By Richard E. Bleil
Happy national pi day!!!!!
I love pi. Dutch Apple Pi, Cherry Pi, mmmmmmm…..
Okay, fine, it’s an old joke. But not many people know what pi actually is. If you have a perfect circle that is one unit in diameter (one inch, one centimeter, one foot, whatever you choose from one point to the exact opposite point), then the distance around the circle will be pi units around.
I think that most people have heard that pi is an “irrational number”. This means that it is never ending (that is, it has an infinite number of digits that never repeat). Because it never repeats, it cannot be expressed as a rational fraction, although 22/7 is a decent approximation (only to two decimal places). Evan as I type this, there are computer algorithms that are calculating pi to even more decimal places, but currently, according to the sources that I have read, it is known to almost 10 trillion digits, and every time a new digit is discovered, a pattern is sought since, if a pattern can be found, it means that pi is not, after all, irrational.
One algorithm for calculating pi is to use polygon shapes as an approximation. For example, if you put a triangle inside a circle, you can approximate pi as the sum of the three sides. This would be a poor approximation, but then making the triangle a square, you’ll get a better approximation. A pentagon (5 sides) will be better still, then a hexagon, heptagon, octagon, and so forth. Every time you add another side, the approximation is better. They just keep adding more and more sides to get better and better approximations.
Irrational numbers are fascinating things. As it turns out, there are far more irrational numbers than there are rational. Between any two rational numbers, there are an infinite number of irrational numbers. This is an odd thought, since there are an infinite number of rational numbers. Such oddities are a feature of infinity. Working with infinity to me always felt a little bit like trying to deal with the quantum world; there are many things possible that seem irrational and impossible.
The concept of pi dates back to the ancient Babylonians, sometime in the 17th century B.C. Babylonia lasted for about 1,400 years, from roughly 1900 to 500 B.C. and was located in Iraq, south of what is today the city of Baghdad. The Babylonians had advanced mathematics, agriculture, astronomy and more. They estimated pi to be approximately 3 1/8, or 3.125. This represents a 99.4% accuracy over 1,500 years before Christ was born!
Mathematics is power. A lot of people purport to dislike mathematics, but from simple math and geometry, there are so many things that can be discovered. Around 400 B.C, Plato estimated the earth to be 40,000 miles. While this is quite far off (today, the circumference of the earth is accepted as 24,901 miles). Plato’s estimate was based on the angle difference of the sun after about half an hour (roughly 1/50 of the day). None the less, Plato’s estimate was only off by about 61%. By 250 BC, Archimedes improved the estimate, saying the circumference is 30,000 miles (about 21% error).
All because of mathematics.
Mathematics is the language of nature and science. Don’t ask me why; I have no idea. If I ever have the chance to talk with God, I would like to ask why, but it is absolutely fascinating to me. These ancient discoveries show the power of math. Lord Kelvin (after whom the Kelvin Tempreature Scale is named) once said that if you can put a number to a topic, then you know something of which you speak. If not, then you know nothing at all.
As a theoretical chemist, I live by this philosophy. Mathematical modeling is how we test our hypotheses. If we are correct, our mathematical model can successfully make predictions, which is an indication that, while we may not be correct, our understanding is at least a little bit better.
Recently, I wrote an article on quantum mechanics. Quantum theory is a mathematical model, although the way it is taught, it is sometimes easy to lose sight of this fact. It’s called an “ab initio” model, meaning it starts from the simple start. The assumptions are that there are negatively charged electrons that move rapidly, and positively charged nuclei that do not move (a reasonable approximation when the speed of the nuclei is compared to the speed of the electrons). A few decades ago, somebody decided to apply this theory to economics, treating dollars as movable akin to electrons, and financial centers (in modern models including citizens) as fixed. This gave rise to financial ab initio models known as “econophysics”, and economic laws that are still being taught today.
It seems like I frequently see or hear something about “still haven’t used my algebra…” The reality is that we all use those skills every day. Every time we divide up a treat equally among people, or hold back on purchases to be sure we can afford it at the checkout, or estimate how much longer we can go before we run out of gas we are using our math skills. Mathematics is responsible for our greatest advances, technology such as your cell phone or GPS, and so much more. My advice? Embrace it.