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How did someone come up with the number “Pi”?

In: Mathematics

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I guess the measured the circumference and the diameter and realised that when you divide them no matter the size of the circle theres this same number that keeps appearing

It is a universal constant for flat surfaces. The number pi is the ratio of the circumference of a circle to its diameter. In a sense a very “natural” number to obtain anytime one confronts a circle on flat land or surfaces.

What I’d like to know is how we can calculate it to the trillionth digit. Is there a formula or piece of code you can plug into a computer to simulate a circle and calculate the number from there?

Edit: Thanks for such detailed answers. I love stuff like this and I’ve always wondered how it worked.

Well, if you think about the well known formula for the area of the circle. πr squared.

Area = mysterynumber * (radius * radius)

Someone ( your boi, Archimedes, but he no longer gets the credit) basically noticed that any time you have a circle, and you already know the radius and rough area of it, the area divided by the square of the radius equals the same thing. Every time.

Then he started pulling sick maths wheelies. If you divide both sides of the equation by (radius * radius) you get.

Area / (radius * radius) = mystery number * 1.

Then he put playing cards in his maths bike spokes and Omg, turns out mystery number is aaalways about 3… Okay 3.1.. okay 3.14… mm closer to 3.142… 3.1417…

And that narrowing down of Pi is still going on to this day.

There’s a [video](https://youtu.be/gMlf1ELvRzc) about how pi is now 3.14159265 (and so on), and there you can see that it wasn’t the same thing before than it is now, because Newton was the one that actually discovered this number. So yeah, in the video they explain it very simply, so, check it out

You have a circle and its diameter is one unit. You want to measure the distance around the circle using geometry.

You can’t measure the distance around the circle, but you *can* measure the length of a straight line. So you draw a shape whose sides are straight lines — a regular polygon, with all the sides and angles equal.

In fact you draw two polygons, inside and outside the circle, [like this](https://en.wikipedia.org/wiki/Method_of_exhaustion#/media/File:Archimedes_pi.svg).

Now there are three important facts about drawing polygons like this:

– You know the distance around the outside polygon will be longer than the distance around the circle.

– You know the distance around the inside polygon will be shorter than the distance around the circle.

– You know enough about the lengths and angles involved to figure out the length of the polygons’ sides with some formulas.

Then you figure out another formula for a polygon with twice as many sides, which you can apply repeatedly. As the polygons have more sides, they start to look like circles; the distance around them gets closer and closer to the actual distance around the circle.

Archimedes used this technique about 2200 years ago, and figured out that pi is somewhere between 3+10/71 and 3+10/70.

That’s the basic idea of one way you could calculate pi to as much precision as you need. Of course our calculating ability has improved vastly since Archimedes (who didn’t even have the Arabic decimal arithmetic system that we use today). And we’ve also discovered new techniques that produce more precision with less arithmetic.

They’ve been measuring areas and lengths of circles, and figured out that they are related to the diameters of those same circles. Seeing how they couldn’t quite put a finger on that number’s exact value despite it being the same for all circles, they’ve decided to denote it with a special letter rather than some specific digits.