MATH SOLVE

4 months ago

Q:
# Can anyone tell me the algorithm of Pi

Accepted Solution

A:

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,￼