Calculating π by hand: the Chudnovsky algorithm

I cannot understand how you can get rid of that big number raised to the power of k when k is an odd number.Of course when k is zero,the negative sign disappears.There are only products and divisions so a negative number raised to an odd power would give a negative result.This is what I got in my Excel with multiple iterations.The result alternates.I wonder if the formula is right!

I meant negative big number...

Welcome to the skinhead club!

Pls someone give this man a calculator 🤣

Wishing to punish a little embedded controller today (a Teensy 4.0) , I had it calculate pi to 1000 places using a 1593 algorithm that converges linearly. It took 151 seconds and required 1662 iterations using 1008-digit numerals. Now to try something a bit more modern...

Did you know you could have got 13 digits from just k=0 if you did the work to calculate sqrt(10005) more accurately?

It hurts that he puts his decimal in the middle.

Manual floating point math is insanity. My puny AMD Ryzen 12GB RAM LAPTOP calculates PI to 100+ million digits like this:
** PI Computation ( 100000000 digits )
TIME (COMPUTE): 247.011 seconds.
TIME (WRITE)  : 52.9288 seconds.

Here's a 250 million digit run:
** PI Computation ( 250000000 digits )
TIME (COMPUTE): 517.892 seconds.
TIME (WRITE)  : 124.382 seconds.

500 million digit run crashes due to insuficient memory.

Matt, why on earth are you subtracting? Reverse add for godssake!! Say, if I wanted to do (32-19), then I'll be like, what should I add to the last digit of 19 to make it match the last digit of 32? It's a 3. I note it down, and then add it to 19, which now becomes 22. Then I say what should I add to the first digit of 22 to make it equal the first digit of 32? It's a 1 (or 10 to be more correct). Note it down, add it to 22 which now equals the first number. That's it, we're done. The numbers you note down give the answer.

It’s amazing how useless feats get this guy si much following, I’m fed up, bye

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It's fascinating how all the constants are actually related.

Chud bros we won

OK,I found my mistake!

Any specific reason he didn’t use linear approximation for sqrt(10005)?

YeahH Awesome video great upload!!

I knew that this algorithm converged quickly, but ... wow!

Me who calculate pi upto 10 digits just by 355÷113

don't tell anyone but this is my idea of entertainment

i dont know how you got pi i put it into desmos and got 0.311 and when i put 1 for k i got some number times 10^12

Hair today, gone tomorrow. Well technically, hair yesterday, gone today but you get the idea. Oh and all that stuff about calculating Pi by hand was quite interesting too.

2 times the first denominator (k=0) is close to e….????

Billions must Pi

How do we know our approximations of pi are accurate if we don’t have the full value?

CHUD

Perfect activity for the retired seniors.

outrageous acts of science

lets chud it up rq

billions must calculate pi

how boards does this man has goddamn

Not using the approximation sign when calculating for x after removing x squared made my head quake.

That square root estimation is the exact same as estimating with calculus. If the derivative of sqrt(x) is 1/(2sqrt(x)) then the sqrt(10005) estimation is sqrt(10000)+5/(2sqrt(10000)) which is 10000+5/(2*100) => 10000.025.

Hmmmm.... Since all factors are multiplied with each other, having ANY of them off by a promille will have the result off by that promille as well. Maybe you should have done that root approximation at least a second or better a third round with its derivative (its accuracy is squared each round). But each year, we have some interesting things to learn from those experiments :D
By the way: Digit wise, when calculated by hand, the chudnovsky algorithm seems not to be the best. What you did this year (2024: the schoolbook Taylor series for acot with a 7 term decomposition of pi) had the potential of being nearly twice as fast as chudnovsky in regard to the chrunched decimal digits. I am curious as to when you will manage to break the record of Shanks :D

P.S.: By the way: With to the last digit optimized manual calculation, Shanks expression is even faster than that of chudnovsky. That's mainly caused by the fact that optimized division with such simple factors as are used in those Pi-calculations is by far faster than any algorithm using multiplication, especially against any algorithm using binary split to collect products, where you are not able to limit the accuracy of intermittent results. In the latest incarnation of my "human numbers library", Shanks calculation to 600 digits, for example, comes out at less than 1,2 million digit manipulations (half of parker pi-day 2024 and a quarter of chudnovsky at the same accuracy). And that is still without using periodicity of numbers.

Usage of periodicity gives only a little reduction at smaller accuracy (higher iterations usually don't result in factors that grant periodicity), bringing Shanks at 600 digits down to 930'000 digit operations. At 160 accuracy, Shanks needs only 68'000 digit operations - which already a single person could handle on a very long rainy weekend.

Fazit of that Pi-day: I had two weeks of fun following your incitation. Thanks! And more of that, please!

i never saw your videos with hair so you look great

I'd say K=0 and k=1 is not really K approaching infinity.

when you forget to bring your calculator to a math exam

Aristotle had the same problem. Should have used an abacus.

Using the Chudnovsky algorithm?

The maths classroom has risen

I mean, the actual sqrt of 10005 is 100.02499687......
Thats such a microscopic error that im not surprised it was perfect for that many digits anyway