I'm just feeling generally quite pleased with myself, since it's a long time since I did any decent maths, and even longer since I actually came up with something "original" (I say that because it's original to me, but I suppose others might know it).

Effectively, it's a series of numbers between 1 and 2 that includes the golden ratio, and is discovered by solving increasingly lengthy polynomial expressions (or cheating with spreadsheets). B

_{1}is 1, B

_{2}is the golden ratio, and B

_{∞}is 2. The properties of the golden ratio are present in all the numbers, to varying extents and with various modifications - for example, the Fibonacci recurrence still applies, but Q

^{n+1}is equal to different combinations of lower powers. The numbers probably show up much less in nature, I'm sure, but it would be interesting to see if there are any examples of them around..

Anyway, details would probably get boring, but suffice it to say, I had a lot of fun finding these numbers, and they make a lot of nice elegant sense :o)