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First 2010 batch

posted Mar 2, 2010, 1:07 PM by Eddie Woo   [ updated Mar 2, 2010, 1:32 PM ]
Random files. That's what the site is named for, so here are some more! I've got four for you, and they come from all different places:
  • Parallel lines preserve the ratios of intercepts on transversals (a geometry proof from year 9). I realise it's a bit of a mouthful, but it's a very handy application of similar triangles. It's an incredible time-saver once you come down to it. It's worth noting that this proof requires you to already have established that the interval joining two sides of a triangle parallel to the third side divides the two sides in the same ratio (also a mouthful - that's similar triangles for you).
  • Rule for differentiating powers of x (derivation of a calculus principle from year 11). Though we go all the way from first principles, it's quite a straightforward process and the result is very elegant (which is why it is so easy to remember and use in practice).
  • Tolerance (notes from a workshop delivered to ISCF leaders). We live in a pluralistic age with lots of competing beliefs - religious and secular. I think it's really important that we treat each other with respect even if (especially if) we disagree about what we believe. That's what this workshop was about.
  • The Prodigal Son (manuscript of my talk on Luke 15:11-32). I gave this talk last Friday and (I think) it was generally well received. I rushed through it and didn't quite finish it before the bell went, so you might find the manuscript helpful.
That's all for now! Enjoy.