It’s the (slightly delayed) monthly chat between @reflectivemaths (Dave Gale) and me on whatever maths has caught our eyes.

This month:

  • Why protractors and set squares? You can find centres of rotation.
  • Why constructions? Colin launches an impassioned defence and compares them to Killer Sudoku
  • Dave has some great ideas for improving the Mathematical Instruments package, while Colin wants to shake up the calculator industry
  • Exams: do you deserve full marks for a lucky guess? Neither of us think so, but the GCSE disagrees. Outrage ensues, before Dave suggests not ranting about exams yet again.
  • Dave goes shopping for horse-balls but only finds confusingly-priced pizza [link]. We fail to discuss the density of prawns. Colin suggests the reason is ‘economics’. Dave brushes this off. Dave is unhappy about the convention in some puzzles that A=1, B=2 and so on ((which I’m not going to typeset in LaTeX because it’s NOT ALGEBRA)) but Colin thinks he’s being oversensitive.
  • Stephen Hawking lets the side down with a Perfect Formula. Even for charity, even with some actual statistics behind it, that’s a case for the Maths Police.
  • Dave interrupts the football commentary with a super-relevant query: is half a million chickens a lot to rehome ((Possibly on the other side of the street.)) ?
  • Colin’s reading: Dead Reckoning by Ronald Doerfler, which has inspired him to try to do 1/97 in his head (it’s 0.010309278350515463… - he could go on, but your calculator couldn’t.)
  • The World Cup seeding system: how England, Holland and Italy managed to fall foul of it by picking silly friendly opponents.
  • Dave interrupts the football commentary again to explain that that last month’s answer was $\frac{5}{11}$; gold stars to @srcav and @notonlyahatrack
  • This month’s World Cup puzzle:

    How many possible World Cup tournaments are there? There are 32 teams in eight round-robin groups (each with six games, each of which has three possible results) and 16 knock-out games (each with two possible results). We’re not interested in the actual number: just how many digits long it is.

  • Colin doesn’t understand Graham’s Number and isn’t really sure how to say ‘Knuth’

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* Updated 2014-09-21 to fix a link.