609 digits of π from 1,000 terms in the series: π ≈ 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127…
taylor.txt (586K) - 1,000 terms used to calculate the approximation of π above. taylor.txt.xz (26M, 57M uncompressed) - Compressed taylor.txt with first 10,000 terms. newton.bc (610K) - bc script that uses the terms to calculate π. The lines in newton.bc to truncate π at the end of the script were manually added. prepare_taylor.sh (0.8K) - Syntax highlighted - Bash script that reads taylor.txt and outputs newton.bc. taylor.py (1K) - Syntax highlighted - Python script to generate taylor.txt - ./taylor.py >taylor.txt
sqrt3.sh (0.8K) - Syntax highlighted - If the sqrt(3) at the end feels a little handwavy, this script will generate √3 using taylor.txt. A small amount of precision will be lost (607 digits of √3 and 606 digits of π from 1,000 terms).
Most sources give the following formula for Newton's 1665 π calculation: 0∫1⁄4 x1⁄2(1-x)1⁄2 dx = [ x1⁄2 - 1⁄2x3⁄2 - 1⁄8x5⁄2 - 1⁄16x7⁄2 - 5⁄128x9⁄2 - 7⁄256x11⁄2 - … ]
This produces digits at the same rate as the equation given in the video. newton-orig.sh (0.8K) - Syntax highlighted - Uses the integral from 0 to 1⁄4.