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Though mathematics is not my forte I found your artical interesting. As a Forester I was drawn to your the title of your book "The mystry of five in nature". My mind went to the biology term- 'Contact Parastikeits' (spelling may be off) which follows Fibonaccis sequence 1,1,2,3,5,8... Have you found the "Mystery" to follow this sequence?
Dave Peckham