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Calculate pi from the infinite series 4/1 - 4/3 + 4/5 - 4/7 + ...
This expansion was formulated by Gottfried Leibniz: http://en.wikipedia.org/wiki/Leibniz_formula_for_pi
I helped rubenmoran create the sum of a sequence of numbers and he replied with a command for the sequence: 1 + 2 -3 + 4 ...
This set me thinking. Transcendental numbers!
seq provides the odd numbers 1, 3, 5
sed turns them into 4/1 4/3 4/5
paste inserts - and +
bc -l does the calculation
Note: 100 million iterations takes quite a while. 1 billion and I run out of memory.
If you want a sequence that can be plotted, do:
seq 8 | awk '{print "e(" $0 ")" }' | bc -l | awk '{print NR " " $0}'
Other bc functions include s (sine), c (cosine), l (log) and j (bessel). See the man page for details.
Exactly the same number of characters, exactly the same results, but with bc
To do hex to binary: echo 'ibase=16; obase=2; 16*16' | bc # prints: 111100100
To do 16*16 from decimal to hex: echo 'ibase=10; obase=16; 16*16' | bc # prints: 100
You get the idea... Alternatively, run bc in interactive mode (see man page)
using bc is for sissies. dc is much better :-D
Polish notation will rule the world...
-l auto-selects many more digits (but you can round/truncate in your head, right) plus it loads a few math functions like sin().
allows you to use floating point operations in shell scripts
When you've got a list of numbers each on its row, the ECHO command puts them on a simple line, separated by space. You can then substitute the spaces with an operator. Finally, pipe it to the BC program.
defines a handy function for quick calculations from cli.
once defined:
? 10*2+3
Easily convert numbers to their representations in different bases. Passing
"ibase=16; obase=8; F2A"
to bc will convert F2A (3882 in decimal) from Hex to Octal, and so on.
Useful for quick calculations at the command line. $math_expr is any arithmetic expression (see sample output):
4.5*16+3^2
s(3.1415926/2)
More options in the bc man page.