Het Oneindige Leven Van Pi

De verhouding van de omtrek van een cirkel tot zijn diameter is altijd hetzelfde: 3,14159 ... en voor altijd (letterlijk!). Voor altijd. Dit irrationele getal, pi, heeft een oneindig aantal cijfers, dus we zullen nooit de exacte waarde achterhalen, hoe dichtbij we ook lijken te komen. Reynaldo Lopes verklaart de enorme toepassingen van pi voor de studie van muziek, financiële modellen en zelfs de dichtheid van het universum.

Try to measure a circle. The diameter and radius are easy, they're just straight lines you can measure with a ruler. But to get the circumference, you'd need measuring tape or a piece of string, unless there was a better way.

Now, it's obvious that a circle's circumference would get smaller or larger along with its diameter, but the relationship goes further than that. In fact, the ratio between the two, the circumference divided by the diameter, will always be the same number, no matter how big or small the circle gets.

Historians aren't sure when or how this number was first discovered, but it's been known in some form for almost 4,000 years. Estimates of it appear in the works of ancient Greek, Babylonian, Chinese, and Indian mathematicians. And it's even believed to have been used in building the Egyptian pyramids.

Mathematicians estimated it by inscribing polygons in circles. And by the year 1400, it had been calculated to as far as ten decimal places. So, when did they finally figure out the exact value instead of just estimating? Actually, never!

You see, the ratio of a circle's circumference to its diameter is what's known as an irrational number, one that can never be expressed as a ratio of two whole numbers. You can come close, but no matter how precise the fraction is, it will always be just a tiny bit off.

So, to write it out in its decimal form, you'd have an on-going series of digits starting with 3,14159 and continuing forever! That's why, instead of trying to write out an infinite number of digits every time, we just refer to it using the Greek letter pi.

Nowadays, we test the speed of computers by having them calculate pi, and quantum computers have been able to calculate it up to two quadrillion digits. People even compete to see how many digits they can memorize and have set records for remembering over 67,000 of them.

But for most scientific uses, you only need the first forty or so. And what are these scientific uses? Well, just about any calculations involving circles, from the volume of a can of soda to the orbits of satellites.

And it's not just circles, either. Because it's also useful in studying curves, pi helps us understand periodic or oscillating systems like clocks, electromagnetic waves, and even music.

In statistics, pi is used in the equation to calculate the area under a normal distribution curve, which comes in handy for figuring out distributions of standardized test scores, financial models, or margins of error in scientific results.

As if that weren't enough, pi is used in particle physics experiments, such as those using the Large Hadron Collider, not only due to its round shape, but more subtly, because of the orbits in which tiny particles move.

Scientists have even used pi to prove the illusive notion that light functions as both a particle and an electromagnetic wave, and, perhaps most impressively, to calculate the density of our entire universe, which, by the way, still has infinitely less stuff in it than the total number of digits in pi.

 

Bron: TED.com