Chips as a hyperbolic paraboloid

To avoid crum­bling, chips, packed in cylin­dric tubes, are baked on roasting sheets, which form flat shells into a shape of hyper­bolic parab­o­loid, a surface of the second order.

A hyper­bolic parab­o­loid is curved, it looks like a saddle, still it’s a ruled surface! By defi­n­i­tion, a ruled surface can be formed by a contin­uous move­ment of a straight line, which is called gener­a­trix.

There are two straight lines, which pass through every point of both a hyper­bolic parab­o­loid and a hyper­boloid of one sheet.

A prop­erty of linearity can be easily demon­strated by using chips, which are packed in tubes.

Make a straight cut in a lid of a tube. Take one slice from a pile of chips and put it into a tube through this hole. You can do it without breaking a slice, you only need to put and turn it in such a way, that a gener­a­trix of a hyper­bolic parab­o­loid passes the hole every time.

Other models in “Conic sections”