.....the nature of mathematical truth.....I did come across some ideas on 'Phi' the 'Divine Ratio' when working for my rationalised value for Pi. Please see: http://www.the-light.com/cal/bbv_pi-radian.jpg
Phi - the golden ratio for 'regular decagon' is linked to Fibonacci series via the *quadratic equation: k^2 - k -1 =0 that give the value (k =phi =[1 +/- (sqrt 5)]/2 to give k =1.61803398874 &
(minus 0.61803398874). The negative value is ignored, since two positive quantities (radius & chord length) do not result in negative.
I palced some working of this value at pages 221-222; of my book - Towards A Unified Technology (1982). And I add:
"As a corollary, it can be stated that the ratio between the circumference of a circle to the inscribed 'chord length of the decagon' is 10.166437494..... Also, Pi * phi =5.08320187469 and pi/phi = 1.94116106507".
I am still searching, myself as to: WHY I attempted these calculations? I NEVER thought of Phi later - especially after I kept my 'Metric Time/Calendar Year' calculations over the shelf for gestation.
Brij Bhushan Vij <[EMAIL PROTECTED]>
20050305H2094(decimal) PM(IST)
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda.
*****The New Calendar Rhyme*****
Thirty days in July, September:
April, June, November, December;
All the rest have thirty-one; accepting February alone:
Which hath but twenty-nine, to be (in) fine;
Till leap year gives the whole week READY:
Is it not time to MODIFY or change to make it perennial, Oh Daddy!
And make the calendar work with Leap Week Rule! ***** ***** ***** *****
From: "ewc" <[EMAIL PROTECTED]> Reply-To: "ewc" <[EMAIL PROTECTED]> To: "U.S. Metric Association" <[email protected]> Subject: [USMA:32376] Re:Phi (l) Date: Sat, 5 Mar 2005 09:07:53 -0000
Hi Stephen (Humphreys)
I kind of get the impression Phil is looking for more of a hard ball game - but I will let things run a while - maybe get in a bit of net practice first.
Has anyone on other groups you are a member of ever pointed out that 'metric' has a parallel etymological development in both Greek and Sanskrit - and thus must go back to some 'Indo-European' root far back in prehistory. Or that, in addition to this, our best guess as to what that root word is is something like 'menes' - that is to say the moon, (and of course the measurement of calendars and tides etc.).
Of course this means, in literal terms, that all users of metric systems are lunatics
best regards
rob
PS (see 'The Origins of Metrology' D M Macdonald, Cambridge 1992, p 4 ff)
PPS Am much amused to see Phil discussing the nature of mathematical truth when he does not appear to have heard of Quine's NF.
http://www.wvquine.org
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