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a road up a mountain

A road up a conical mountain is being planned. Can you devise a measure of "steepness" for the road? Does your measure depend on where you are on the road? Can you devise a measure of "curvy-ness" for the road? Does your measure depend on where you are on the road? What about a hemispherical mountain? What problems could/would you set for your students based on this applet?