# To Determine the Geographic center of a continent, is balance point the accepted method and is equivalent to finding the centroid?

This is not exactly a pure Earth Science question but I'm not sure GIS SE is a suitable place either.

"The Google" suggested I watch CBS Sunday Morning's The debate over the geographical center of North America and I complied.

The video explains that Rugby North Dakota (48.37 N, 99.99 W) was determined to be the "geographic center" of North America by balancing a cutout of the continent on a pin.

This method weights each point by its vector to the center; a point twice as far will be weighted twice as much.

The second determination was done in a bar by utilizing the well known standard string, globe and beer methodology. It was found to be inside Hanson's bar itself in Robinson North Dakota (47.14 N 99.78 W).

The third determination was done using a personal computer and google maps> perimeter coordinates2:

Professor Peter Rogerson1 took latitudes and longitudes from all around the edges of North America, and plugged those coordinates into a special algorithm that he designed, to find the center.

”You have to take into account that the Earth’s surface is curved, and you want to find that balance point in a proper way.

This turns out by sheer coincidence to be near Center North Dakota (47.12 N, 101.30 W)!

So back to the balance point with it's vector distance from center weighting.

Questions:

1. When finding the geographic center of a continent is balance point the accepted method?
2. Is this mathematically equivalent to finding the centroid?
3. "bonus points" how did Rogerson convert a perimeter to a balance point? Has this been published?

1Peter A. Rogerson, Department of Geography, State University of New York Buffalo

2hat tip to @EarlGray for their very helpful comment!

• "The third determination was done using a personal computer and google maps:" No, google maps was not part of the determination. It is used just for visualization purpose. It is fair to say that it was done collecting all the curvilinear coordinates of the boundary of North America and then correctly projected (with or without a personal computer ... those calculations were done manually, with same precision degree, until the 50/60s ... Reg. Q3, I don't think it is published in this form, but it must be based on a method Prof.Rogerson already published. Ask him directly. Jun 2, 2021 at 7:57
• @EarlGrey I'm shy so will stick to Stack Exchange. Also, I've amended that part of the question accordingly. Wow, thank you for taking the time to read through my longish post so carefully!
– uhoh
Jun 2, 2021 at 8:01
• I'll put this here en.wikipedia.org/wiki/Geographical_centre
– f.thorpe
Jun 3, 2021 at 2:44
• @farrenthorpe that's a nicely-written, concise and definitive summary and that can't be said for all Wikipedia articles. It links to the 1964 USGS publication Geographic centers of the United States which has an excellent introduction and addresses the center of North America as well (48°10' N, 98°35' W)
– uhoh
Jun 3, 2021 at 2:58