### Question I Stumbled Across

Posted:

**Wed Jul 04, 2018 9:25 pm UTC**So, I’m working through the SICP book (which is really good) to refresh my scheme knowledge. The math behind one of the exercises confused me though — while the math I have to do to solve the problem is pretty trivial (it took me <5 minutes), I’m really confused as to where this came from. It’s got to do with calculating Fibonacci numbers in logarithmic, as opposed to linear time. Here’s the text of the exercise:

I understand the math, but I have no idea where it comes from. It’s pretty obvious that the transformations a <- a + b and b <- a are a case of Tpq, but where does that come from? The initial transformations could be a case of a whole load of different transformation families. Where does the specific one in the text come from, and why does it work? Couldn’t there be some other family of transformations that works?

I’m really not much of a math guy — I’ve had some college calculus, but no linear algebra or anything ‘beyond’ that in a standard curriculum.

Thanks!

**Spoiler:**

I understand the math, but I have no idea where it comes from. It’s pretty obvious that the transformations a <- a + b and b <- a are a case of Tpq, but where does that come from? The initial transformations could be a case of a whole load of different transformation families. Where does the specific one in the text come from, and why does it work? Couldn’t there be some other family of transformations that works?

I’m really not much of a math guy — I’ve had some college calculus, but no linear algebra or anything ‘beyond’ that in a standard curriculum.

Thanks!