HOW TO CONSTRUCT POLYGONS GIVEN THE SIDE

We have learnt how to construct polygons inscribed in a circumference. Now, we are going to construct polygons when we know the length of the side of this polygon.

We can use a general method:

 GENERAL METHOD

But we also have specific methods for each polygon:

TRIANGLE

 
 SQUARE

 

PENTAGON




 HEXAGON


HEPTAGON


OCTAGON

ART AND GEOMETRY

Maybe you think that technical drawing is difficult and it is hard to find the point of learning it. But geometry, polygons and star polygons have been used long time ago in architecture and art. For instance, geometry is one of the main characteristics of Islamic artistic designs. 

Islamic Tessellation

Islamic wooden panel

Islamic decoration made of plaster

We also can found geometries in Western Art and architecture, especially  in the rose windows of the churches carried out around the medieval time. The rose windows or wheel windows flourished especially in France, where they appear in practically every important Gothic cathedral, as Notre Dame in Paris.  These windows ususally had stained glass placed in them.

 

 

Rose Window of Leon Cathedral

 

Notre Dame. Paris

In our next project we are going to use geometry to construct a stained glass window. You can find some ideas here: 

 

Although the basic geometry is the same, there is considerable variety possible in the resulting patterns. This animated diagram illustrates just a small number of the alternative patterns – in no logical sequence – which are capable of being formed by following different selections of the guidelines of the basic divided circle, in this case, the central circle of the three above, the circumference being divided into twelve parts. (From: http://catnaps.org/islamic/geometry.html)

Remember that for this project each group needs:

  -          Black A2 cardboard
  -          White pencil
  -          Compass (or yarn)
  -          Cutter
  -          Glue   
  -          Cellophane paper

REGULAR STAR POLYGONS

A star polygon is a star-shaped polygon that is formed by joining together the non-consecutive vertices in a regular polygon. 

To construct a star polygon inscribed in a circumference, we need to follow the same steps to draw a regular polygon, it depends on how many points of a star we want to draw.

So we must start finding the star points as they were the polygon vertices. Then we can join the non-consecutive points skipping one vertex, two or three vertices if the polygon has enough vertices to construct it. 

For example, the heptagon has two possible star polygons, skipping one vertex or two vertices.

Seven Pointed stars

             {7/2}                                              {7/3}

Here you can find the regular polygons and the star polygons that we can draw: