In calculus there is a thing called Taylor Series which provides an easy way to calculate many irrational values to arbitrary precision. Pi/4 = 1 – 1/3 + 1/5 – 1/7 + … (from http://www.math.hmc.edu/funfacts/ffiles/30001.1-3.shtml ) Keep adding those terms until the number of digits of precision you want stabilize. Taylor’s theorem is a powerful … Read more
You’re missing the multiplication operator. Also, you want to do 4/3 in floating point, not integer math. volume = (4.0 / 3) * Math.PI * Math.pow(radius, 3); ^^ ^
>>> import math >>> import numpy as np >>> import scipy >>> math.pi == np.pi == scipy.pi True So it doesn’t matter, they are all the same value. The only reason all three modules provide a pi value is so if you are using just one of the three modules, you can conveniently have access … Read more
%lld is the standard C99 way, but that doesn’t work on the compiler that I’m using (mingw32-gcc v4.6.0). The way to do it on this compiler is: %I64d So try this: if(e%n==0)printf(“%15I64d -> %1.16I64d\n”,e, 4*pi); and scanf(“%I64d”, &n); The only way I know of for doing this in a completely portable way is to use … Read more
This style ensures that the maximum precision available on ANY architecture is used when assigning a value to PI.
>>> import math >>> import numpy as np >>> import scipy >>> math.pi == np.pi == scipy.pi True So it doesn’t matter, they are all the same value. The only reason all three modules provide a pi value is so if you are using just one of the three modules, you can conveniently have access … Read more
Summary: It’s not a coincidence; _PyHASH_INF is hardcoded as 314159 in the default CPython implementation of Python, and was picked as an arbitrary value (obviously from the digits of π) by Tim Peters in 2000. The value of hash(float(‘inf’)) is one of the system-dependent parameters of the built-in hash function for numeric types, and is … Read more
The Monte Carlo method, as mentioned, applies some great concepts but it is, clearly, not the fastest, not by a long shot, not by any reasonable measure. Also, it all depends on what kind of accuracy you are looking for. The fastest π I know of is the one with the digits hard coded. Looking … Read more
Since I’m the current world record holder for the most digits of pi, I’ll add my two cents: Unless you’re actually setting a new world record, the common practice is just to verify the computed digits against the known values. So that’s simple enough. In fact, I have a webpage that lists snippets of digits … Read more