X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f996b,ef84650dd3e606e5 X-Google-Attributes: gidf996b,public X-Google-ArrivalTime: 2001-09-29 23:42:40 PST Path: archiver1.google.com!news1.google.com!sn-xit-02!supernews.com!news.tele.dk!small.news.tele.dk!130.133.1.3!fu-berlin.de!uni-berlin.de!212.120.170.35!not-for-mail From: grue@mail.ru (Timofei Shatrov) Newsgroups: alt.ascii-art Subject: Re: what is it? Date: Sun, 30 Sep 2001 06:44:37 GMT Lines: 53 Message-ID: <3bb6b68f.9018917@News.CIS.DFN.DE> References: <3BB60DC7.2060108@sdf.lonestar.org> <3BB6163F.6E2BBA44@rz.uni-karlsruhe.de> <3BB624DA.8010902@sdf.lonestar.orgNAYSPAM> NNTP-Posting-Host: 212.120.170.35 X-Trace: fu-berlin.de 1001832158 17693424 212.120.170.35 (16 [101885]) X-Newsreader: Forte Free Agent 1.21/32.243 Xref: archiver1.google.com alt.ascii-art:8191 On Sat, 29 Sep 2001 20:45:30 +0100, Oak3 tried to confuse everyone with this message: > >--------------040607050806000902080208 >Content-Type: text/plain; charset=us-ascii; format=flowed >Content-Transfer-Encoding: 7bit > >very interesting...but, 1 : 1.6180339 is not = 1.6180339 - 1 >One is a ratio, the sum of the other is a decimal >what i find interesting is where the square root of 5 came from? > >I assume its from a theorem that im not familiar which you have employed. >Can you possibly elaborate further.? Phidian number a=(sqrt(5)+1)/2 is the solution of the equation x^2-x-1=0. It has some interesting properties. sqrt - square root. ^ - power 1. It's famous "golden rule" which was used for the first time by Leonardo da Vinci. 2. a^2=a+1, 1/a=a-1 3. 1 a= 1+ ---------- 1 1+ -------- 1 1+ ---- ... 4. a=sqrt(1+sqrt(1+sqrt(...)))) 5. Fibonacci numbers. 1 F(n)= -------*(a^n-(-1/a)^n) sqrt(5) 6. And you can meet it in many other occasions. If you divide height of average human to the height of his legs you'll got Phidian number. -- Grue Mike Throll comic strip at: http://grue.freeservers.com Bugsoft Perm at: http://bugsoft.freeservers.com