OK, this one is going to be short, because quite honestly I cannot follow the proof in detail at all. Either I don’t have the required continued fraction mathematics, or I can’t follow advanced calculus proofs any more. Probably option C: all of the above. For a quick refresh of what continued fractions are, see here and here. […]
READ MOREThe ancient Greeks (and pretty much everyone in the art world from the Renaissance onwards) were kind of fascinated with the golden ratio, or φ (phi). To see why it might be seen as interesting, let’s take a look at a geometric view of the golden ratio. Consider a rectangle: the sides of this rectangle are in the golden ratio if you can subtract a square based on the shorter side and are left with another smaller rectangle which is also in the golden ratio. Inception! […]
READ MOREBack in my days at Kings College, there was a movement to try and make sure that we mathematics students could write. There was a general worry that because we expressed ourselves tersely and symbolically in the language of mathematics we would forget how to express ourselves correctly in the language of English. So, while I was there, we had to write two essays, one at the end of our first year and one at the end of the second. The essays should be on a mathematical subject, maybe even with a proof or two, but it had to be preponderantly a narrative. (If you think about it, this is the same worry that developers might not be able to express themselves clearly and concisely to their users, which is why there’s so much emphasis on “written and verbal communication” in job descriptions.) […]
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