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Subject: "RE: Never Ending Spiral"     Previous Topic | Next Topic
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Blake Parkins (Guest)
guest
Mar-12-01, 01:43 PM (EST)
 
"RE: Never Ending Spiral"
 
   Hi,

I know little about math so please excuse the ambiguity of this post. I'm looking for the name and information of the phenomenon the describes a spiral that can get smaller and smaller without ending-like a nautilus shell.

I looked through this site and previous posts on the forums, but because I don't know the name of this principal, I was rather limited. Any help you could provide would be greatly appreciated. Thanks. Blake


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alexb
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672 posts
Mar-13-01, 00:29 AM (EST)
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1. "RE: Never Ending Spiral"
In response to message #0
 
   You are talking of what is known as the logarithmic, or equiangular, spiral. It was discovered by Decartes in 1638. You may want to have a look at the https://www.cut-the-knot.com/Curriculum/Geometry/Mirabilis.shtml>Spira Mirabilis page.

The spiral is mentioned in several place. In paticular, I. Stewart explains in "Life's Other Secrets" why Nautilus' shell pattern resembles that spiral. The book makes a wonderful reading.


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Blake Parkins (Guest)
guest
Mar-13-01, 03:44 PM (EST)
 
2. "RE: Never Ending Spiral"
In response to message #1
 
   >You are talking of what is
>known as the logarithmic, or
>equiangular, spiral.

Alex,

Thank you for your help. Math is a field that I don't understand, but I can appreciate your site on some level.

I have seen this spiral illustrated in squares within squares getting infinitely smaller. Could you point me to this represenation of the spiral? Thanks again. Blake


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alexb
Charter Member
672 posts
Mar-13-01, 03:49 PM (EST)
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3. "RE: Never Ending Spiral"
In response to message #2
 
   Have a look into

The Divine Proportion by H. E. Huntley
Dover, 1970

page 66.

This is related to the Golden Ratio and Fibonacci numbers.


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