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The Golden Ratio has the unique property that its reciprocal always produces the same decimal and the reciprocal of the decimal will always produce the integer 1. This means that the continued fraction can be constructed without bothering with a calculator! The continued fraction uniquely only has 1's in it. This also means that the successive fractions can be generated without consulting the diagram. For each fraction, we add 1 and then flip it over (make the reciprocal) for each new fraction. Thus, the first number is 1, producing the fraction 1/1. That is its own reciprocal. To this is added 1 (1/1), resulting in the fraction 2/1. The reciprocal of that is 1/2, our second fraction. To that is added 1 again (now 2/2), resulting in the fraction 3/2. The reciprocal of that is 2/3, our third fraction. To that is added 1 again (now 3/3), resulting in the fraction 5/3. The reciprocal of that is 3/5, our fourth fraction. As this continues, we might notice that the procedure generates fractions that all consist of successive Fibonacci Numbers! This is why ratios of Fibonacci numbers approximate the Golden Ratio, they are all solutions to the unique continued fraction for the Golden Ratio!
Recall that: the whole is the longer part plus the shorter part; the whole is to the longer part as the longer part is to the shorter part. If we call the whole n and the longer part m, then the second statement above becomes n is to m as m is to n − m,
Did the Greeks Discover the Irrationals? Philip Hugly and Charles Sayward Abstract A popular view is that the great discovery of Pythagoras was that there are irrational numbers, e.g., the positive square root of two. Against this it is argued that mathematics and geometry, together with their applications, do not show that there are irrational numbers or compel assent to that proposition.
Originally posted by Pinkorchid
01001000 01001001 00100000 01000111 01010101 01011001 01010011 00101100 00001101 00001010 01001001 00100000 01001101 01000001 01011001 00100000 01001110 01001111 01010100 00100000 01000010 01000101 00100000 01001001 01001110 00100000 01010100 01001000 01000101 00100000 01001101 01000001 01000111 01001001 01000011 01000001 01001100 00100000 00110001 00110000 00100000 01000010 01010101 01010100 00100000 01001001 00100000 01000011 01000001 01001110 00100000 01010100 01001000 01001001 01001110 01001011 00100000 01001100 01000001 01010100 01000101 01010010 01000001 01001100 01001100 01011001 00100000 01000001 01001110 01000100 00100000 01000010 01001111 01011001 00100000 01001001 01010011 00100000 01010100 01001000 01000101 00100000 01001001 01001110 01010100 01000101 01010010 01001110 01000101 01010100 00100000 01010101 01010011 01000101 01000110 01010101 01001100 01001100 00100000 01001100 01001111 01001100
In the interests of full disclosure here is the link for deciphering above.
home.paulschou.net...
Originally posted by fulllotusqigong
reply to post by deometer
There was no Golden Ratio in Egyptian mathematics. That's an error of Western projection onto a nonwestern culture.
Text
[PDF] Architecture and Mathematics in Ancient Egypt by Corinna Rossi ... www.ircps.org/publications/aestimatio/pdf/.../2005-02-01_Symons.p... File Format: PDF/Adobe Acrobat by S Symons - Related articles Aestimatio 2 (2005) 11--15. Architecture and Mathematics in Ancient Egypt by Corinna Rossi. Cambridge:Cambridge University Press, 2004.Pp. xxii + 280. ISBN ...
Originally posted by Helious
reply to post by ErroneousDylan
An excellent thread my friend, that I may add was posted in the perfect forum for the subject matter so don't worry about one or two people who refuse to open there mind to possibilities. I found it to be thought provoking, well written and really quite honestly beautiful.
I find the way the universe works when described by math and geometry to be astounding and this thread for me was a brilliant read, thanks again for sharing.
Originally posted by karen61057
reply to post by ErroneousDylan
The pentagram was only made an evil symbol in the 20th century. Before that it was always a symbol of protection and was not associated with evil.
I think the first Wolfman movies from the 40's with Lon Chaney was were the pentagram enclosed within a circle making it a pentical was first associated with evil in the minds of the American public. It was the mark of the werewolf or the mark of the beast according to the Gypsy queen.
Originally posted by AfterInfinity
reply to post by ErroneousDylan
In order to express divinity through mathematics, we assume that we have the mathematical understanding to both invent and incorporate such concepts on an algorithmic or equational structure...
And the truth is, we simply don't have that broad of an understanding in mathematics yet. The sheer infinite nature of what we're trying to express, in and of itself, indicates that we don't have the number of factors necessary to even partially express the divinity...
And if we do, it will always be incomplete.
Originally posted by fulllotusqigong
reply to post by Morpheas
Yep -- you mean Corrina Rossi isn't correct?
You better read her book like I have done. Yeah sorry to burst your CIA mind controlled bubble.
Originally posted by fulllotusqigong
reply to post by Morpheas
Her book is online as a pdf.
Here you go. Pdf of a book on Egyptian mathematics disproving they use the Golden Ratio -- read it and weep.
First of all, it is essential to mention that there is no direct evidence in any ancient Egyptian written mathematical source of any arithmetic calculation or geometrical construction which could be classified as the Golden Section….It might even be suggested that they would not have liked the concept of the convergence to a number they could not reach, since the mathematical sources seem to indicate that the Egyptians were particularly fond of completion to the unity.509
The Golden Section - the Number and Its Geometry www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phi.html Jump to What is the Golden Ratio (or Phi)?: What is the golden section (or Phi)? Also called the golden ratio or the golden mean, what is the value of the ..
Originally posted by ErroneousDylan
reply to post by fulllotusqigong
No no, sir. You are misinterpreting what I have said. I only stated the "3:2 or 2:3" to cover in case I had written it like that previously. You could make a ratio of Venus Day / Earth Year and create any order you want in it. VenusDay:EarthYear or EarthYear:VenusDay. It just so happens that if you order it in one way it is "3:2". I am well aware that a perfect fifth is 3:2 and not 2:3.
no direct evidence in any ancient Egyptian written mathematical source
Originally posted by fulllotusqigong
You have stated it can be either 2:3 or 3:2 and I am saying that your declaration of such is admittance that you are using the Golden Ratio aka the Fibonacci Series. You have then stated you are aware that the Perfect Fifth is 3:2 and not 2:3 and I am saying you are wrong -- the Perfect Fifth is non-commutative which means that for 2/3 is it C to F and for 3/2 is it C to G.
Architecture and Mathematics in Ancient Egypt - Google Books Result books.google.com/books?isbn=0521829542...Corinna Rossi - 2004 - Architecture - 280 pages Finally. let us go back to the problem of 4i and the Golden Section. First of all. it is essential to mention that there is no direct evidence in any ancient Egyptian written mathematical source of any arithmetic calculation or geometrical construction which could be classified as the Golden Section.