astronomy.
The Middle Easterners had a whole school dedicated to Mathematics. Article 3 mentions
the “House of Wisdom” which was a school devoted to science. The school, located in modern
day Baghdad, was a place where many intelligent people collaborated discovered many ideas.
One in particular was Muhammad ibn Musa Al-Khwarizmi. He did everything from mathematics
to philosophy. He was primarily known for his algebra and his work with reducing fractions. He
made a book called “The Compendious Book on Calculations” which had three sections. The
second section was all about computing area of objects. He used the 62832/20000 as the
estimate as pi. This was approximately 3.1416 and was believed to been received from
communication with Hindu astronomers. At this point historians began to see similarities in the
math of different cultures. It is believed that as civilizations grew different cultures began to
share ideas. For example, when Alexander the Great took power he introduced Greek culture all
the way to India; another would be the Silk Road. Through these events and many like it the
world became much smaller and people’s knowledge grew exponentially.
I have learned more than I could imagine about these different cultures. At the beginning
of the year I did not quite know what to expect, I knew nothing about the Babylonians, Chinese
or Middle Eastern. It was my impression that the only people who actually had geometry and
math where the Egyptians, Greeks and Romans. It was a complete shell shock to find out that the
Babylonians were working with completing the square or that they had fractions, multiplication
and division. I thought that completing the square came around maybe by the time of Newton
however I was way off. With the realization of completing the square it greatly increased their
ability to calculate area and initiated the thought of solving for unknowns. I never even thought
of China or Arabians having math but they were just as advanced, in my opinion, if not more that
their western neighbors. They had many writings and institutions that helped them become one
of the more advanced civilizations. I also never knew how old a lot of the math we used today
was. I assumed pi was a relatively new discovery but was greatly mistaken. It is incredible that
by the fifth century they Chinese had an approximation that was so close to the one I use today
and they did it all without a calculator. It has opened up a new view on these cultures. I had
greatly taken them for granted and now realize just how advanced they really were. It is
incredible to see the amount of accuracy they achieved so many years ago and how a lot of these
cultures were working on the same thing but arrived at the answer different ways. It just goes to
show what individuals can do when they put their minds something. When there is a will, there is
a way.