So how do can you fit a square peg into a round hole? Is there a process you can follow to construct inscribed regular polygons? Remember, any regular polygon will fit into a circle.
You can construct inscribed regular polygons on your own using a compass, a straightedge, and a protractor. Make sure you have everything ready, along with a piece of paper, and follow along with the videos below.
As you watch the videos, use the study guide to follow along if you'd like. Click the button below to download the study guide.
Inscribing with a Protractor
Inscribing with a Compass
In this video, I will show you how to practice drawing polygons inscribed into a circle.
First off, we should recognize that drawing an irregular polygon inscribed in a circle is very easy. A hexagon, for example, has six sides and six vertices. As long as the six vertices all fall on the circle, we can connect them with straight lines to form a hexagon, like this…
Drawing a regular hexagon takes a little more effort. Fortunately, the method I am going to show you next will not only help you draw inscribed regular hexagons, but also inscribed polygons with any number of sides. First, we should start with a straight line that travels through the center of the circle, essentially cutting the circle in half. One of the points of intersection will be a vertex of the polygon. Then we should calculate what angle is needed at the center of this circle to identify the next vertex. To do this, we will divide three hundred sixty degrees by the number of vertices we need for our polygon; in this case, 6. So three hundred sixty divided by six is sixty degrees, therefore we can measure sixty degrees along the edge of the original line with a protractor, and mark where the next vertex will occur… We could rotate the protractor and repeat the process around the circle…
With careful measurement and a steady hand, you can accurately and reliably draw regular polygons inscribed in a circle. Good Luck!
In this second video about drawing regular, inscribed polygons, I would like to share with you a technique that utilizes a compass as a measuring tool instead of a protractor. Let's start with a circle again, and we will set the radius of the circle to be 5 inches. By setting a compass to a specific distance, we can mark points around the circle that would create a regular polygon. The formula needed to determine these points is as follows: the length of the compass is equal to two times the radius times the sine of one hundred eighty divided by n, where n is the number of sides in your regular polygon. Let's try drawing a regular pentagon, which has 5 sides and will be inscribed into a circle with a radius of five. Following the order of operations, we can simplify inside parenthesis first – 180 divided by 5 is 36. Then, the sine of 36 degrees (make sure your calculator is set to degrees) is approximately 0.58779. Finally, two times five times this value is 5.8779.
When our compass is set to this length, we could draw arcs that intersect the circle with the needle point set on point D… And repeat the process by setting our compass' needle at these intersections… Now we have five, equally spaced points around the circle. When connected, the resulting shape is a regular pentagon.
Now you give it a try with another polygon. Good Luck!
Question
In order to divide the circle into equal angles that allow you to draw an inscribed regular polygon, what do you need to divide 360 degrees by to get the measures of the angles?
