This is the first section of Chapter 5: Measurement of Circles. The objective is to determine the relationship between the diameter and the circumference of a circle.

Section 5.1: Exploring Circles

This section starts with five definitions: radius, diameter, circumference, arc and chord. It is important to note that there are two definitions for each of these terms. For example, the "radius" can refer either to the line segment itself, or to the length of that line segment.

Section 5-1 Exploring Circles 1

Determining the Relationship Between Diameter and Circumference (Kelley Homeroom)

This is the activity Mrs. Kelley's homeroom class did to help determine the relationship between the diameter and the circumference of a circle. They developed a hypothesis, they tested it, and they concluded that the circumference is always about 3.2 times the the diameter.

We went a step further, thinking that if we had more precise measuring tools, we should be able to find a more exact value than 3.2. We introduced the notion of $latex \pi \approx 3.14159...$, which denotes the ratio of the circumference to the diameter of a given circle.

Section 5-1 Exploring Circles 2

Determining the Relationship Between Diameter and Circumference (Barr Homeroom)

This is the same activity, done by Mr. Barr's homeroom.

Section 5-1 Exploring Circles 3

Examples

We finished off with these three examples.

Section 5-1 Exploring Circles 4

Section 5-1 Exploring Circles 5