Ratios and Areas: An Unusual Pie Chart Problem
Here is a short problem with several levels of difficulty. The problem itself is poorly designed, as we’ll see, but still provides several useful lessons, dealing with measurement, rounding, and ratios.
Month: November 2024
When Newton’s Method Fails – and Why It’s So Good When It Doesn’t!
Last time, we saw how Newton’s method works. Here, we’ll look at a question about why it might not work, which will lead to a deep examination of how iterative methods work in general, from which we will discover why Newton’s method is as good as it is. I have to say, as I read …
When Newton’s Method Fails – and Why It’s So Good When It Doesn’t! Read More »
Solving Equations with Newton’s Method
Last time we solved some of the equations connected with a segment of a circle using Newton’s Method. Let’s take a closer look at the method – how it works, why it works, and a few caveats.
How to Find Any Part of a Segment of a Circle
Recent questions have dealt with calculations of various parts of a segment of a circle (chord, arc, sagitta, etc.). How, for example, can you find the arc length if you know the chord length and the height? The definitive explanation of these questions is found in a classic page from Ask Dr. Math, written by …