How can I calculate pi using Bash command

Question

I am learning bash scripting. While exploring the math functions i am came across a command which calculated the value of pi. seq -f '4/%g' 1 2 99999 | paste -sd-+ | bc -l Although i understand how the basic seq command works, I am unable to understand how does the above command works. Can anybody please clarify how does it work.? JavaScript questions and answers, JavaScript questions pdf, JavaScript question bank, JavaScript questions and answers pdf, mcq on JavaScript pdf, JavaScript questions and solutions, JavaScript mcq Test , Interview JavaScript questions, JavaScript Questions for Interview, JavaScript MCQ (Multiple Choice Questions)

Answer 1

This calculates the value of π using Gregory–Leibniz series: seq -f '4/%g' 1 2 99999 generates the fractions: 4/1 4/3 4/5 4/7 4/9 4/11 4/13 4/15 4/17 4/19 The paste pipeline paste -sd-+ combines those with alternate delimiters - and +. Finally, bc -l performs the arithmetic to give the result. EDIT: As noted in the comment, this sequence converges very slowly. Machin's formula has a significantly higher rate of convergence: Using the same expansion for tan-1(x): to compute π, we can see that it produces the correct value to 50 digits1 using just the first 50 terms of the series: $ { echo -n "scale=50;"; seq 1 2 100 | xargs -n1 -I{} echo '(16*(1/5)^{}/{}-4*(1/239)^{}/{})';} | paste -sd-+ | bc -l 3.14159265358979323846264338327950288419716939937510 With just 100 terms, the value of π is computed accurately to more than 100 digits: $ { echo -n "scale=100;"; seq 1 2 200 | xargs -n1 -I{} echo '(16*(1/5)^{}/{}-4*(1/239)^{}/{})';} | paste -sd-+ | bc -l 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 1 Pi