X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 107c0a,299d0bc3500e024c X-Google-Attributes: gid107c0a,public X-Google-Thread: 10ffde,299d0bc3500e024c X-Google-Attributes: gid10ffde,public X-Google-Thread: 109d8a,535e80416e502a8c X-Google-Attributes: gid109d8a,public X-Google-Thread: f4886,dbda22a9ac78d3f2 X-Google-Attributes: gidf4886,public X-Google-Thread: f996b,535e80416e502a8c X-Google-Attributes: gidf996b,public X-Google-ArrivalTime: 1994-08-05 12:41:56 PST Newsgroups: sci.bio,alt.sci.physics.plutonium,sci.chem,alt.ascii-art,sci.math Path: bga.com!news.sprintlink.net!hookup!yeshua.marcam.com!zip.eecs.umich.edu!newsxfer.itd.umich.edu!ncar!uchinews!prospero.bsd.uchicago.edu!greyshadow From: Rudrik Greyshadow Subject: Re: PARASITES INSIDE OF VIRUSES? Message-ID: <1994Aug5.190816.27554@midway.uchicago.edu> X-Xxmessage-Id: X-Xxdate: Fri, 5 Aug 1994 13:32:10 GMT Sender: news@uchinews.uchicago.edu (News System) Organization: Sword Dale, Lord Mayor X-Newsreader: Nuntius Version 1.3d3 References: <31e91i$5fk@dartvax.dartmouth.edu> Date: Fri, 5 Aug 1994 19:08:16 GMT Lines: 70 Xref: bga.com sci.bio:4955 sci.chem:7564 alt.ascii-art:10894 sci.math:17561 Felix Lee, ponders the complexities of the golden rect.: > The golden ratio (tau) is (1 + sqrt(5))/2, which is approximately > 1.618. This number has the property that > tau / 1 = (tau + 1) / tau > And it's the only real number with that property. Note this relationship can also be expressed as: tau-1 = 1/tau and 1/(tau-1)=tau and tau^2 = tau+1 [snip snip] > > A golden rectangle is a rectangle where the ratio between the lengths > of the two sides is tau. Like so: > ___________________________________________ > | tau : 1 | > | : | > | : | > | : | > | : | > | : | > | tau : | > | : | > | : | > | : | > | : | > | : | > |________________________:________________| > > The top has a length of (tau + 1), and the side has a length of tau, > giving a ratio of (tau + 1) / tau = tau. [deleted] as you can see by looking at the ratio of its sides. The smaller > rectangle has the same shape as the whole rectangle. You can't fool me: all rectangles have the same "shape" ;-) The important thing is the ratio of the sides (Ie. Length/Width = tau) remains constant for each new rect. created when you "remove" perfect :) squares from the figure. ___________________________________________ | 1 : (tau - 1) | L/W = tau/1 = tau | : | | : | Next iterations: | : | | : (tau - 1) | L/W = 1/(tau-1) = tau | : | | 1 : | L/W = (tau-1)/(2-tau)=tau | : | | :................| L/W = (2-tau)/(2tau-3)=tau | : | | : (2 - tau) | etc.... | : | |________________________:________________| > Classical art and ancient Greek architecture uses the golden ratio > pretty often. The golden rectangle is supposed to be the most > aesthetically pleasing rectangle....... OK put in the Disney Classic "Donald Duck in Mathemagic Land" and voila... I new I had heard this stuff before. :) -- Greyshadow