So one of my guilty pleasures is doing Stuff’s two daily trivia quizzes.  That and crossword puzzles.  And…well you probably don’t want to hear about the other ones…  (Ed. Thanks).  Now Stuff has started up a new quiz called Three Strikes.  In this one you get six or seven things that need to be arranged in some order and three tries to see if you can get it right.  Yesterday they did the planets in order from the sun (nailed it). But today, well, here comes some geography: arrange these countries from largest to smallest according to their geographic size:

Okay – so I can either go on gut feeling here and have a go or, can I use some maps to help?  Let’s start here:

This is a world map with the countries in question outlined in black. (Ed: Oh, I see what’s going on here…this is just another excuse for you to talk about map projections, isn’t it.  ISN’T IT!)  Going by this, I might form my preliminary guesses – I’ll clearly go with Russia first (it’s massive!), then Canada, the US (tough call there), China, Australia, Brazil (another tough call) and finally India.  But wait, I’ve got to be a bit careful using this, as a closer look should draw my attention to the distortions in the map – one need only look at Antarctica to see that it might be overestimating its size and extent a wee bit.

That’s down to the map projection, Mercator in this case.  It’s well known that Mercator projections distort the shape and size of land masses as you get closer to the poles.  So Russia, Canada and the US appear larger than they actually are in a relative sense, but their shapes are roughly preserved.  For the record, the map above uses the WGS 1984 Web Mercator (auxiliary sphere) projection – it is a conformal projection meaning that it preserves direction (which makes Mercator great for navigation) and the shape of features but distorts distance and area.  All map projections distort one or more of area, distance, angle or shape – which one we choose to use depends on what we’re willing to sacrifice.  Can I do something to improve this map?

Mais oui, cher lecteur!  I could change the map projection to one that preserves relative area, such as the cylindrical equal area projection.  Here’s what that one looks like:

(The projection was changed by right-clicking the map name, going to Properties > Coordinate System and searching for “cylindrical equal area”)

As we can see, in the process of preserving area we have sacrificed shape and I wouldn’t trust distance measurements unless I was maybe making them east-west.  But at least I’m a bit more confident that the relative areas are more correct.  I’m pretty clear on my smallest country (India), still unclear between Brazil and Australia.  Russia’s the largest and it’s a tight battle between Canada, the US and China.  Any other projections to play with?

That’s a pretty wild one – it’s the Adams Square II conformal (area preserving) projection.  Going by this one, well Australia looks bigger than Brazil now, Russia still leads and I’m going to edge Canada out a bit over the US.  But the more I do this, the more hopeless it feels – I’m not sure I’m ever going to get a clear answer so… (some nice maps on that page, by the way.  And please note that this is one of the few times I might say that a table of data is more effective than a map of those same data.)

In the spirit of I don’t know what, I actually chose to not cheat, and guess what.  I struck out.  Three times.  Didn’t even get close.  But it was fun.  Spoiler alert: here is the correct order:

And for the record (all areas in km2):

  • Russia: 17,098,246
  • Canada: 9,984,670
  • China: 9,596,961
  • United States: 9,525,067*
  • Brazil: 8,515,767
  • Australia: 7,692,024
  • India: 3,287,263

*This appears to be the value for the contiguous US.  If we include Alaska and Hawaii it’s 9,833,517, so really should be above China

Yes, this was just an excuse for me to talk about map projections, but can you blame me? Thanks Stuff!