41β50 of 143 posts
> Note that the calculation of Bernoulli numbers can be done in several ways, one of which requires knowing Ο with good precision This seems to be the catch.
So does it mean that these pi-calculating competitions & record are now going to devolve to special olympiads in pointless storage capacity? What will the super computers going to do in view of this discovery? Fascinating times for humans as well as for the machines...
Οfs: Never worry about data again! - https://github.com/philipl/pifs
The library of babel could be a good "useless" backing though https://libraryofbabel.info/bookmark.cgi?hnexample
Looks interesting! Does anyone know a practical application where something like this would help?
In "nβth digit of π and π^n" are both n the same? In other words, for say π^50 does the formula only give me the 50th digit, or does it give me any arbitrary digit I want?
The article title says "powers of π", so presumably an arbitrary digit.
The abstract and text say the nth digit of \pi^n, and the worked example on page 2 uses the same n=1000 to find the thousandth digit of \pi^{1000}.
Looks interesting! Does anyone know a practical application where something like this would help?
It's another way to help verify super long calculations of pi are correct, and in turn I guess one basic "practical application" of calculating pi to many digits is as part of the suite for verifying new hardware. How do you know that fancy fresh new silicon is actually crunching the numbers correctly, not producing garbage in some subtle way at enough significant digits? While there are lots and lots of checks used to avoid a repeat of hardware bugs of days past (like the forever infamous Pentium FDIV), one simple sanity check/stress test is calculating out numbers like pi a bunch of different ways to huge numbers of digits and making sure the result is always correct. If it's not there's clearly a problem somewhere.
Earlier quoted context omitted.
The article title says "powers of π", so presumably an arbitrary digit.
Iβm not sure thatβs right. The abstract and text say the nth digit of \pi^n, and the worked example on page 2 uses the same n=1000 to find the thousandth digit of \pi^{1000}.