Path: csiph.com!eternal-september.org!feeder.eternal-september.org!nntp.eternal-september.org!.POSTED!not-for-mail From: Tim Rentsch Newsgroups: comp.arch Subject: Re: IA-64 Date: Mon, 23 Mar 2026 21:01:15 -0700 Organization: A noiseless patient Spider Lines: 65 Message-ID: <86qzp95110.fsf@linuxsc.com> References: <10n6ts2$3fjht$1@dont-email.me> <10o9s6b$34qug$1@dont-email.me> <20260304202556.000063d9@yahoo.com> <10oa6tk$38csm$1@dont-email.me> <10onere$3o39t$1@dont-email.me> <86pl5874op.fsf@linuxsc.com> <10p3uoo$bka8$2@dont-email.me> <86y0js6bit.fsf@linuxsc.com> <10p94fc$227s2$1@dont-email.me> <86zf454lds.fsf@linuxsc.com> <10pekdm$hjr$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Injection-Date: Tue, 24 Mar 2026 04:01:18 +0000 (UTC) Injection-Info: dont-email.me; posting-host="49275a8acb80bae5953bf00d88b0bbe4"; logging-data="774486"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18VB0bqVR9DnAaxaPtWKcYbV0SOjNeY/P8=" User-Agent: Gnus/5.11 (Gnus v5.11) Emacs/22.4 (gnu/linux) Cancel-Lock: sha1:wf7YTrmc2ocQflwlZj5K2EXwyL4= sha1:NnDTLDZBjNnBkMmXKa5+qRKqc7w= Xref: csiph.com comp.arch:115530 Terje Mathisen writes: > Tim Rentsch wrote: > >> Terje Mathisen writes: >> >>> Tim Rentsch wrote: >> >> [...] >> >>>> An unrelated item for your reading pleasure... >>>> >>>> Take an unbiased coin and start flipping it. Keep flipping until >>>> the number of heads first exceeds the number of tails. Compute the >>>> fraction: the number of heads divided by the number of flips (which >>>> always gives a number between 0.5 and 1.0). >>>> >>>> Repeat the above process as many times as desired. Compute the >>>> average of all the fractions and what do you get? >>>> >>>> I heard about this yesterday from a friend. That's a hint, of >>>> sorts. (It is now Sunday afternoon where I am.) >>> >>> So, by definition the list of possible sequences start with >>> H ; 1/2 of all >>> THH ; 1/8 >>> TTHHH ; 1/32 >>> THTHH ; 1/32 Sum up to here is 22/32 >>> TTTHHHH ; 1/128 >>> TTHTHHH >>> TTHHTHH >>> THTTHHH >>> THTHTHH >>> etc >>> >>> Here's a wild-assed guess: sqrt(0.5) = 0.707 >> >> That's an interesting idea for how to analyze it. I'm not sure it >> works. One thing I can say for sure is when I tried to replicate it >> in a program I got wrong answers, or maybe it converges very slowly. >> An easy way to get a result that matches the theoretical value is >> just to simulate the coin flips using a random number generator. To >> save you the trouble of doing that the ultimate value is pi/4 (and >> it converges VERY slowly). > > So related to calculating pi by picking two random numbers and use > them as coordinates into a [0..1 x 0..1] square. If that's true I don't see how or why it's true. I haven't tried to understand the derivation I was given earlier. > pi/4 =~ 0.78539816, so a bit larger than my wild-assed guess. :-) I thought your guess was pretty reasonable. I didn't have an opportunity to make a guess because I knew the answer before I understood the method. >> Incidentally, the hint mentioned above is that I heard about it on >> pi day, March 14th. :) > > I did not grok that hint. :-( Definitely a very subtle hint. I didn't really expect anyone to get it, but I wanted to at least give an opportunity. And I've been surprised before by how smart some netizens are.