Find the Shortest Route through the World's Capitals 

Get the list of positions of the capitals of the countries in the UN.

In[1]:=

X countries = CountryData["UnitedNations"];

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X capitals = EntityValue[countries, "CapitalCity"];

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X positions = EntityValue[capitals, "Position"];

Find the shortest route through the capitals.

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X {distance, perm} = FindShortestTour[positions];

This is the total length of the route.

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X distance

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Draw the route.

In[6]:=

X GeoGraphics[{GeoPath[positions[[perm]]], Red, Point /@ positions}, GeoRange -> "World", GeoCenter -> 40, GeoBackground -> "StreetMapNoLabels"]

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Draw the route with an azimuthal projection.

In[7]:=

X GeoGraphics[{GeoPath[positions[[perm]]], Red, Point /@ positions}, GeoProjection -> {"LambertAzimuthal", "Centering" -> {0, 40}}, GeoRange -> "World"]

Out[7]=