why is pi 3.14…. What is so special about this exact number and how did we know this invite number is a circle?
In: Mathematics
[removed]
There’s not anything special about it as such. It’s just the number that defines circleyness. If you measure the distance straight across a square, and measure the distance around the edge, and divide one by the other, you get 4. So, in a sense, 4 is the number that defines squareyness. In a similar way, measuring across a circle (the diameter) and measuring around the edge (circumference) and dividing them gives 3.14… etc.
The thing is, pi crops up in a bunch of different places. There are a load of equations that seem to have nothing to do with circles that magically have pi in them. The secret is that there’s a circle hiding somewhere in the background. Whenever you see pi, there’s a way to translate the problem to being about circles.
Now, how did we calculate it? Well one of the first methods was to take a circle that’s 1 unit across, draw a square around the outside of it so that each edge just touches the circle, and draw another square inside of it so that each corner touches the circle. The outer square has a perimeter of 4. Using geometry and Pythagoras, we can work out that the inner square has a perimeter of about 2.8 (exactly 2√2). We can then work out that pi is somewhere between those two values. If we use a polygon with more sides (a pentagon, hexagon, heptagon, octagon, etc.) we get shapes that are closer to the circle. This gives us a closer and.closer estimate of pi. This was the method that was used for thousands of years.
Since then, we’ve moved on and have better ways of working out pi. But they all come down to spotting a pattern that relates to the circle, and then building up better and better estimates of what pi is.
One method is to follow the pattern 4×(1-⅓+⅕-⅐+⅑…). The more odd fractions you add and subtract, the closer you get to pi. Try it yourself on a calculator and see 🙂
The trick is working out how these patterns relate to pi, but that goes a bit beyond this post!
It’s circumference of a circle divided by diameter
In a perfect circle, when you divide circumference by diameter, you always get that number. Knowing that is useful for doing other calculations with circles
Pi is the ratio of a circle’s circumference to it’s diameter. It is a constant and applies to all circles, so we didn’t choose it, but rather discovered it.
The circles came first, not the number. And we noticed that all circles have this fundamental property: that their circumference divided by their diameter equals this number. Doesn’t matter the size of the circle, this ratio stays the same.
A lot of comments talking about how you derive pi but not why pi is 3.1415… etc. This is just a consequence of how our number system is set up. We do math with a base 10 system so that every number can be described with a combo of those 10 numbers. If we had base 12 number system, pi would look different but it would be the same irrational number because it is described by an unbreakable physical constraint, which is the ratio of a circle’s perimiter to its diameter.
Latest Answers