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Subject: "Golden Ratio in Algebra"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #398
Reading Topic #398
janco
Member since Sep-1-10
 Sep-01-10, 01:06 PM (EST)
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"Golden Ratio in Algebra"
 
   Looking to find original article referenced in CTK entitled "Golden Bounds for the Roots of Quadratic Equations". Supposedly published by the Math Gazette, v 91, n522, Nov 2007; and, other detailed algebraic discussions of phi.


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  Subject     Author     Message Date     ID  
Golden Ratio in Algebra janco Sep-01-10 TOP
  RE: Golden Ratio in Algebra alexb Sep-01-10 2
     RE: Golden Ratio in Algebra janco Sep-01-10 3
         RE: Golden Ratio in Algebra alexb Sep-01-10 4
             RE: Golden Ratio in Algebra Janco Sep-01-10 5
                 RE: Golden Ratio in Algebra alexb Sep-01-10 6
                     RE: Golden Ratio in Algebra janco Sep-13-10 7
                         RE: Golden Ratio in Algebra alexb Sep-13-10 8
  RE: Golden Ratio in Algebra alexb Sep-13-10 9
  RE: Golden Ratio in Algebra mr_homm Sep-13-10 10
     RE: Golden Ratio in Algebra C Reineke Sep-14-10 11
         RE: Golden Ratio in Algebra mr_homm Sep-14-10 12

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alexb
Charter Member
2602 posts		 Sep-01-10, 01:19 PM (EST)
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2. "RE: Golden Ratio in Algebra"
In response to message #0
 
   >Looking to find original article referenced in CTK entitled
>"Golden Bounds for the Roots of Quadratic Equations".
Have you looked into Math Gazette, v 91, n522, Nov 2007?

>Supposedly published by the Math Gazette, v 91, n522, Nov
>2007;

Was there a misprint in my reference?

> and, other detailed algebraic discussions of phi.

Should you find any, I would be grateful if you let me know.

L. McMullin is a devotee of the Golden Ratio. If anybody knows anything, he does. Check https://www.linmcmullin.net/CAS.html



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janco
Member since Sep-1-10
 Sep-01-10, 04:45 PM (EST)
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3. "RE: Golden Ratio in Algebra"
In response to message #2
 
  


I could not find the Math Gazette v 91 n 522 Nov 2007, and also tried to find article separately to no avail.


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alexb
Charter Member
2602 posts		 Sep-01-10, 04:47 PM (EST)
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4. "RE: Golden Ratio in Algebra"
In response to message #3
 
   > I could not find the Math Gazette v 91 n 522 Nov 2007, and also tried to find article separately to no avail.

Do you mean to say that the reference is incorrect?


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Janco
guest
 Sep-01-10, 10:37 PM (EST)
 
5. "RE: Golden Ratio in Algebra"
In response to message #4
 
   yes, the reference appears to be incorrect


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alexb
Charter Member
2602 posts		 Sep-01-10, 10:40 PM (EST)
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6. "RE: Golden Ratio in Algebra"
In response to message #5
 
   >yes, the reference appears to be incorrect

Now I got it. I'll check it at the first opportunity. Probably within a few days. I'll report the result here.


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janco
Member since Sep-1-10
 Sep-13-10, 10:04 AM (EST)
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7. "RE: Golden Ratio in Algebra"
In response to message #6
 
   any luck with the original reference?


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alexb
Charter Member
2602 posts		 Sep-13-10, 10:06 AM (EST)
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8. "RE: Golden Ratio in Algebra"
In response to message #7
 
   The nearest place where I have access to the Math Gazette is Rutgers U., whose library has been closed for the first two weeks of September.


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alexb
Charter Member
2602 posts		 Sep-13-10, 04:37 PM (EST)
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9. "RE: Golden Ratio in Algebra"
In response to message #0
 
   I am just back from the library. The reference is correct.


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mr_homm
Member since May-22-05
 Sep-13-10, 06:21 PM (EST)
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10. "RE: Golden Ratio in Algebra"
In response to message #0
 
   Perhaps you might like this as well; I wrote it a few years ago. It is not the highest quality exposition you'll ever see (in my opinion), but the results are pleasing, I think.

https://home.comcast.net/~stuartmanderson/fibonacci.pdf


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C Reineke
Member since Jul-9-10
 Sep-14-10, 08:27 AM (EST)
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11. "RE: Golden Ratio in Algebra"
In response to message #10
 
   Ok, then I dare to post a German source again:

https://www.mathe-seiten.de/fibonacci.pdf


Kind regards

Chris


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mr_homm
Member since May-22-05
 Sep-14-10, 10:26 PM (EST)
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12. "RE: Golden Ratio in Algebra"
In response to message #11
 
   Thank you! I do not read German without a dictionary at hand, but I follow the mathematics of course, and the figures are quite enjoyable. I see that the figure in my short note is found on page 31, and it looks as if it was produced with GnuPlot, just as mine was (I think I recognize the formatting quirks).

I found that result many years ago when playing with the Fibonacci series, and finally got around to writing it up a few years back. I also found a nice recursion which produces high Fibonacci numbers from much lower ones. If I can find it among my old papers, I'll post it. Of course, I assume it is well-known, but I haven't seen it anywhere.

--Stuart Anderson


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