5) Constructions

These beautiful geometric patterns can be constructed using a compass and a straight-edge, or using a computer. All of these drawings were done by students. These beautiful patterns can be found in unexpected places: in a stained glass cathedral window, and in ornamental designs.

The circle is the basis for many patterns, and is easily drawn with a compass ... lines are drawn with the straight-edge (ruler).

To create geometric designs like the student drawings above, you need to know a few basic constructions. The first construction is creating an equilateral triangle, the basis for many patterns:

The second construction is the bisector of an angle, a line that divides the angle into two equal parts. Using both compass and straight-edge, the bisector of an angle can be constructed as shown below:

To create a simple design using angle bisectors, construct an equilateral triangle, then bisect all three angles. You can color the design in many different ways: using colored pens or pencils, or on a computer. This simple design was drawn on a computer, using a painting program:

The perpendicular bisector of a line segmentis a line that goes through the midpoint of the segment, forming right angles. Constructing the perpendicular bisector of a segment will give you a right angle ... Right angles are almost always found in architecture, and in our student designs, also.

Using the perpendicular bisector in a circle, you can draw a square ... A square can be used in many different designs ...

The Russian people use these designs to decorate eggs at Easter.

We can bisect the four sides of a square ... connecting the points gives us an octagon, an eight-sided figure. A hexagon is a six-sided figure. If you leave the compass at the same radius as your circle, and make arcs all the way around, joining the points will give you a hexagon ...

The hexagon lends itself to many designs ... Every snowflake is a hexagon, and every one is different.

Using these basic geometric constructions, students did these colorful drawings. Try some of your own. The possibilities are endless!

Go to Topic 6 Angles of a Polygon