Pi (π) is an irrational number representing the ratio of the circumference of a circle to its diameter.
Sounds simple right? But what if I told you that π just shows up all over the place, even when we aren’t talking about circles? It shows up in electromagnetism, complex numbers, quantum mechanics, Fourier analysis, and basically anywhere where you have a loop! If we miscalculated π to be only a liiiitttllleee bit different, the way we have defined our ENITRE UNIVERSE would be indescribably different. That doesn’t seem so simple anymore, does it?
This video is incredible. It’s the best video I’ve seen (and… I’ve seen a lot of videos… it’s not something I’m proud of) about π. It actually describes how versatile and crazy important π is, without focusing only on how cool irrational numbers are.
I’m sure it would be easy to convince you that π is interesting. If you still aren’t convinced… then you didn’t watch the video 😉
I’m sure it would be easy to tell you π matters because π is used all the time by really smart people (lawlz – not me)… Just like how we know astrophysicists matter, even if we have no clue how they work… But I want you to take a second, if you can to think about this: if you took a string and wrapped it around a circle to find the circumference of the circle, you will never be able to tell me the exact circumference without using π. The circumference of any circle must always be irrational, just like pi.
That is mind boggling to me because that means that you can’t EVER measure a circumference exactly. WHATTTT? You can only CALCULATE circumference exactly (assuming you agree that π has been calculated accurately). That also means that you cant EVER know the exact volume or surface area of a sphere just by measuring it, and you can’t EVER know the volume or surface area of a cylinder just by measuring it. If you don’t think that’s crazy, then… I dunno… go watch Cosmos or something.
So how did we find pi?
Well. We drew REALLY big circles in the sand and measured the circumference and diameter. You could also do some math! Gross, I know. There were many methods to finding pi, and many people contributed to finding this number over time, but since pi is irrational, we will never know all of it. No matter how hard we try… We can NEVER fully know all of life’s secrets.
Wanna know something else important about π? I think π is one proof that math is discovered and NOT invented. Maybe this seems blantantly wrong or obviously true to you, but let me tell you, this is a hot debate in the math world (as hot as anything can get in the math world at least). There are strong arguments for either case, but I believe that math is discovered, we merely invent the terms. If you don’t think that this is a fascinating debate, then I either did a bad job of explaining π, or you don’t care about knowledge.
HOW does π prove such an abstract idea you ask? Well… as humans, we didn’t invent circles, did we? No. They existed. Or at least the orbit of the Earth around the sun existed before we knew what π was. Shapes exist in nature. Patterns in nature can be described using shapes. We discovered a relationship between the properties of circles AND it shows up all over the place without us even guessing that it would.
“…π. Put a smile on your face ten miles wide. Looks so good bring a tear to your eye. Sweet… π”~Warrant (these are the real meaning behind their lyrics)