Path: csiph.com!news.mixmin.net!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail From: Ben Bacarisse Newsgroups: comp.programming Subject: Re: Another little puzzle Date: Sun, 25 Dec 2022 01:55:35 +0000 Organization: A noiseless patient Spider Lines: 26 Message-ID: <875ye0p7qg.fsf@bsb.me.uk> References: <86pmcczcak.fsf@linuxsc.com> <87wn6krsc5.fsf@bsb.me.uk> <868riwzxu3.fsf@linuxsc.com> <875ye0qvs0.fsf@bsb.me.uk> MIME-Version: 1.0 Content-Type: text/plain Injection-Info: reader01.eternal-september.org; posting-host="7ed47a7083f99d1bb1c39d5dcca97764"; logging-data="2542400"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/E3B4WKKvebausou1+uhNu1MMAkujsMj4=" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/27.1 (gnu/linux) Cancel-Lock: sha1:rD5wwHN8UCxAMTiAgAHLocbytbQ= sha1:q0GfJAzUiSOpMnSH1tkLml4u25o= X-BSB-Auth: 1.61009983c026fbc6ca79.20221225015535GMT.875ye0p7qg.fsf@bsb.me.uk Xref: csiph.com comp.programming:16148 Mike Terry writes: > ... But actually the balancing line idea wasn't my proper thinking - > that was that we "counter-balanced" the circle by adding a new weight > somewhere on the circle. There is a unique such place where such a > weight can go, and a unique weight that works. Or just find the point in the (weightless) disc where it balances. That's the vector average. > The "average" for the > x_i is then directly OPPOSITE the counter weight. This is all > assuming we don't start with an exactly balancing sample! > The mass of > the counter-weight is the magnitude of your vector sum, indicating the > "strength" of the average... The distance from the centre is then a measure of the strength of the average. I like the physical metaphor of a balanced disc, but I prefer the idea of finding the balance point directly rather than the mass and location (on the circumference) of a counterweight. -- Ben.