Crisps: 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.