I find maths work a lot easier if I use the printed course books rather than the pdf versions, so for the past few weeks I’ve been eagerly awaiting the delivery of my MS221 materials. However, last night I finally snapped and printed out the first two sections of Chapter A1 from the pdf copy, and today I’ve been working my way through Section 1, which is about the golden ratio.

It’s been fantastic so far – a really fascinating topic, and a very compelling start to the course. The golden ratio is introduced through a rectangle problem:

**The Rectangle Problem**

Suppose that a rectangle has a square removed from one end, leaving a rectangle the same shape as the original rectangle. What is the ratio of the lengths of the sides of the original rectangle?

My homemade (and thus not exactly to scale!) diagram of a golden rectangle

The first activity involved trying to estimate the ratio by working out the ratio of rectangles with a shorter side of length 1 and a longer side of various lengths between 1.5 and 2. It was wonderful feeling, getting closer and closer to an accurate value for the ratio, even though of course we had already been told the actual value – I think it was enjoyable anyway, just because it gave me a sense of how mathematical discoveries might have felt when they were originally made; the pleasure of finding a pattern and confirming it with experiments, I guess!

After that, we moved on to using algebra to solve the problem, and I’m pleased to say that I managed to do the activities involving the quadratic equation formula and rationalising the denominator without too much trouble. I’m not sure whether it’s just because I’m a more ~~aged~~ seasoned OU student now, but I’m having a much easier time with MS221 so far than I did with the previous maths course, MST121, which I took in 2006. And I’m certainly finding it more interesting than M366, which is quite reassuring, considering how many maths courses I’m planning to take in the next few years!

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