Can’t Wrap Your Head Around Pi? Here’s a Cool Visual to Help

Oh, you tin try. For example, 22/7 is simply a beauteous bully approximation. But it's not pi. (We could person celebrated Pi Day connected July 22, since astir of the satellite uses the day-month-year format for dates, and that would beryllium 22-7.)

But possibly you’re not inclined to instrumentality my connection for it. So here's what I'm going to do: I'm going to usage a brute-force algorithm I made successful Python to make each imaginable integer fractions and spot if 1 of them equals pi.

No Pi successful Python

What’s a brute-force method? It’s a mode of solving a occupation that doesn't necessitate cleverness, conscionable a ton of work. My programme starts with the fraction 1/1 and methodically ratchets it up by adding 1 to the numerator oregon the denominator. Here's the recipe:

- Take the fraction (u/v) and comparison to pi
- If u/v is little than pi, adhd 1 to the numerator (u+1)
- If u/v is greater than pi, adhd 1 to the denominator (v+1)
- If u/v is equal to pi, you win. You conscionable proved that pi is rational.

So the bid starts similar this: 1/1, 2/1, 3/1, 4/1, 4/2, 5/2, 6/2, 7/2, 7/3, 8/3 … I mean, you could bash this connected paper, but you’d soon spell mad. I ran my programme to iterate 1,000 times. (If you privation to spot the code, present it is connected Google Colab.) Then I plotted the decimal worth for each 1,000 fractions (Since the horizontal axis goes from 1 to 1,000, I'm utilizing a log standard to compress it.)

After 1,000 runs, I person a fraction of 760/242. This is simply a good worth for pi. It's close to 2 decimal places—the modular 3.14, which is what a batch of radical usage anyway. But it's not pi. Oh, well, however astir 500,000 iterations?