Which Country is the Closest when you are in the USA
Geometry & Trigonometry
Which foreign country is closest to the geographic centre of the continental USA, and how is 'closest' even defined? This idea uses distance metrics and a Voronoi diagram to answer precisely.
Introduction
Pick a point near the geographic centre of the continental USA (for example, Lebanon, Kansas). Measure the distance from that point to the nearest border of each neighbouring country using great-circle distance, then repeat for a grid of points across the country. The boundaries between 'nearest country' regions form a Voronoi diagram, the same construction used for phone masts or school catchment areas, but drawn on the surface of a sphere rather than a flat plane.
Guiding Questions
- From the middle of the USA, which foreign country is closest? What does 'closest' mean exactly?
- Compute great-circle distances from a chosen US point to nearby countries' closest borders.
- Map the regions of the USA closest to each foreign country — a Voronoi diagram on a sphere.
- How do the answers change if you measure to capitals instead of borders?