There are many different formulas for deriving digits of pi, and the history of mathematics has a bunch of people trying to brute force inefficient formulas for pi out to a few digits, as they develop more efficient methods.

Archimedes drew a circle and put some polygons around the inner and outer limits to determine that it was somewhere between 22/7 and 223/71, accurate to within 2 digits. That general polygon method was used by Ptolemy to calculate out to 3 digits, and used by Chinese mathematician Zu Chongzhi to estimate pi at 355/113, accurate to 7 digits.

The polygon method was very tedious, requiring many, many calculations in order to advance just a few digits.

The Liebniz formula was a breakthrough (discovered by Indian mathematician Madhava of Sangamagrama), because discovering that pi/4 was equal to the infinite series 1 - 1/3 + 1/5 - 1/7 . . . meant that someone could calculate some number of digits accurately, and then continue the calculation in a way that reports what is known so far, and can continue down the line towards a more precise result. Still, by itself, it was a very slowly converging algorithm, requiring 5 billion terms just to get to 10 digits of accuracy. Mathematicians got to using other tricks (that, if I'm being honest, I don't understand) to make it faster.

Then Ramanujan discovered series that were rapidly converging (including the one in this meme) where although calculating each term might require a lot of calculations, it would spit out 8 digits for each term you fed it. It became the preferred method for calculating digits of pi, and when computers were developed, they were able to make use of that computational efficiency. It still remains the basis for how a computer will calculate a few million digits of pi.