Ok, pi is probably a bit over the head of your average 5 year old. I know the definition of pi is circumference / diameter, but is that really how we get all the digits of pi? We just get a circle, measure it and calculate? Or is there some other formula or something that we use to calculate the however many known digits of pi there are?
In: 716
Archimedes found a way back in ancient Greece. He was big on geometry and trigonometry.
Let’s say you have a regular polygon inscribed in a circle. (This means that every corner of the polygon touches the edge of the circle.) If you know the radius of the circle and the area of the polygon, you can do some trig to get the area of the regular polygon with twice as many sides inscribed in the circle.
So we can start with a hexagon. It’s easy to get the area of a hexagon. Then we can use the trig formula to get the area of the 12-sided polygon inscribed in the circle. Then we can do it again to get the area of the 24-sided polygon. Then 48-sided, 96-sided and so on as far as we want.
A polygon with that many sides is really close to a circle. Like, you’d have to look really close to even see the difference. So pi is really close to the area that you calculated for the polygon. But you can go as far as you want, approximating pi as well as you want.
One way to do it – Draw a circle in a square. Start throwing darts at the square. Count how many darts land in the circle and divide that by the number of darts that land in the square. That number is going to be approximate pi/4. Then as you throw more darts that approximation will get closer
Measure a wheel circumference.
Now measure the diameter.
Divide the circumference by the value of the diameter.
When you try to divide it, division will never end. Well, you can try it, but you’ll spend the rest of your life.
This is pi. A proportion.
π = 3.141692654…
Oi is simply the ratio between the diameter of a circle and the distance around the edge of the circle, it’s not a made up number, it’s literally nature, if a “circle” doesn’t follow this ratio, it’s not a circle, it’s some weird oval
One of the more basic “formula” approaches roughly goes:
– There are certain angles that have easy, exact trigonometry values. For example: sin(pi/6) = 1/2 (that is: 30 degrees)
– Because calculus, we happen to know some ways of calculating certain trig functions as an infinite sum of normal polynomial values. Inverse sin is one of them.
– From the first, if we calculate the inverse sin of 1/2, then multiply by 6, we have determined the value of pi. From the second, we can do that just with this polynomial. So, taken together, we can write down a formula where the more terms we add, the closer we get to the exact value of pi.
Proving the formula isn’t particularly simple — but you can look it up easily enough.
There are quite a few formulas like this; they tend to have varying properties in terms of how hard they are to calculate, and how quickly they reach a given accuracy.
There are some very interesting ways, like dropping lots of sticks on top of a pattern with many parallel lines: [Buffon’s Needle](https://prancer.physics.louisville.edu/modules/pi/pi.html).
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It’s a little hard to ELI5 without involving formulas unfortunately!
To calculate Pi, we use a simple formula that relates the circumference and diameter of a circle. The formula is: Pi = C/d, where C is the circumference (the distance around the circle) and d is the diameter (the distance across the circle, passing through the center).
To use the formula, we just need to measure the circumference and diameter of a circle. We can do this with a ruler or a tape measure, or with more precise tools, like a caliper or a micrometer. Then we divide the circumference by the diameter to find the value of Pi. For example, if the circumference is 10 inches and the diameter is 3 inches, then Pi = 10/3 = 3.33.
The value of Pi is the same for all circles, no matter how big or small they are. This is because the formula for Pi is based on the basic properties of circles, like their symmetry and their geometric relationships. The value of Pi is also an irrational number, which means it can’t be written exactly as a fraction or decimal, but it can be approximated to any level of precision.
I’d pay a medium good money if he or she could invoke the great deceased mathematicians of the past to read this ELI5 topic. I think when all was said and done, their comments would look like a reddit thread. 🙂
Edit: And which would be the first to use the term “dafuqisthis?”
If you’re looking for a method that a 5 year old would understand, I’d go with inscribed and circumscribed polygons of a unit circle. The perimeter of the polygons will converge to 2*pi as the number of sides goes up.
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