Hello to Mr. Haas' Math Class in Liberty!

Greetings from the North Atlantic! We are cruising along at a steady eight to ten knots trying to evade a storm system coming at us from the north. Our sails have torn; we've been buffeted by gales; and almost run over by tankers. It's been quite an adventure so far!

My brother asked me to convey to you some applications of mathematics and why studying it is worth your time. You might notice when you look at our course on iBoat Track that it seems we've gone much further north than we needed to on our voyage to the Strait of Gibraltar. Why wasn't the shortest path a straight line? Now look at our track using Google Earth. Does it make sense now? Many problems arise when trying to project a three-dimensional surface such as the Earth onto a two-dimensional surface like your screen. Although a line is the shortest path between two points in general, if you are constrained to travel on a sphere the shortest path is along a great-circle route, i.e. a course that divides the sphere into two equal halves. All the maps of the world that you've seen have limitations in representing long distances. Some maps preserve distance better than others, but distort other features in the process. Can you name three ways of representing the three-dimensional Earth onto a two-dimensional map?

In the mean time, listen to my brother. The math that he is teaching you will take you far. Perhaps across the Atlantic, to the moon, or even beyond!