Answer :
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,