Hamilton's Math To Build On - copyright 1993

Drawing Circles

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* Drawing Circles

Remember: To draw a circle, set the compass for the radius of the circle.

Remember: Radius = diameter/2.

When drawing circles with a compass, the metal point end is placed at the center point of the circle and the other point (generally a pencil lead) is placed on the paper. The pencil point end of the compass is turned around until it gets back to the starting place.

For larger circles, trammel points can be used. Trammel points are devices that can be attached to straightedges to make circles. One trammel point has a metal point and the other has a pencil lead or pen tip. Trammel points are used just like a compass.

In this exercise, you are going to cut circles out so that the circumferences can be rolled to find their lengths. For you to be successful with this practice, it is necessary that the compass or trammel points used to draw these circles maintain its accuracy.

The ideal tool is a compass or trammel points that have a razor for an end point, instead of a pencil lead or pen tip; however, I have not been able to find this tool on the market. If you can find one or rig up one that will maintain the accuracy needed, your measurements will be more exact. If not, do your best with scissors or an Exacto knife and realize that there may be a slight deviation in measurements because of the tools used.

The tools and materials needed for this exercise are:

  1. Trammel points or compass.
  2. A piece of at least 9" square foam board, cardboard, etc. (Any material which can be cut by scissors or a razor and will hold its shape is OK.)
  3. A straight edge ruler, scissors or razor, and a pencil.
  4. Something to draw a 3' line on.
First: Set your trammel points or compass for four inches.

Second: On a piece of foam board, stiff cardboard, or the side of a box, use the trammel points or compass to draw a circle.

Third: Cut the circle out.

Fourth: With your straightedge, (on a separate piece of paper, cardboard, or on the floor etc.) draw a straight line approximately three feet in length. Mark an end point for this line.

Fifth: On the circle you've just cut, mark a starting point. Place the starting point of the circle exactly on top of the endpoint of the line. Roll the circle down the line until the starting point on the circle meets the line again. Mark the line at this point.

Sixth: Measure the distance between the two points. If the circle is exactly 8" in diameter (4" radius) and if you roll the circle without slipping, the distance is 25 1/8".

If the diameter of your circle is not exactly 8", multiply whatever the diameter of your circle is by . This will give you the measurement for the circumference of your circle. If you aren't convinced that d gives you the measurement of the circumference of any circle, draw, cut, roll out and measure more circles with different diameter measurements. Quit when you are convinced that d is the correct formula for the circumference of a circle.

On to Drawing Arcs

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18 September 1995
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