tag:blogger.com,1999:blog-7316540411043272154.post4231334729609935078..comments2023-10-15T06:49:44.736-04:00Comments on The Paolo Review of Books: The Golden RatioPaolohttp://www.blogger.com/profile/11418352985678394660noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-7316540411043272154.post-40181168296856493792007-05-03T10:31:00.000-04:002007-05-03T10:31:00.000-04:00You might be right, Pythagoras and his disciples f...You might be right, Pythagoras and his disciples focused much of their attention on rational numbers so it is difficult to understand their relationship with phi. <BR/><BR/>Pythagoras believed that infinity was a force for destruction in the universe and that mathematics was a war between the finite and the infinite so for him the whole numbers were the purest of numbers, I suppose 1 being the purest of numbers or the farthest from infinite. So you can begin to understand why he would be averse to irrational numbers. <BR/><BR/>The pentagram was the symbol of his society which of course exemplifies the golden ratio in that in any given straight line, the intersecting section is in the proportion of phi to the larger section of that line so he was obviously somewhat obsessed by the concept.<BR/><BR/>The more you read about the golden ratio the more it boggles the mind such as the relationship between phi and fractals.<BR/><BR/>Thanks for the links, it is a fascinating subject.<BR/><BR/>:)Paolohttps://www.blogger.com/profile/11418352985678394660noreply@blogger.comtag:blogger.com,1999:blog-7316540411043272154.post-50102579430326653542007-05-03T04:45:00.000-04:002007-05-03T04:45:00.000-04:00I didn't know that about the proportion of drones ...I didn't know that about the proportion of drones to bees in a beehive. The Wikipedia article on <A HREF="http://en.wikipedia.org/wiki/Fibonacci_number#The_bee_ancestry_code" REL="nofollow">Fibonacci numbers</A> explains it however. Phi and the Fibonaccis are intimately connected.<BR/><BR/><A HREF="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat2.html" REL="nofollow">Ron Knott</A> at Surrey has what look like some excellent pages on Fibonaccis and Phi in nature.<BR/><BR/><I>Why does nature like using Phi in so many plants? <BR/><BR/>The answer lies in packings - the best arrangement of objects to minimise wasted space.</I><BR/><BR/>Was it the golden ratio or the existence of irrational numbers that spooked Pythagoras? Well Phi is an irrational number anyway, of course.<BR/><BR/>Nice blog post Paolo:)gary thomsonhttps://www.blogger.com/profile/02613549834877401345noreply@blogger.com