Tall, Dark, and Mysterious


Measuring Earth - first day

File under: This One Time, At Mathcamp, Those Who Can't, Queen of Sciences. Posted by Moebius Stripper at 1:59 pm.

The term “geometry” comes from two Greek terms meaning “measurement of Earth.” Today, I brought a beach ball - which came with meridians, but I had to draw in the lattitudes - to a small classroom and taught my first day of a week-long, one-star class (Mathcamp’s easiest level) on surveying, navigation, and mapmaking. We reproduced Eratosthenes’ computation - here’s a good explanation - and figured out how to find our lattitude based on the position of the sun. From there, I explained my own favourite method of finding my way around on a sunny day: point the hour hand of your watch at the sun; halfway between there and the 12 is south. Well, almost - Daylight Savings Time and our discrete time zones introduce a bit of error, but it’s one I’m willing to live with, seeing as the alternative is wasted morning daylight and the inconvenience of having to reset my watch every time I take a trip to the grocery store.

But by far the coolest topic I covered today (thanks, L, for bringing my attention to this) was that of the sun compass, based on simple knowledge of the relationships between a sun’s position in the sky at certain lattitude and the lengths of shadows it cast, which the Vikings were able to use to sail either directly east or directly west. The tip of a shadow of a pin moves in a hyperbola whose curvature is greater the closer the date to a solstice - it’s a straight line at the equinoxes - and it’s easy enough to create one. I wish I’d known this when I had time to work it into my lessons in more detail, but it might make a good independent project, or an assignment for some other class.