Mathematics Entertainment for the Millions

The following sections are included:

• About the Author
• Contents
• Introduction

Most people recall the concept of arithmetic as the subject that they learned in elementary school. For them, this concept consists largely of the four basic operations: addition, subtraction, multiplication, and division. Throughout the course of their schooling, this extended to doing computation with fractions and perhaps square root extraction. In our constantly-developing technological world, when these tasks are required today, most folks revert to the calculator to do the arithmetic calculations. When the knowledge or concept of arithmetic is limited to its barest form of usefulness, much of the beauty of mathematics gets lost. Actually, arithmetic lends itself beautifully to some very simple entertaining aspects. When you get to the end of this chapter, you will find what some might consider a mind-blowing phenomenon in arithmetic. However, let’s start off with an easy little puzzle-type question that requires a little bit of arithmetic insight.

The focus of logical reasoning is an integral aspect of all branches of mathematics. Logical reasoning is often seen as a key element of genuine problem-solving skills. The topics selected to exhibit logical reasoning can not only vary greatly, but can also exhibit the delight that one can have with some of the amazing aspects of mathematics. The examples that we will encounter throughout this chapter will manifest themselves in such areas as probability, clever strategies for solving problems, arriving at unexpected phenomena, and other entertaining aspects which exhibit some logical reasoning. Logical reasoning also has limits which could be entertaining. On the one hand, logical reasoning is often key to solving problems. Yet, on the other hand, one needs to be careful and not abuse logical reasoning. For example, making generalizations based on what appear to be convincing patterns can also be misleading. To see such surprising and unexpected disappointments to proper expectations can also be a form of entertainment, and also a caution for future conjectures. Let’s begin by considering the following example.

Entertaining an audience with geometry takes on a different perspective. First of all, the fact that it’s visual requires that you have a way to exhibit the various unusual aspect of geometry that you are about to share. Furthermore, it is important that the presentations you make are done in a somewhat dramatic fashion that will eventually exhibit the amazing aspects that you would like your audience to properly appreciate. We will begin with an everyday observation which very few people take note of, and yet are awed by the phenomenon. Begin with the following question: Have you ever wondered why sewer covers are always round? Well, as an entertainer you might want to let your audience ponder this question a bit. All kinds of unexpected responses can be awaited. As you can see in Figure 3.1, the answer is rather simple: the circular cover cannot fall into the hole…

Mathematics can be made entertaining in many ways, unfortunately, this is often neglected in the school setting, where meeting curriculum standards overarches everything else. Teaching to the test is the worst anti-entertainment aspect of the instructional program. As we have seen so far, entertainment in mathematics can take on many variations. Yet, the delivery of these entertainment ideas — the enthusiasm of the presenter — is most essential. Curious mathematical challenges can frequently inspire an audience, especially if the solution is awe inspiring! Here we now provide some curiosities that should serve well to inspire your audience.

The following section is included:

• Final Thoughts