# Clandestine Maths Club: cosines and sequence alignment

15 January 2012, by

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So another week, and more exciting maths formulae posted up on the Softwire whiteboards.

Luckily, I’ve managed to unearth one of the members of clandestine maths club; the lovely Kenny Hung, so I got him to explain some of the latest puzzles to me. No-one else has yet come forward.

“This first one is an attempt to prove the thing in the top two lines (whenever Θ is between 0 and Π/2 and p is between 0 and 1, then cos(Θ)p ≤ cos(pΘ)). I was responsible for posing the question, from my first year at uni, as it popped into my head one day and it was bugging me.

The middle section was an attempt using differentiation (which turned out to be a correct way forward), and the bottom bit is using a bunch of complex analysis doing the same thing.”

“The second one is a run of a sequence alignment algorithm – an algorithm that calculates the minimum number of gaps to introduce into two lists such that for any index where both lists have a non-gap element, the elements are the same.”

I’ll leave the mathematicians amongst you to double check our sums, and I’ll try and find out from Kenny before my next post exactly why the maths club find this such a relaxing way to break from programming!

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