Inversive geometry is a nice way to introduce the idea of geometry mappings, which can lead to the study of the PoincarĂ© disk. With a little effort, the ideas are accessible, and there are an abundance of concepts to learn … Continue reading

# Category Archives: Content tools

We are looking at how to introduce Taylor series, and we wanted to start with approximations to and Seems like a good application for a graphing utility. We had the students start by looking at a polynomial like It takes … Continue reading

Inverse functions can be a challenge to think about. Tinkering with examples via a graphing utility is a good way to build comfort. You can begin with desmos.com. Let's try a fairly simple, but sufficiently interesting example: Launch desmos.com. Enter … Continue reading

Most of the functions we look at in high school math are continuous everywhere they are defined. But not always. Graphing piecewise functions with software requires defining the function on distinct intervals. Grapher (on the Mac) provides a nice facility … Continue reading

The square root of two is irrational. That doesn't mean it is unreasonable. It just means it cannot be written as the ratio of two integers. We've known this since at least the time of the Pythagoreans of ancient Greece. … Continue reading