Geometric and Algebraic Meaning of Determinants

A recent question led me to look back in the Ask Dr. Math archives for questions about the definition and deeper meaning of determinants. Next week, we’ll see another old question for additional background, followed by the new question.

What are Length and Width?

One of the recent discussions I showed last week dealt with the meaning of length, and I promised more about that. Here we will look at some older questions about the ambiguity of words  like length, width, depth, and height.

Clarifying Definitions: Triangle, Rectangle, Circle

(A new question of the week) Several recent questions involved details about definitions of geometrical objects, so I thought I’d group them together, because each is relatively short. We’ll be looking at the definitions of triangles (do we need to say “exactly three sides”?), rectangles (did Euclid use an exclusive definition?), and circles (can the …

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The Book Stacking Problem

(An archive question of the week) A recent question asked about a well-known problem about stacking books (or cards, or dominoes) so that the top one extends beyond the base, giving a link to one of many explanations of it – but one, like many, that doesn’t quite fill in all the details. Doctor Rick …

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Fine Points on Polygons and Polyhedra

Last time, looking at degenerate polygons, I mentioned some other issues pertaining to the definition of a polygon. Let’s take the opportunity to look at them. This post supplements what was said previously in What is a Polyhedron … Really?

Degenerate Polygons

We’ve been looking at degenerate figures, starting with the most interesting case, degenerate conic sections. But other things can also be degenerate, so we should take a look at some of these, which perhaps arise even more often. We’ll examine triangles that aren’t triangles, rectangles that aren’t rectangles, and bigger polygons – or smaller polygons! …

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