I am ashamed to tell you to how many figures I carried these calculations, having no other business at the time.Isaac Newton Newton's embarrassment at having computed 15 digits, which he did using the arcsinlike formula Illustration
The history of efforts to determine an accurate value for the constant we now know as is almost as long as the history of civilization itself. By 2000 B.C. both the Babylonians and the Egyptians knew to nearly two decimal places. The Babylonians used, among others, the value and the Egyptians used . Not all ancient societies were as accurate, however --- nearly 1500 years later the Hebrews were perhaps still content to use the value 3 , as the following quote suggests.
Also, he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.old Testament, 1 Kings 7:23
Despite the long pedigree of the problem, all nonempirical calculations have employed, up to minor variations, only three techniques.