# Straightness on Cylinders and Cones

• Oct 6th 2010, 09:57 PM
matgrl
Straightness on Cylinders and Cones
a.) What lines are straight with repsect to the surface of a cylinder or a cone? Why? Why not?

b.) Examine:
• Can geodesics intersect themselves on cylinders and cones?
• Can there by more than one geodesic joining two points on cylinders and cones?
• What happens on cones with varying cone angles, including cone angles greater than 360 degress?
• Oct 7th 2010, 03:19 PM
CaptainBlack
Quote:

Originally Posted by matgrl
a.) What lines are straight with repsect to the surface of a cylinder or a cone? Why? Why not?

b.) Examine:
• Can geodesics intersect themselves on cylinders and cones?
• Can there by more than one geodesic joining two points on cylinders and cones?
• What happens on cones with varying cone angles, including cone angles greater than 360 degress?

Since both cylinders and cones are developable surfaces the geodesics correspond to straight lines on the flattened surface (for the appropriate flattening anyway).

CB
• Oct 8th 2010, 07:15 AM
matgrl
CB,

You stated, since both cylinders and cones are developable surfaces the geodesics correspond to straight lines on the flattened surface (for the appropriate flattening anyway).

Could you further explain how you know this, and if anyway possible how you could prove this statement?