The Fastest Way to the Coast

Find out the shortest possible path to get to a point of the US border from each capital of the conterminous US states.

Take the list of capitals.

In[1]:=

capitals = EntityValue[ EntityClass["AdministrativeDivision", "ContinentalUSStates"], "CapitalCity"]

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Take the polygon of the US.

In[2]:=

us = EntityValue[Entity["Country", "UnitedStates"], "Polygon"]

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Compute the closest point of the polygon boundary for each respective state capital.

In[3]:=

borderpoints = Flatten[Nearest[First[us], GeoPosition[capitals]]]

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Draw all the geodesic paths.

In[4]:=

GeoGraphics[{us, Point[capitals], Red, Arrowheads[0.015], Arrow /@ GeoPath /@ Thread[{capitals, borderpoints}]}]

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