(20') Sextants (Wikipedia) and earlier navigational tools - they could double as surveying instruments.
1) Hands-on primitive version (while talking like pirates, but with Franciscan prayers and rowers "singing soft, sad songs" in background); 16th-century equivalent: the backstaff (but not as primitive as our combination of trianble & carpenter's level)
2) Modern update of traditional instrument in use on relatively calm seas; explanation of use;
3) Closer look at the standard sextant of the 18th Century: the sextant Captain Cook used;
4) What Humboldt used: the (slightly high-end) tools of the time, but with the skills expected from every ship's captain and officers
5) A WWII-era sextant: its developer and basic principles;
6) Celestial navigation with instruments developed by various cultures (Polynesians, Arabs)
7) "How does X work?" - the difference between "how do you make it work" and "how it works"; example: how GPS works; more about GPS; step-by-step GPS tutorial;
Free iPhone apps related to navigation demonstrations: "Skytime", "AstroCLock", "Thedolite", "Elevation", "Trig Solver" (actually does just triangles, but that's what we want), and maybe (advanced users:) "Spyglass". The same or similar apps exist for Android.
Upcoming math challenge: how accurate is the "Theodolite" app? But first: How long is 1/10,000 of a degree of latitude? in feet? in meters?
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