# Is a box a cylinder?

My Calculus 3 professor defines a cylinder as any shape that has identical cross sections for any plane parallel to the base. He used this to explain why he refers to a box as a cylinder. This is confusing, as it muddles the differentiation of solids for me. Is this a common definition?

• The definition is standard in math literature. Oct 6, 2016 at 0:07
• @JackyChong I'm only familiar with Euclid's cylinder, I'd love a reference. Oct 6, 2016 at 0:08
• Oct 6, 2016 at 0:10
• Your professor is getting prisms mixed up with cylinders. Wikipedia will set him or her straight (en.wikipedia.org/wiki/Prism_(geometry), en.wikipedia.org/wiki/Cylinder_(geometry)) Oct 6, 2016 at 0:11
• @RobArthan en.wikipedia.org/wiki/… Oct 6, 2016 at 0:16

2. If $$X$$ is a topological space (such as a rectangle) and $$I = [0, 1]$$ is the unit interval, one sometimes speaks of $$I \times X$$ or $$X \times I$$ as the "cylinder over $$X$$", see for example the mapping cylinder and suspension.