Name: Nigel Ayling

Who is asking: Parent
Level: All

What is the mathematical definition of a prism, I am confused by the following definitions as they appear to be contradictory

Oxford Dictionary Definition

noun: Geometry - a solid geometric figure whose two ends are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms.

Hutchinsons Encyclopedia Definition

In mathematics, a solid figure whose cross section is constant in planes drawn perpendicular to its axis. A cube, for example, is a rectangular prism with all faces (bases and sides) the same shape and size.

A cylinder is a prism with a circular cross section

Please help

Hi Nigel,

Actually the two definitions are suprisingly consistent.

Take the second one. A Cube has the top and the botton congruent and parallel. In fact, similar, equal (together) is a clumsy way to say congruent or same size and shape.

So for example, a standard 'triangular prism' (used for splitting light) has a top and bottom triangle which are congruent and parallel. Any other slice parallel to these would be another triangle congruent to the top and bottom.

The difference (unnecessary) is that the SECOND definition says that the top and bottom (considered as horizontal) must be connected by VERTICAL faces. I.e the line joining any bottom vertex (or the center) to the corresponding top vertex (or center) must be perpendicular to the base and top.

Then the sides would all be RECTANGLES.

The first is broader (and I think more common). The lines joining corresponding vertices (or centers) are all parallel to one another, but could be in any direction. Few properties or results, or even formulae about prisms require the 'perpendicular axis' property. The general principle in math would be to ADD such a restriction ONLY IF it actually made things simpler (e.g. gave simpler results).

I would go with Oxford! [Seems like a good general principle comparing Oxford with most other dictionaries!]

Walter Whiteley

The glossary in the Resource Room at Math Central has the definition of a prism as

- a geometric solid with two bases that are congruent, parallel polygons and all other faces are parallelograms. It is referred to as a right prism if the faces are rectangles. It is named according to the shape of its bases. e.g. triangular prism which agrees with the Oxford definition. I am suprised that the definition you give from the Hutchinsons Encyclopedia includes a circular cylinder as a prism.

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