The Golden Ratio
I'm behind on putting together my notes for some of the books that I've recently read. One that I finished not long ago was �The Golden Ratio: The Story of Phi. The World's Most Astonishing Number.� by Mario Livio. This book held a special interest as it is part of what makes NeoPhi what it is. I've always had a love of math and incorporating that into my domain name just seemed like a nice tie in, besides it just sounds good.
Unlike a lot of other books I've read lately, the author wasn't pushing a point of view as much as summarizing all that is currently known about the number. He does spend time discrediting various theories about where phi was used. For example the pyramids are not influenced by phi. I think you have to have some interest in math to really enjoy the book even though is it approachable to a general audience.
Below are some usually paraphrased references from the book that I think are worth mentioning:
[2] pi is the best known special number.
[3-4] Given a line AB with a point C between AB, if the ratio between AC/CB is equal to AB/AC, then the line has been cut into the Golden Ratio.
[4] This ratio is 1.6180339887...
[5] The discovery that some numbers are irrational caused some mathematics to build tombs for those making the discoveries, as if they were already dead.
[12] It isn't known if the cardinal numbers: one, two, three, ... preceded the ordinal numbers: first, second, third...
[13] The concept that two hands and two nights are both manifestations of the number two, took centuries for humans to grasp.
[14] Many early languages exhibit the counting/labeling of one, two, three, four, many. Most don't go beyond unique names for four. One theory is that four is the maximum that a human can quickly �see� without counting.
[18] Modern numerics are based around a place-value system first invented by the Babylonians.
[22] Numerology. Modern day example is the Y2K scare.
[33] Perfect numbers are equal to the sum of their divisors. 6=1+2+3, 28=1+2+4+7+14.