## A Hole in a Cube

(A new question of the week) Here is an interesting little question about how drilling a hole affects volume and surface area. We’ll have one answer, and several explanations.

(A new question of the week) Here is an interesting little question about how drilling a hole affects volume and surface area. We’ll have one answer, and several explanations.

(A new question of the week) Sometimes we have lots of quick questions and a number of long discussions, neither of which seems suitable for a post. This time I’ve chosen to combine two distantly related questions, one recent and one from several months ago, both involving tangent lines to functions.

(A new question of the week) Two recent questions involved using trigonometric functions to model real-life (or nearly so) situations, one about breathing, the other about a Ferris wheel. Both can be done by writing a sinusoidal function; the second can be done in other interesting ways as well.

Terminology and definitions in mathematics sometimes vary according to context. Here we’ll look at the ideas of relations, functions, and their domains, and discover that they look different from different perspectives.