| It may not sound like a difficult task, but | | | | because 360 is divisible by 24 different |
| constructing hexagons and other polygons can | | | | numbers including 3, 4, 5, 6, 8, 9, 10, and |
| be a frustrating and daunting task for | | | | 12. To construct an equilateral triangle, for |
| children and adults. A sketch of a square is | | | | example, first divide 360 by three to get |
| fairly simple to make as the corners are | | | | 120. Make dots at 0, 120, and 240, join the |
| familiar right angles that most people have | | | | dots, and enjoy a perfectly drawn equilateral |
| no trouble creating. Every other regular | | | | triangle. Squares are constructed by marking |
| polygon from equilateral triangles to | | | | dots at 90 degree intervals, pentagons at 72 |
| dodecagons and beyond can be a challenge | | | | degree intervals, octagons at 45 degree |
| without a highly developed ability to | | | | intervals, nonagons at 40 degree intervals, |
| recognize and construct a variety of angles. | | | | decagons at 36 degree intervals, and |
| Thankfully, there is a slick technique for | | | | dodecagons at 30 degree intervals. "But what |
| constructing all sorts of regular polygons | | | | about a heptagon?" you may ask. Even numbers |
| based on the fact that all regular polygons | | | | that don't divide evenly into 360 can be |
| fit neatly inside of a circle.For the | | | | approximated using this method. For example, |
| uninitiated, a regular polygon is a closed | | | | a heptagon (seven sided polygon) can be |
| figure with equal length sides and equal | | | | approximated quite well using 51 degree |
| angles. A pentagon with three centimetre | | | | intervals. It will be hard to tell with the |
| sides and 108 degree angles is a regular | | | | naked eye that you were one or two degrees |
| pentagon. Regular polygons are the figures | | | | off.One limitation of this method is that |
| that are most commonly used to represent each | | | | there is only one size of circle available, |
| family of polygons.To experience the most | | | | so all of the polygons come out quite large. |
| success with this method, it is recommended | | | | With a little ingenuity, this limitation can |
| that you use a full circle protractor. A half | | | | be overcome. One simple solution is to cut |
| circle protractor will work just fine except | | | | out a circle of paper and place it on top of |
| the procedure changes slightly. The basic | | | | the round protractor. Any paper circle |
| procedure for the full circle protractor is | | | | smaller than the round protractor can be |
| to place the protractor on a piece of paper, | | | | used. Make the dots around the edge of the |
| make a bunch of dots, and join the dots. The | | | | paper circle lining them up with the scale on |
| trick is dividing the 360 degrees of the | | | | the protractor. The paper circle becomes an |
| circle by the number of vertices in the | | | | intermediate protractor that can be used just |
| regular polygon, and making dots at the | | | | as the regular protractor, but it will make a |
| resulting interval. In a hexagon, for | | | | smaller polygon.Another limitation is that |
| example, there are six vertices, so divide | | | | your students might not be at the point where |
| 360 degrees by six to get sixty degrees. | | | | they can divide or find multiples of large |
| Starting at zero degrees, make a mark every | | | | numbers. In this case, you could tell your |
| sixty degrees around the full circle | | | | students at which numbers to make the dots, |
| protractor; there will be dots at 0, 60, 120, | | | | or create paper protractors with just the |
| 180, 240, and 300 degrees. Join the dots, and | | | | intervals marked on them for each |
| voila; you have a perfect regular hexagon. | | | | polygon.This is the quickest and most |
| With a half circle protractor, it is | | | | efficient method I have seen for constructing |
| necessary to establish a center point first, | | | | regular polygons. It takes little time to |
| so when you rotate the protractor to complete | | | | teach and little time to learn, and it makes |
| the dots on the other side, it can be lined | | | | the construction of regular polygons a simple |
| up properly with the zero point and the | | | | and painless activity for students. And if |
| center point.The really nice thing about | | | | you need a bit of a challenge, try the 180 |
| using a 360 degree circle to construct | | | | sided polygon with two degree intervals. I'll |
| regular polygons is that it works for all of | | | | bet you never guessed you could make one of |
| the regular polygons that one would encounter | | | | those so easily! |
| in an elementary or primary school. This is | | | | |