Perimeter -- or distance around -- is a measurable property of simple, closed curves and shapes. When the figure is a circle, we use the term circumference instead of perimeter. Because the perimeter of an object is a length, we need to measure using units of length such as centimeters, decimeters, meters, inches, feet, etc.
The circumferences of circular objects can be difficult to estimate. Let's use a bicycle wheel as an example. How long is its circumference? Use masking tape to make a mark on the floor or table to indicate the starting point. Estimate the distance of one rotation of the wheel or bowl rim, namely the circumference, by placing another piece of tape on the floor or table. Note 2
Roll the wheel to find the actual circumference. Was your estimate too short or too long?
There is a relationship between the circumference and diameter of a circle, which we will explore here in a number of ways. A diameter is a chord -- a line segment joining two points on the arc of a circle -- that passes through the center of the circle. Diameter also refers to the distance between two points on the circle, measured through the center. Let's first look for patterns in the measurements of circles.
The three designs below show a circle between a regular hexagon and a square.
Print a PDF image (be sure to print this document full scale) of the designs to work on Problems A1-A3.