A geography dozen

Over the past year or so, I’ve been cobbling together a C++ program that holds information about various geography topics. It’s far from complete, but here’s a dozen of fun facts I’ve discovered with its help:

1. Which triple of capitals forms the closest thing to an equilateral (spherical) triangle?
   {Dodoma, Tanzania - Brasilia, Brazil - Reykjavik, Iceland}.
   Indeed, the ratio between the shortest and longest sides of this triangle is an impressive 0.9985.

2. What about a quadruple forming a regular tetrahedron?
   {Belmopan, Belize - Ulan Baator, Mongolia - Windhoek, Namibia - Wellington, New Zealand} with a ratio of 0.9356.

3. Which pair of neighbours have the closest areas?
   {Lithuania - Latvia} with a ratio of 1.01148.

4. Which pair of neighbours have the closest populations?
   {Turkey - Iran} with a ratio of 1.0006, although that might have changed by now.

5. What’s the longest sequence of neighbouring countries with increasing area?
   It turns out there’s a couple of 9-lengthers, but my personal favourite is
   {Kosovo - Montenegro - Bosnia - Croatia - Serbia - Hungary - Romania - Ukraine - Russia}.
   Incidentally, this is the question that originally inspired me to begin this project.

6. What about increasing population?
   This time there’s a seemingly unique length 11 sequence, which curiously starts from the same patch of Europe:
   {Montenegro - Kosovo - Macedonia - Bulgaria - Serbia - Hungary - Romania - Ukraine - Russia - China - India}.

7. How many countries are winners, in the sense they are (nonvacuously) larger in area than all their neighbours?
   16, the smallest of which is the Dominican Republic.

8. What about the losers?
   54, the largest of which is Mongolia.

9. Which country has the most neighbours that are larger in area than itself?
   It’s a two-way tie between Slovakia and Zambia, at 5 apiece.

10. Start with a pair of countries and find the shortest sequence of neighbouring countries that connects them, if such exists. What is the longest this shortest sequence can be?
    19, starting from Lesotho and reaching either Papua New Guinea or Eastern Timor, depending on your mood. In particular:
    {Lesotho, South Africa, Mozambique, Tanzania, Kenya, Ethiopia, Sudan, Egypt, Israel, Jordan, Iraq, Iran, Pakistan, India, Myanmar, Thailand, Malaysia, Indonesia} and now whichever final destination you prefer.

11. Which two capitals are the farthest away from each other?
    The winner is {Taipei, Taiwan - Asuncion, Paraguay} at 19,930 km,
    silver goes to {Madrid, Spain - Wellington, New Zealand} with 19,855 km,
    and bronze to {Quito, Ecuador - Singapore, Singapore} at 19,727 km.
    What delightful variety! On a related note, it’s curious that if you were in Wellington and headed along the shortest route toward Madrid, you’d be going south-west initially - while if you headed instead for Lisboa, you’d start by going south-east!

12. Which two capitals of non-neighbouring countries are the closest to each other?
    The undisputed winner is {Helsinki, Finland - Tallinn, Estonia} at only 82 km.
    There’s a number of Lesser Antilles country pairs with distances in the 88-200 km range, but those seem like cheating somehow.
    Therefore I award silver to {Manama, Bahrain - Doha, Qatar} at 141 km,
    and bronze to {Sofia, Bulgaria (!) - Prishtina, Kosovo} at 176 km.

Feel free to suggest other interesting questions!