In case you aren’t mathematically inclined, or have been away from the news/geometry for a while, today is March 14…also known as Pi Day!
So for those of you who haven’t read my about me, I’m about a stone’s throw away from my BS in math with a concentration in pure mathematics (redundancy anyone?), and one of the most fascinating classes I’ve taken was “History of Math.” It was actually quite amazing to look back and see the clever ways the Babylonians, Indians, Egyptians, and other ancient peoples were able to solve problems that we are handed the tools for in eighth grade. Although we all have a better idea of what was going on during the Scientific Revolution, I think more ancient mathematics are utterly fascinating.
Babylonians – 1800-1600 BC
Although many early peoples studied math, I would lay claim that it really started to pick up with the Babylonians. From clay tablets covered in Cuniforms, we learned just how far math had advanced up until that point. Although they didn’t have 0, a decimal point, and used a number system with a completely different base (base 60 – which is why we use 60 minutes in an hour, 360 degrees in a circle, and so on), they could still do fairly advanced algebraic equations. They also knew how to solve the same problems that could be solved with the Pythagorean theory well before its creation and figuring out the square root of 2 to several places (which we see made things a little sticky later on).
Egyptian – 1600-1350 BC
Egyptians handled problems a little differently – it seems from historical findings (the Moscow tablet) that their focus was more word problem based than practicing multiplication tables (as was evidenced by some Babylonian tablets). Some of you have probably heard of the Rhind papyrus which gives evidence of quite extensive knowledge of arithmetic and geometry (multiplication, unit fractions, linear equations), and even topics that are still being extensively researched today: harmonics, series, and an area I’ve done research in, prime numbers (although my application was specifically into applying some of their sieve measures to determine the finiteness/infiniteness of the primes contained in the Fibonacci sequence).
The most memorable thing I learned was how Egyptians used perfect squares to solve geometric problems involving rectangles. We all learned that LxW=Area; however, they didn’t cover that in ancient Egypt. So if a farmer needed to know the area of his land, what did he do?
Essentially he took it and made it into a big square missing a corner. He subtracted the missing area from the big area and got the area of his green plot of land. Amazingly clever right???
Greek – 600-529 BC
Probably one of the biggest influences Greek mathematics has had on modern (in my opinion), is definitely the shift to deductive reasoning. Instead of basing things directly on observation and probability, there was a shift to extreme precision and logic. From the Greeks we get the discovery of irrational numbers (like our very own pi that we’re celebrating today!), forming the basis of integration (simplestly put as finding the area under a graphed curve), and famously (in some circles), Euclidean Geometry.
And then of course everyone’s favorite, Archimedes.
Archimedes accomplished many things, including some precursers to integration (modern calculus) by finding the area under an arc and…duh duh dunnnnn, giving a way more accurate value of pi! And then there’s all his work with geometry and the area of conics.
Erastothenes discovered a sieve I’ve personally drawn inspiration from during some of my research, which he used to filter out prime numbers. The inklings of this already existed with the Egypitians, but it was really fleshed out and used by him. During this time there were also great leaps made in geometrical and arithemetical measures of geometry, giving us many of the formulas we use today. Really it could be summarized that “If it’s geometrical, it’s probably Greek!”
And you may have heard of the great legend of the square root of two. No? Maybe? When working on the Pythagorean theory, it was discovered that it was irrational, meaning it can’t be expressed as a ratio (it’s decimially 1.41421… and so on), which was a huge secret, because that’s how they worked with numbers…by utilizing ratios. Legend has it that the guy who divulged it, Hippasus, was murdered! By the gods through drowning, which is a little boring, but that’s okay!
Chinese Mathematics – 300 BC
I would say it’s safe to assume that not a lot is said about the following cultures and their contributions, but the Greeks weren’t the only people to contribute great things to mathematics. Unfortunately, due to a huge book burning ordered in 212 BC, not a whole lot is known about the Chinese mathematical knowledge before then. We do know they also knew the Pythagorean theorem, and computed pi to its most accurate value (7 decimal places) for the next thousand years. They also had their own systems for algebra and had great surveying, artistic, and engineering feats that make it apparent that they had extensive mathematical knowledge; however, due to lack of records it is really hard to give any more information 😦
Indian Mathematics – 700BC-1500AD
The Indians, much like the other mathematical cultures, had the Pythagorean theorem figured out (which leads me to believe it shouldn’t be called that, but whatever), and had their own variations on approximations of pi. They also sometimes utilized a binary number system and began work on one of my favorite areas, the Fibonacci numbers, and it’s from them (and some mistranslation) that we get some aspects of trigonometry (sine, cosine, etc.). And how useful is that decimal? Being less…geometrically and ratio inclined, they give the first records of a decimal place system. As the story of zero I heard goes, someone was counting with pebbles and took one away. And what remained? Nothing, but there was still an empty hole there, where it was apparent that there was something, and that something should be recorded too. Zero may not sound that important, but it’s very difficult to do math without even the concept. We also get pi up to eleven places, which is an incredible accomplishment!
Hindu-Arabic – 700AD-
Some also refer to this as the Islamic Empire era, although I learned it as Hindu-Arabic. It’s from this culture that we get algorithm and algebra, and if you ever wondered who thought it would be a good idea to teach that class to everyone, it’s these guys. The strides that they made in mathematics are equatable in importance and scope to the Greeks. The Greeks may have given us deductive thought, but it was the Hindu-Arabic culture that began to focus on creating methods to solve generalized formulas. They formed the ideas behind how to set up an equation, and it’s really one of the first times where a people concentrated not on solving a specific problem (others were reinventing the wheel each time so to speak), but on creating a way to form a template that could be applied to a wide array of a similar type of problem, which was the specific goal of arguably the most famous Hindu-Arabic mathematician (and my favorite), Al-Karaji.
I’m going to stop here, mainly because these were the fundamentals, but I think it’s amazing to see what kind of things were obviously important (trigonometry, the Pythagorean theorem, etc.) enough to be discovered by multiple, geographically and chronologically isolated cultures, and then the concepts that are so intuitive to us (zero, decimal places, irrational numbers) that took hundreds of thousands of years to discover.
I just thought that I should honor a little of the history behind all of mathematics today, in honor of pi. A lot of people have the knowledge that yeah, I use it to find areas, and I use math to figure out my change or spreadsheets, but that there is so much more to it than that. So, enjoy a slice and have a happy pi day!