11–20 of 23 posts
I had never heard of this product formula before, so I whipped up a quick python program: http://pastebin.com/FBR8rWxv All I can say is wow, that formula slow to converge on pi. The product after 100 million terms is: 3.141592637878503 You can see that 100M terms only gets you 8 decimals of precision.
I had never heard of this product formula before, so I whipped up a quick python program: http://pastebin.com/FBR8rWxv All I can say is wow, that formula slow to converge on pi. The product after 100 million terms is: 3.141592637878503 You can see that 100M terms only gets you 8 decimals of precision.
edit: Oh that's interesting. Python 2 gave me 0, Python 3 worked fine.
I had never heard of this product formula before, so I whipped up a quick python program: http://pastebin.com/FBR8rWxv All I can say is wow, that formula slow to converge on pi. The product after 100 million terms is: 3.141592637878503 You can see that 100M terms only gets you 8 decimals of precision.
For another famous, but also very slow series converging to pi, try pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...
What makes this expansion particularly painful is that usually Taylor expansion is done around a point where x is small, such that the x^n numerators of subsequent terms get progressively smaller. But in this case the numerator is always 1, so the series depends entirely on the denominator for convergence.
Meanwhile, the denominator doesn't grow by the usual increasing factorial terms common to Taylor series, but grows only linearly. So both effects combined cause this expansion to take a very long time to converge.
I had never heard of this product formula before, so I whipped up a quick python program: http://pastebin.com/FBR8rWxv All I can say is wow, that formula slow to converge on pi. The product after 100 million terms is: 3.141592637878503 You can see that 100M terms only gets you 8 decimals of precision.
maybe I'm missing something (haven't tried to debug it), but that just results in 0. edit: Oh that's interesting. Python 2 gave me 0, Python 3 worked fine.
I had never heard of this product formula before, so I whipped up a quick python program: http://pastebin.com/FBR8rWxv All I can say is wow, that formula slow to converge on pi. The product after 100 million terms is: 3.141592637878503 You can see that 100M terms only gets you 8 decimals of precision.
If speed of convergence is what you seek, i've yet to discover a more impressive case than a surprisingly simple method attributed to Gauss using the geometric and arithmetic means of two numbers. Three times around the loop and it's already correct to five decimal places: http://pastebin.com/674YJ9VM
https://en.wikipedia.org/wiki/Approximations_of_π#Efficient_...
I had never heard of this product formula before, so I whipped up a quick python program: http://pastebin.com/FBR8rWxv All I can say is wow, that formula slow to converge on pi. The product after 100 million terms is: 3.141592637878503 You can see that 100M terms only gets you 8 decimals of precision.
What is being tested with 100million function calls?
http://www.jstor.org.sci-hub.cc/stable/10.4169/amer.math.mon...
Then if you want your answer plug in x = π/2 inevitably Wallis formula leads to either Stirling formula or the derivation of ζ(2)=π^2/6.
So for someone to solve it just by drawing some rectangles and finding the area is pretty amazing.