Chips as a hyperbolic paraboloid

AVI video (768×576, 23.4 MB)
MP4 video (768×576, 8.6 MB)
В zip-архиве (AVI, 9.7 MB)



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.