Question

Can anyone tell me the algorithm of Pi

Answer 1

Answer:

representations are thought in the form utilized by Horner's method. E.g., in the decimal system we have

(1)√2= 1.41421 ... = 1 + 1/10 (4 + 1/10 (1 + 1/10 (4 + 1/10 (2 + 1/10 (1 + 1/10 ( ... )))))),π= 3.14159 ... = 3 + 1/10 (1 + 1/10 (4 + 1/10 (1 + 1/10 (5 + 1/10 (9 + 1/10 ( ... )))))),

But was there a positional system in which π was known? As S. Rabinowitz has realized, there indeed was such a system albeit an unusual one. The starting point was the series



which also can be written as



or, in the Horner form,



representations are thought in the form utilized by Horner's method. E.g., in the decimal system we have

(1)√2= 1.41421 ... = 1 + 1/10 (4 + 1/10 (1 + 1/10 (4 + 1/10 (2 + 1/10 (1 + 1/10 ( ... )))))),π= 3.14159 ... = 3 + 1/10 (1 + 1/10 (4 + 1/10 (1 + 1/10 (5 + 1/10 (9 + 1/10 ( ... )))))),

But was there a positional system in which π was known? As S. Rabinowitz has realized, there indeed was such a system albeit an unusual one. The starting point was the series



which also can be written as



or, in the Horner form,