Month: March 2019

Area of a Triangle: Heron’s Formula II

Last time we looked at a very useful formula for finding the area of any triangle, given only the lengths of its sides. Today I want to look at several problems in which the formula has been used, some of them surprising.

Awkward Sequence Problems

(A new question of the week) Having just discussed some pattern or sequence problems that were poorly posed, let’s look at some recent questions about sequences, some of which are quite complicated, and others seem to be just wrong.

Uncertain Sequences

We’ve often pointed out that pattern or sequence problems, when nothing is given but a list of numbers, are not really math, in the sense that there is no one correct answer. They are psychology questions: What would a math teacher think is an interesting sequence to ask about? Mathematically, any number could come next, …

Uncertain Sequences Read More »

Building Patterns and Sequences

In the past (last May and November), we discussed ways to find patterns or sequences in numbers, sometimes leading to a formula. This included an example where the sequence turned out not to be just a provided list of numbers, but a process that generated the numbers. I want to focus on that type of …

Building Patterns and Sequences Read More »

L’Hôpital’s Rule: One More Example

(A new question of the week) Having just looked at L’Hôpital’s Rule, we can conclude with a look at a recent question about it, to illustrate the reality of struggling to apply it (and the process we go through to help a student find an error).