Hi profpat, thanks for taking the time to read me theory. While
www.threes.com is a great website for all things three, it isn't actually my site, it's run by someone called Micheal Eck in the USA.
In paragraph 6, I mention the golden mean which is the dividing line between two opposites. I have never really thought about the pythagorean triad that you mentioned in the link, but it is similar to what I wrote. Notice that in that link it says, 'the Triad was considered by the Pythagoreans as the most beautiful number, as it is the only number to equal the sum of all the terms below it, and the only number whose sum with those below equals their product'. I think that shows that 3 was noticed all those years ago. I guess you could say that it is the same in the fact that there is an overlap (the golden mean) where all opposites join. If they are opposite (extremes), then they must both have a golden mean, something in common that they are both extreme from, if you get me.
Thanks for the link to wikipedia triads. I haven't come across some of them before but I have come across Becks' cognitive triad as I'm a psychology student at university and it makes sense.