Okay, so honestly, I always hated calculating pi back in school. Felt like ancient magic or something. But recently, I saw this video mentioning you could actually get a decently close value yourself, using just basic arithmetic. Got me curious, you know? Could I really figure out pi myself? Specifically, I wanted to try hitting at least three decimals correctly – 3.141. Seemed like a neat little weekend challenge.
Started digging around online. Forget all those fancy algorithms you hear about. Found out about this one simple thing called the Leibniz formula. Sounded complicated, but the core idea? Pretty straightforward. Basically, you just keep adding and subtracting fractions – fractions where the bottom number is an odd number.
Here’s the recipe:
- Start with 1.
- Subtract 1 divided by 3 (so, 1/3).
- Then add 1 divided by 5 (1/5).
- Then subtract 1 divided by 7 (1/7).
- Then add 1 divided by 9 (1/9)… and you get the pattern.
- Just keep going like that forever, using odd numbers for the bottom.
The promise? That if you do this a LOT of times, multiplying the final result by 4 gets you closer and closer to pi. Sounded almost too easy. But hey, easy is good.
Fire up the computer? Nah, felt like cheating. Wanted the “doing it” experience. Grabbed my trusty calculator (the one on my phone, obviously) and my notebook. Yeah, actual pen and paper. Felt kinda retro.
Started punching away:
- Term 1: +1
- Term 2: -1/3 = -0.3333333333
- Term 3: +1/5 = +0.2
- Term 4: -1/7 ≈ -0.1428571429
- Term 5: +1/9 ≈ +0.1111111111
- … and so on.
Added them after each step. After maybe 10 terms? I got something like… 0.760. Multiplied by 4? 3.04. That’s way low. Pi is about 3.14. Barely hit one decimal.
Kept going. Another 10 terms, slowly watching the number grow. By term 50, my running total before multiplying by 4 was roughly 0.780. Times four? 3.12. Getting closer, but still only 3.12. Needed 3.141.
This was getting tedious. Started doing batches of 100 terms. Instead of writing every single one, I’d note down the result every 100 additions/subtractions. Patience wearing thin, but the number was inching up. Felt like filling a swimming pool with an eyedropper.
Hit term 500. Running total around 0.7846. Times four? 3.1384. Okay! Now we’re getting somewhere. 3.14… almost. But I needed it to be at least 3.141 solidly.
Pushed to term 1000. Final add/subtract sequence done. Crossed my fingers. The sum came out to about 0.785148. Held my breath. Multiply by four: 3.140592.
Stared at it. 3.140592… compared to the real pi 3.141592… Yeah! The first three decimals were spot on: 3.14. Sweet! That fourth digit? 0 vs 5? Close enough for my challenge. Mission accomplished. Felt genuinely pleased.
Learned a couple things doing this:
- Patience is key. A thousand terms took a while, even skipping steps.
- Simple works. No advanced degree needed, just persistence.
- Pi is weird. Seeing those numbers slowly creep up towards that magic 3.141… it feels different than just being told it’s pi.
So yeah, calculating pi yourself? Totally possible. Surprisingly satisfying. Would I do a thousand terms by hand again? Not a chance. But glad I did it once!
