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Apologies if this is a duplicate question, putting the word "surveying" into a search on this site is not very effective.

I'm interested in science education, and I was recently reminded of the old story of Gauss's maps of Hanover. While it had already been known for a couple thousand that the earth was round, it was still rather remarkable when Gauss was commissioned to make these maps in 1818, and discovered that the angles of his largest surveying triangle did not sum to 180 degrees. It may have even been the earliest known measurement of the earth's local curvature in a particular region. More importantly, it triggered his lifetime of research in differential geometry.

I'm interested in exploring hands-on experiments people can do with simple tools and no black-box calculations (i.e. GIS software) to get in touch with the shape of the earth around them. I've studied differential geometry from a mathematician's perspective, and I'm wondering if anyone here knows of a resource on surveying with an eye towards DG, or on DG with an eye towards surveying here on earth. An ideal resource would discuss (but not necessarily prove) some of the basic theorems about Gaussian curvature, and also discuss some of the practical aspects of how an individual confined to the surface could make the necessary measurements. It would also be fantastic if is discussed coordinatizing the surface of the earth using the position of the sun and stars (i.e., calculating your own coordinates), although that seems like a bit more of a stretch for one coherent resource.

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    $\begingroup$ You know about this? aps.org/publications/apsnews/200606/history.cfm $\endgroup$ – Deane Yang Nov 12 '17 at 19:31
  • $\begingroup$ Eratosthenes and the well is an interesting story, but really he's assuming a globally spherical geometry and then using a single measurement to deduce the radius. It's certainly related and I think it makes a good introduction, but I don't think it quite falls into what I'm looking for, which has more to do with local geometry. $\endgroup$ – Xander Flood Nov 13 '17 at 11:01

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