Last week we looked at problems about counting diagonals in a polygon, and the very similar problem of counting handshakes when everyone in a group shakes with everyone else. In the course of searching for those problems, I also found some very different problems that are also about handshakes. We’ll look at those here, just …
(A new question of the week) An interesting geometry question came to us in July, about the area of overlap between two squares. The discussion was not long, but leads to some interesting ideas.
We’ll spend the next couple weeks looking at various counting problems. This topic, called combinatorics, is often studied along with probability, but many of the topics we’ll see here feel more like geometry problems! Here, we’ll be counting the diagonals of a polygon, and handshakes between people at a party.
As many schools get into a new semester, this may be a good time to take a look at ways to use our service as effectively as possible.
To close out this series on the definition of the derivative, I want to look at a few questions about alternative versions of the definition, primarily the “symmetric difference quotient”. We’ll see that this leads to a slightly different result, not always equivalent to the original, and we’ll observe some associated ways that calculators can …
(New questions of the week) We’ve had a number of brief discussions recently, which feel too small on their own for a post; but several happen to be dealing with similar types of issues. These four questions, all from July, involve limits or derivatives at edges or holes in the domain of a function. Let’s …
We’ve looked at the meaning of the derivative, and of its various notations, including dy/dx. This leads to the next question: What does dx or dy mean on its own? This was touched on last time, but there’s a lot more to say that I couldn’t fit there. We’ll look at more advanced approaches to …
(A new question of the week) We have had a lot of interesting questions recently. This one involved inverse trigonometric equations that led to cubic and quartic equations. We’ll observe here one of the benefits of embedding the original discussion in a blog format where I can add information that will help you, the reader, …
Challenging Inverse Trig and Polynomial Equations Read More »
Last week we looked at the meaning of the derivative. In doing so, we mostly used the notation “”, but mentioned another in passing. Here I want to look at our answers to several questions about the different notations you will see.
(A new question of the week) Last week we looked at a recent question about an attempt to write a proof using the contrapositive, which was foiled by difficulty in negating a statement. Two weeks later, we had another question about the same sort of issue, but with a different problem in the negation. In …